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Mathematical modelling of the diurnal regulation of the MEP pathway in Arabidopsis Alexandra Pokhilko1, Jordi Bou-Torrent2, Pablo Pulido2, Manuel Rodrıguez-Concepci on2 and Oliver Ebenh€ oh1,3 1

Institute for Complex Systems and Mathematical Biology, King’s College, University of Aberdeen, Meston Building, Aberdeen, AB24 3UE, UK; 2Centre for Research in Agricultural Genomics

(CRAG), CSIC-IRTA-UAB-UB, Campus UAB Bellaterra, 08193 Barcelona, Spain; 3Cluster of Excellence on Plant Sciences (CEPLAS), Heinrich-Heine-University, Universitä tsstraße 1, D-40225 Dü sseldorf, Germany

Summary Authors for correspondence: n Manuel Rodrıguez-Concepcio Tel: +34 935 636 600 ext. 3222 Email: [email protected] €h Oliver Ebenho Tel: +44 7580078809 Email: [email protected] Received: 23 October 2014 Accepted: 30 November 2014

New Phytologist (2015) doi: 10.1111/nph.13258

Key words: 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway, Arabidopsis thaliana, isoprenoids, mathematical modelling, plant metabolism, systems biology, whole plant physiology.

 Isoprenoid molecules are essential elements of plant metabolism. Many important plant isoprenoids, such as chlorophylls, carotenoids, tocopherols, prenylated quinones and hormones are synthesised in chloroplasts via the 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway. Here we develop a mathematical model of diurnal regulation of the MEP pathway in Arabidopsis thaliana.  We used both experimental and theoretical approaches to integrate mechanisms potentially involved in the diurnal control of the pathway.  Our data show that flux through the MEP pathway is accelerated in light due to the photosynthesis-dependent supply of metabolic substrates of the pathway and the transcriptional regulation of key biosynthetic genes by the circadian clock. We also demonstrate that feedback regulation of both the activity and the abundance of the first enzyme of the MEP pathway (1-deoxy-D-xylulose 5-phosphate synthase, DXS) by pathway products stabilizes the flux against changes in substrate supply and adjusts the flux according to product demand under normal growth conditions.  These data illustrate the central relevance of photosynthesis, the circadian clock and feedback control of DXS for the diurnal regulation of the MEP pathway.

Introduction The 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway uses the central carbon intermediates pyruvate and glyceraldehyde 3phosphate (GAP) to produce isopentenyl diphosphate (IPP) and dimethylallyl diphosphate (DMAPP), the universal prenyl diphosphate precursors of all isoprenoids. This essential plastidlocalized pathway is hence required for the production of metabolites involved in photosynthesis (chlorophylls, carotenoids, tocopherols, prenylated quinones), regulation of growth (gibberellins, cytokinins, abscisic acid, strigolactones) and interaction with the environment (isoprene, monoterpenes, diterpenes) (Vranova et al., 2013). Production and consumption of these products for photosynthesis, growth, defence and other processes might change during the day depending on the type of plant and environmental conditions (Hemmerlin et al., 2012; Vranova et al., 2013). For example, poplar and other plant species emit the volatile product isoprene (produced in a single enzymatic step from DMAPP) specifically during the daytime, in parallel to the light-dependent accumulation of DMAPP (Magel et al., 2006). However, very few data are available on the diurnal kinetics of Ó 2015 The Authors New Phytologist Ó 2015 New Phytologist Trust

other MEP pathway products and intermediates, especially in plants that do not emit large amounts of volatiles like Arabidopsis thaliana (Gibon et al., 2006). The scarce availability of metabolic and kinetic data is mostly related to the technical difficulties in measuring MEP pathway metabolites, which require mass spectrometry and other high-resolution techniques (Xiao et al., 2012; Zhou et al., 2012; Li & Sharkey, 2013). Mathematical modelling provides a complementary way to analyse the regulatory principles of biological processes, allowing us to integrate existing data and to predict the behaviour of the system following perturbations (Goryachev & Pokhilko, 2008; Pokhilko et al., 2012; Seaton et al., 2014). Here we used a combination of theoretical and experimental approaches to create a model of diurnal regulation of the MEP pathway in A. thaliana. In this model we considered several levels of regulation. The first level reflects the dependence of the MEP pathway on the availability of its substrates (FloresPerez et al., 2010), which in turn depends on photosynthetic activity (Gerhardt et al., 1987). Second, the circadian clock regulates the transcript abundance of key MEP pathway genes (Covington et al., 2008; Cordoba et al., 2009; Vranova et al., 2013) and thus the accumulation of downstream products (Dodd et al., New Phytologist (2015) 1 www.newphytologist.com

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2005; Dudareva et al., 2005; Fukushima et al., 2009). The third level represents a feedback control of the first and main rate-determining enzyme of the pathway, 1-deoxy-D-xylulose 5phosphate (DXP) synthase (DXS), by MEP-derived products (Guevara-Garcıa et al., 2005; Cordoba et al., 2009; Hemmerlin et al., 2012; Banerjee et al., 2013; Han et al., 2013; Ghirardo et al., 2014).

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Experimental methods Plant material All of the Arabidopsis thaliana (L.) Heynh. mutants and transgenic lines used here are in the Columbia (Col) background. The only exception is the double null mutant lhy-21/cca1-11, in the Ws-2 accession (Pokhilko et al., 2012). Mutants hdr-3 (SALK_026807) and psy-1 (SAIL_804F06) were obtained from NASC (http://www. arabidopsis.info/), whereas transgenic lines 35S:DXS (Carretero-Paulet et al., 2006) and 35S:DXS-GFP (Pulido et al., 2013) were previously available. Seeds were surface-sterilized and grown under the indicated light regime on plates with medium lacking sucrose as described (Pulido et al., 2013). For experiments involving the seedling-lethal hdr-3 and psy-1 mutants, seeds from heterozygous plants were plated and only albino (homozygous) individuals were selected. For fosmidomycin (FSM) treatment, Col seeds were germinated on top of a sterile disc of synthetic fabric (SefarNitex 03-100/44; Sefar, Heiden, Switzerland). At Day 10, the disc with the seedlings was transferred to fresh medium supplemented with 100 lM FSM and samples were collected at different times afterwards. Quantification of transcript and protein concentrations RNA isolation, cDNA synthesis and quantitative-PCR (qPCR) experiments were performed as described (Pulido et al., 2013) using the UBC/UBC21/PEX4 (At5g25760) gene (Czechowski et al., 2005) for normalization. Primer sequences for qPCR reactions are listed in Supporting Information Table S1. Protein extraction and Western blot analysis were carried out as described (Pulido et al., 2013). Model description MEP pathway submodel In an initial step, we developed a kinetic model of the MEP pathway without any diurnal regulation (the MEP submodel), based on the ordinary differential equations model by Rios-Estepa (RE) simulating the production of essential oils in specialized cells of grandular trichomes of peppermint plants (Rios-Estepa et al., 2010). We adopted the RE model to describe the reactions of the MEP pathway in A. thaliana rosettes, which produce the MEP pathway intermediates DXP, MEP, 4-(cytidine 50 -diphospho)-ME (CDP-ME), 2phospho-4-(cytidine 50 -diphospho)-ME (CDP-MEP), ME-2,4cyclodiphosphate (MEcPP), 1-hydroxy-2-methyl-2-en-butenyl 4-diphosphate (HMBPP), DMAPP and IPP (Fig. 1; Supporting Information Methods S1). Abbreviations for MEP pathway enzymes and metabolites are presented in the legend to Fig. 1. New Phytologist (2015) www.newphytologist.com

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Fig. 1 Schematic representation of processes included in the modelling of the diurnal regulation of the 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway in plants. Metabolites: DXP, 1-deoxy-D-xylulose-5-phosphate; CDP-ME, 4-(cytidine 50 -diphospho)-ME; CDP-MEP, 2-phospho-4(cytidine 50 -diphospho)-ME; MEcPP, ME-2,4-cyclodiphosphate; HMBPP, 1-hydroxy-2-methyl-2-en-butenyl 4-diphosphate; DMAPP, dimethylallyl diphosphate; IPP, isopentenyl diphosphate. Enzymes: DXS, DXP synthase; DXR, DXP reductoisomerase; MCT, MEP cytidylyltransferase; CMS, CDPME kinase; MDS, MEcPP synthase; HDS, HMBPP synthase; HDR, HMBPP reductase. Graph shows circadian oscillations during day (white) and night (grey) periods for transcripts encoding the key clock transcription factors CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) and LATE ELONGATED HYPOCOTYL (LHY) (blue dashed line) and typical MEP pathway and downstream pathway enzymes (black solid line). The thunder vector indicates light-triggered production of triose phosphates in source tissues (TPso) by photosynthesis during the day. Only minor flux of TPso is directed to the MEP pathway, whereas most of fixed TPso are used for sucrose (suc) synthesis in source leaves and exported to sink tissues. At night, starch degradation is a main source of carbon for the MEP pathway (starch synthesis from TPso during the day and its degradation at night are not shown for clarity). In sink tissues degradation of sucrose produces hexose-phosphates (HPsi) and triose-phosphates (TPsi), which are consumed for growth. A minor part of TPsi is also used as a substrate of the MEP pathway. GAP, glyceraldehyde 3-phosphate; PYR, pyruvate.

In addition to the conventional linear MEP pathway, we included in the model the allosteric inhibition of DXS activity by MEP intermediates IPP and DMAPP (Banerjee et al., 2013) and the post-transcriptional regulation (PTR) of DXS protein abundance (Guevara-Garcıa et al., 2005; Cordoba et al., 2009). We assumed that nonactive DXS complexes with IPP and DMAPP (DI and DD, respectively) could be prone to covalent modification and that the resulting nonfunctional modified form of DXS (DXSna) is then targeted for degradation (Pulido et al., 2013) (Supporting Information Fig. S1). The concentrations of DI and DD were determined by a rapid equilibrium approximation for complex formation. The PTR control of DXS protein abundance was additionally described through inhibition of DXS translation by IPP/DMAPP-derived product Pmep (Fig. S1). The dynamic equations for Pmep, various fractions of DXS protein and final equations for IPP and DMAPP are: Ó 2015 The Authors New Phytologist Ó 2015 New Phytologist Trust

New Phytologist dPmep ¼ kPmep  ðIPP þ DMAPP  PmepÞ dt dDXSac ¼ Vtr0  ð1 þ Kfb =ð1 þ Pmep=KiPmep ÞÞ  kturn  DXSa dt  knaDXS  ðDI þ DDÞ dDXSna ¼ knaDXS  ðDI þ DDÞ  kturn  DXSna dt dIPP ¼ mHDRIPP  mIPPI  mconsIPP  kPmep  IPP þ knaDXS  DI dt dDMAPP ¼ mHDRDMAPP þ mIPPI  mconsDMAPP  kPmep  DMAPP dt þ knaDXS  DD DXSa ¼ DXSac =ð1 þ IPP =KdDI þ DMAPP =KdDD Þ Here DXSac is the sum of free, active DXS (DXSa) and its nonactive complexes with IPP or DMAPP (DI = DXSa·IPP/KdDI, DD = DXSa·DMAPP/KdDD); DXSna is nonactive free DXS, targeted for degradation. The equation for DXSa was derived from the mass balance conservation for DXSac (DXSac = DXSa + DI + DD). Vtr0 is a relative minimal rate of DXS translation (proportional to DXS mRNA), knaDXS is the rate constant of the release of nonactive DXS from DI and DD complexes, kturn is the rate constant of the turnover of DXS protein, parameters KiPmep and Kfb set up the range and strength of the PTR feedback. Because the molecular identity of Pmep is unknown, we assume that the flux of IPP and DMAPP to Pmep is negligible compared with the rate of their consumption. The feedback parameters were estimated based on available data (Methods S1). The values of the model parameters are presented in Table S2. The steady-state concentrations of MEP metabolites were estimated from the published data (Benz et al., 1983; Magel et al., 2006; Nogues et al., 2006; Behnke et al., 2007; Zhou et al., 2012; Li & Sharkey, 2013; Wright et al., 2014). Based on the metabolite concentrations and reported values of the MEP flux (0.3 mM DXP in chloroplasts h1) (Nogues et al., 2006; Wright et al., 2014), we deduced the expected optimal concentrations of MEP enzymes in chloroplasts of the rosette tissue, which are presented in Table S3 together with the steady-state metabolite amounts. Next we extended the model by including diurnal regulation of MEP pathway. Diurnal regulation In order to explore the diurnal regulation of the MEP pathway through substrate (GAP) availability, we connected the MEP submodel to our model of the diurnal kinetics of carbohydrate metabolism, which describes photosyntheticand sucrose-derived production of GAP in source and sink tissues (Fig. 1) (Pokhilko et al., 2014). Next we introduced the reactions of the MEP submodel in both source and sink tissues, which allowed us to describe the kinetics of the MEP pathway in a whole plant (Methods S1). The effects of the circadian clock were modelled through activation by the circadian protein complex of CIRCADIAN Ó 2015 The Authors New Phytologist Ó 2015 New Phytologist Trust

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CLOCK ASSOCIATED 1 (CCA1) and LATE ELONGATED HYPOCOTYL (LHY) of the first and last steps of the MEP pathway and of the rate of consumption of its products (Fig. 1; Methods S1). The carbohydrate model already includes a description of the clock, which was necessary to describe the diurnal regulation of carbohydrate metabolism and carbon partitioning between sucrose and starch (Pokhilko et al., 2014). Therefore, connecting the MEP submodel to the carbohydrate model results in a comprehensive, fully regulated model of the MEP pathway. The model parameters of diurnal regulation and the amounts of the MEP pathway enzymes were varied to achieve better correspondence with existing data on MEP pathway kinetics. Mid-day concentrations of metabolites are presented in Table S4 together with the enzyme concentrations. The sensitivity analysis demonstrated that the model is robust to parameter variations. For all parameters, a two-fold change causes < 1.1-fold changes in the MEP flux (Fig. S2). Therefore, the key properties of the model, such as substrate dependence (Fig. S2a), mild circadian effect (Fig. S2a,b) and regulation of the pathway flux on demand by downstream products (Fig. S2c) are conserved under parameter variations. The system of ordinary differential equations was solved using MATLAB, integrated with the stiff solver ode15s (The MathWorks UK, Cambridge, UK). A MATLAB version of the model is provided in Methods S2.

Results and Discussion Model structure A MEP pathway model was previously developed to study the production of essential oils (monoterpenes) in peppermint leaves (Rios-Estepa et al., 2010). This model did not take into consideration either the diurnal cycles of light and dark or the feedback regulation of the pathway, and it was mainly focused on the production of downstream products. However, it provided a useful background for the model presented here. We started the development from a submodel, which describes the enzymatic reactions of the MEP pathway in chloroplasts and includes the feedback regulation of DXS activity and abundance by downstream products as described later. Next, to analyse the diurnal regulation of the MEP pathway in a whole plant, we connected this submodel to our recently developed models of carbohydrate metabolism and circadian clock (Pokhilko et al., 2013, 2014). This allowed us to describe the diurnal influx of carbohydrate substrate and circadian regulation of the MEP pathway. Therefore, three main levels of diurnal regulation of the A. thaliana MEP pathway are included in the presented model (represented in green, blue and red in Fig. 1). The first level is related to the diurnal regulation of the MEP pathway substrate GAP, which together with dihydroxyacetone phosphate forms a plastidic pool of triose-phosphates (TP). TP have different origin in source and sink tissues, as described in the carbohydrate model (Fig. 1). In source tissues TP are derived mainly from photosynthesis, with some minor flux from starch New Phytologist (2015) www.newphytologist.com

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degradation at night. This results in a dramatic increase of TP amounts in the presence of light compared with darkness (Gerhardt et al., 1987; Arrivault et al., 2009). By contrast, pyruvate, the other substrate of the MEP pathway, is much less sensitive to changes during the day (Arrivault et al., 2009). This is possibly due to the glycolytic origin of pyruvate, which is believed to be imported to chloroplasts from the cytosol (Furumoto et al., 2011; Trowbridge et al., 2012). Therefore, in our model we used GAP (TP) as the substrate most appropriate to help understand the diurnal regulation of the MEP pathway kinetics. To account for the earlier-mentioned differences in the origin of GAP in the source and sink tissues and describe the diurnal regulation of the MEP pathway in a whole plant, we added MEP pathway reactions in both source and sink compartments in the full model. A second level of diurnal regulation is related to the circadian clock, which has been proposed to regulate the transcription of some MEP pathway genes, including those encoding DXS and the last enzyme of the pathway, hydroxymethylbutenyl diphosphate reductase (HDR) (Fig. 1) (Covington et al., 2008; Cordoba et al., 2009; Vranova et al., 2013). In addition, the consumption of MEP-derived prenyl diphosphates is regulated by the first enzymes of downstream pathways that also show a diurnal regulation. For example, the gene encoding phytoene synthase (PSY), the first enzyme of the carotenoid biosynthesis pathway (RuizSola & Rodrıguez-Concepcion, 2012), shows a peak of

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transcription in the morning, like DXS and HDR, suggesting that the MEP pathway is coordinately regulated with downstream pathways by the clock (Covington et al., 2008). Therefore, we added the parallel circadian regulation of these steps in the model (Fig. 1). The third level of diurnal regulation is related to the feedback mechanism that modulates DXS protein concentrations and activity by downstream products (Guevara-Garcıa et al., 2005; Cordoba et al., 2009; Banerjee et al., 2013; Han et al., 2013; Ghirardo et al., 2014). The activity of DXS is downregulated upon accumulation of MEP pathway products (IPP and DMAPP), which allosterically inhibit DXS activity (Banerjee et al., 2013; Ghirardo et al., 2014). On the other hand, when IPP and DMAPP decrease either by consumption by downstream pathways (Rodrıguez-Villalon et al., 2009; Ghirardo et al., 2014) or by a specific inhibition of MEP pathway enzymes (GuevaraGarcıa et al., 2005; Cordoba et al., 2009; Han et al., 2013), the abundance of DXS protein is upregulated. Feedback regulation of the first enzyme of a linear pathway by downstream products (Fig. 1) is expected to have a strong regulatory effect (Heinrich & Rapoport, 1974). Therefore, we used the model to explore the possible consequences of DXS feedback regulation for the system’s kinetics. The model is described in more detail in the Materials and Methods section. Here we analysed the effects of the earlierMEcPP DXP DMAPP IPP GAP

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Fig. 2 Dependence of 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway kinetics on the supply of glyceraldehyde 3-phosphate (GAP) in the model. (a) Variation of steady-state values of MEP pathway flux predicted by the MEP submodel at different concentrations of GAP. (b) Diurnal kinetics of the most abundant metabolites of the MEP pathway and GAP in the whole model. Simulation was run under a 12 h : 12 h, light : dark cycle, which is indicated by white and black rectangles on the x-axis. The total concentration of each metabolite (X) in a whole plant (Xtot) is shown. (c, d) Diurnal kinetics of MEP pathway flux (c) and GAP concentrations (d) in a whole plant and in source and sink tissues according to the model. The total concentration of each metabolite X in a whole plant (Xtot) is a sum of its respective source (Xso) and sink (Xsi) concentrations (Xtot = XsoVso + Xsi (1Vso)), with a ratio of sourceto-sink volumes taken from the carbohydrate model as Vso = 0.75 (Pokhilko et al., 2014). Xtot, Xso and Xsi are shown by solid, dotted and dashed lines, respectively. The insert in (c) shows diurnal variations of the MEP pathway flux on a logarithmic scale. New Phytologist (2015) www.newphytologist.com

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Photosynthetic dependence of the supply of GAP GAP concentrations in plant chloroplasts depend on photosynthesis and fluctuate between 0.02 mM during the day and 0.001 mM at night (Gerhardt et al., 1987; Arrivault et al., 2009; Arnold & Nikoloski, 2011). These values are below the Km of the DXS enzyme, 0.11 mM (Ghirardo et al., 2010), resulting in a strong direct dependence of the MEP pathway flux (Fig. 2a) and metabolite amounts (Fig. S3a) on GAP concentration. Clearly, this regulation by substrate availability holds also for the wholeplant model. Figure 2(b) shows the diurnal dynamics of GAP and the most abundant MEP pathway intermediates, that is, MEcPP, DXP, DMAPP and IPP in decreasing order of abundance (Benz et al., 1983; Nogues et al., 2006; Behnke et al.,

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mentioned three levels of diurnal regulation of MEP pathway kinetics using both simulations of the MEP submodel and the whole model. Most simulations of the whole model were run under 12 h : 12 h, light : dark diurnal cycles, unless otherwise stated. The concentrations of model components are presented as millimoles per litre in a chloroplast compartment.

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Fig. 3 Circadian effects on the 2-C-methylD-erythritol 4-phosphate (MEP) pathway. (a–c). Experimental quantitative-PCR (qPCR) measurements of diurnal timecourses of 1deoxy-D-xylulose 5-phosphate (DXP) synthase (DXS), 1-hydroxy-2-methyl-2-enbutenyl 4-diphosphate reductase (HDR) and phytoene synthase (PSY) expression in the wild-type (Ws) and lhy-21/cca1-11 mutant Arabidopsis thaliana plants. The samples were collected from plants grown under 12 h : 12 h, light : dark diurnal cycles. mRNA concentrations are represented relative to those at time 0 in Ws plants. The graphs show average and  SE of the mean of n = 3 independent samples. Day and night periods marked by white and black bars on the xaxis. (d–f) The circadian effects of the transcriptional regulation of MEP enzymes in the model. MEP pathway flux (d, f) and metabolite concentrations (e) were calculated with (solid lines) or without (dashed lines) circadian regulation. For the model simulations without circadian regulation, the value of circadian function g (t) was set to its average value 0.84. The simulations were done in 12 h : 12 h, light : dark (d, e) and 8 h : 16 h, light : dark (f) diurnal cycles. The fluxes in a whole plant (d) or in sink tissues only (f) are shown.

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2007; Zhou et al., 2012; Weise et al., 2013; Wright et al., 2014). A separate analysis of MEP pathway activities in sink and source tissues revealed that the dependence on light of GAP concentrations and hence of MEP pathway flux and amounts of intermediates is especially relevant in the source tissues because both pathway flux and metabolite amounts fall almost to zero in darkness (Figs 2,S3). This prediction of the model is in agreement with the available data, which demonstrate that DMAPP concentration in the source leaves of poplar (an isoprene-emitting species) follows the GAP time course and photosynthesis (Magel et al., 2006). The light dependence of the MEP pathway flux is less pronounced in sink tissues (Fig. 2c) because here GAP is derived from sugars (Fig. 1) and consequently this substrate is always available at relatively high concentrations (0.01– 0.05 mM) (Fig. 2d), resulting in only approximately two-fold activity changes (Fig. 2c). By contrast, in source tissues photosynthetically derived GAP is not available during the night, resulting in almost zero activities (Fig. 2c,d). Interestingly, the model predicts that the amplitude of diurnal oscillations of the MEP pathway flux in sink tissues decreases on shorter days compared with longer days (Figs 2c,S3d). The strong correlation between GAP New Phytologist (2015) www.newphytologist.com

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DXR Fig. 4 Experimental data on 1-deoxy-D-xylulose 5-phosphate (DXP) synthase (DXS) protein accumulation in wild-type and mutant Arabidopsis thaliana plants with different isopentenyl diphosphate (IPP)/dimethylallyl diphosphate (DMAPP) concentrations. (a) The amount of DXS protein in wild-type (Col) seedlings grown for 10 d under long day (LD) conditions (16 h : 8 h, light : dark diurnal cycles) without inhibitors and then transferred to fresh medium supplemented with 100 lM fosmidomycin (FSM) for the indicated times. The concentrations of DXP reductoisomerase (DXR) protein in the same samples are shown as a control. (b) Col plants and heterozygous lines defective in 1-hydroxy-2methyl-2-en-butenyl 4-diphosphate reductase (HDR, the enzyme that produces IPP and DMAPP in the last step of the 2-C-methyl-D-erythritol 4phosphate (MEP) pathway) or phytoene synthase (PSY, which diverts MEP pathway products into the carotenoid pathway) were grown under LD conditions. At Day 18, homozygous hdr-3 and psy-1 individuals were clearly identified based on their albino phenotype (picture). Samples from Col and homozygous mutants were used to estimate DXS and DXR protein concentrations by Western blot analysis.

content and MEP pathway flux suggests that chloroplast GAP concentrations can be good diagnostic markers for MEP pathway activity, which at the whole plant level is a combination of source and sink activities and is predicted to oscillate substantially throughout the day (Figs 2c, S3d). Circadian regulation of MEP pathway genes The rhythmic pattern of expression of genes encoding key enzymes of the MEP pathway, such as DXS and HDR (Phillips et al., 2008), as well as those regulating the metabolic flux to downstream pathways that use MEP-derived prenyl diphosphates, such as PSY (Rodrıguez-Concepcion, 2010), are wellknown (Hsieh & Goodman, 2005; Covington et al., 2008; New Phytologist (2015) www.newphytologist.com

Cordoba et al., 2009; Hemmerlin et al., 2012; Vranova et al., 2013). A pattern common to most of these genes is a transcriptional peak in the morning (Covington et al., 2008), suggesting a transcriptional activation by the key clock components LHY and CCA1, which serve as general morning activators (Harmer & Kay, 2005). Our preliminary analysis of DXS, HDR and PSY gene sequences showed the presence of multiple LHY/CCA1binding elements in the promoter regions. To further validate the potential role of the circadian clock in general and the LHY– CCA1 complex in particular in regulating expression of the corresponding genes, we performed qPCR analysis of DXS, HDR and PSY mRNA concentrations in A. thaliana wild-type (Ws-2) and lhy-21/cca1-11 double null mutant plants. Samples were collected either from plants grown under 12 h : 12 h, light : dark or from plants transferred from this photoperiod to continuous light conditions. Our data show that the oscillation profile of all these genes under 12 h : 12 h, light : dark cycles was clearly disrupted in the double mutant plants relative to the wild-type (Fig. 3). In particular, they are downregulated in the morning in the lhy-21/ cca1-11 mutant, which further supports the hypothesis that the LHY–CCA1 complex is activating their transcription. Further demonstrating a circadian regulation of these genes, their rhythmic expression was maintained under free running (continuous illumination) conditions in Ws-2 plants, whereas it remained virtually acyclic in the lhy-21/cca1-11 mutant (Fig. S4). In summary, we provide evidence for a role of the circadian clock in MEP pathway (DXS, HDR ) and downstream (PSY ) gene regulation, most likely through activation by LHY or/and CCA1 (Fig. 1). According to our model, simultaneous regulation by the clock of these three enzymatic steps controlling the production of MEP pathway products and their consumption (Fig. 1) slightly stimulates the MEP pathway flux (Fig. 3d) and increases the production of MEP pathway intermediates (Fig. 3e) when plants are exposed to light during the daytime. Therefore, both substrate (GAP) availability and clock modulation of MEP pathway flux ensure that enough MEP-derived prenyl diphosphates are provided for plastidial isoprenoid biosynthesis during the light phase of a day, when their demand is highest (Walter et al., 2009). Although the model predicts that GAP substrate availability should have a stronger effect on the total – whole plant – flux compared with the clock, the effect of the circadian clock on the MEP pathway flux might be comparable to the GAP substrate effect in sink tissues (Fig. 3f). Regulation of DXS enzyme concentration and activity by MEP pathway products The next level of diurnal control of the MEP pathway is provided by the feedback regulation of DXS activity and abundance (Guevara-Garcıa et al., 2005; Cordoba et al., 2009; Hemmerlin et al., 2012; Banerjee et al., 2013; Han et al., 2013; Ghirardo et al., 2014). DXS activity is allosterically regulated through inhibition by IPP/DMAPP (Banerjee et al., 2013; Ghirardo et al., 2014), whereas DXS protein abundance is also regulated by as yet unidentified MEP pathway products (Guevara-Garcıa et al., Ó 2015 The Authors New Phytologist Ó 2015 New Phytologist Trust

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2005; Han et al., 2013). Although both types of feedback regulation are post-transcriptional, we will further call them as ‘allosteric regulation’ (for DXS activity) and ‘post-transcriptional regulation’ (PTR) (for DXS abundance), for distinction. Although allosteric feedback is fast because it acts immediately when production of the final products IPP and DMAPP is higher than their consumption by downstream processes (Banerjee et al., 2013), changes in DXS protein concentrations due to PTR have been reported to occur slowly (with a time scale of hours) in response to a more persistent alteration in the MEP pathway flux (Guevara-Garcıa et al., 2005; Cordoba et al., 2009). In order to constrain the model, we first aimed to experimentally to confirm the time course of DXS protein accumulation in response to blocking the MEP pathway and determine what intermediates or/and products might be responsible for the DXS PTR response. On the one hand, treatment of plants with clomazone (a specific inhibitor of DXS) or FSM (a specific inhibitor of the next enzyme of the MEP pathway, DXP reductoisomerase (DXR); Fig. 1) was previously reported to result in a steady accumulation of DXS protein, whereas it only marginally affected DXR concentrations (Guevara-Garcıa et al., 2005; Han et al., 2013). We confirmed that the concentration of DXS proteins substantially increased as early as 5 h after the treatment of A. thaliana seedlings with FSM (Fig. 4a). In the presence of the inhibitor, DXS protein concentrations kept increasing for days whereas DXR enzyme concentrations appeared unaffected (Fig. 4a). On the other hand, A. thaliana mutants with a genetic defect in the MEP pathway also show a DXS protein overaccumulation phenotype, whereas DXR concentrations are typically Ó 2015 The Authors New Phytologist Ó 2015 New Phytologist Trust

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decreased (Guevara-Garcıa et al., 2005). We confirmed these observations using the HDR-defective hdr-3 mutant (Fig. 4b), which is unable to produce IPP and DMAPP (Fig. 1). Like other knock-out alleles of the MEP pathway (Hsieh & Goodman, 2005; Phillips et al., 2008), homozygous hdr-3 seedlings display a characteristic albino phenotype (Fig. 4b). A very similar albino phenotype was observed in a PSY-defective mutant (psy-1) that is unable to convert the MEP pathways products into carotenoids, the most abundant group of MEP-derived isoprenoids (Ruiz-Sola & Rodrıguez-Concepcion, 2012). Despite the visual phenotypic similarities (Fig. 4b), it is expected that the concentrations of IPP/DMAPP are reduced in hdr-3 plants but increased when PSY activity is missing in the psy-1 line. Although in agreement with previous observations (Guevara-Garcıa et al., 2005) that DXR protein concentrations were reduced in both types of albino mutants (Fig. 4b), DXS concentrations were upregulated in the hdr-3 mutant but downregulated in psy-1 plants, confirming a negative correlation between IPP/DMAPP and DXS protein concentrations (Fig. 4b). This correlation has also been observed in poplar lines unable to transform DMAPP into isoprene, where a strong increase in plastidial DMAPP concentrations is accompanied by a reduction in DXS protein concentrations (Ghirardo et al., 2014). Together, it is most likely that IPP/DMAPP are the metabolites whose changes eventually trigger the allosteric and PTR feedback responses that modulate DXS enzyme activity and accumulation, respectively. The available data suggest that degradation mainly occurs in nonactive DXS polypeptides (Pulido et al., 2013). Therefore, we assumed in the model that the DXS enzyme allosterically inactivated by IPP/DMAPP binding New Phytologist (2015) www.newphytologist.com

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model, it is mainly allosteric regulation that affects DXS protein accumulation under normal conditions, with PTR having little effect (Fig. S5b). In particular, allosteric regulation leads to an increased abundance of DXS protein (Fig. S5b) due to accumulation of nonactive complexes of DXS with IPP/DMAPP (Fig. S5c) during the light period (Fig. S5c). In our simulations the total amount of DXS protein only oscillates slightly (Figs S5b, 5a), because the concentrations of IPP and DMAPP under normal conditions in A. thaliana are lower than the dissociation constants of their complexes with DXS protein. However, the effect of allosteric regulation under normal conditions should be substantially stronger in isoprene-emitting plants, which have much higher concentrations of IPP and DMAPP compared with A. thaliana (Ghirardo et al., 2014). Similarly, the effect of allosteric regulation on DXS protein content in A. thaliana is increasing under high fluxes as described later.

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Fig. 6 Experimental measurements of diurnal changes in 1-deoxy-Dxylulose 5-phosphate (DXP) synthase (DXS) protein abundance in Arabidopsis thaliana wild-type (Col) and DXS-overexpressing lines. Col plants together with homozygous 35S:DXS and 35S:DXS-GFP lines were grown under 12 h : 12 h, light : dark conditions for 25 d and collected at the time points represented in the scale at the top. (a) DXS transcript abundance as estimated by quantitative-PCR (qPCR) analysis. Values are presented relative to the concentrations in Col plants at time 0 h and correspond to the mean and the  SD of n = 4 independent samples. The dashed line marks a three-fold increase in DXS transcript levels. (b) Western blot analysis of the same samples with antibodies specific for DXS (upper panels) or DXP reductoisomerase (DXR) (lower panels). Arrowheads mark the position of the indicated proteins. The symbols correspond to the time points simulated for wild-type plants (circles) and lines with a three-fold increase in DXS concentrations (triangles) in Fig. 5(a).

(Banerjee et al., 2013) would be prone to covalent modifications, rendering nonfunctional polypeptides that would then be targeted to degradation. The PTR regulation of DXS protein abundance was additionally described through inhibition of DXS translation by IPP/DMAPP-derived products (Fig. S1). We used the model to explore the impact of the feedback regulation of DXS on MEP pathway kinetics. The model suggests that, although under normal conditions the diurnal kinetics of the MEP pathway flux and metabolites were set to be similar in the presence or absence of feedbacks (Fig. S5a), the kinetics of DXS protein is affected by the feedback regulation. In our New Phytologist (2015) www.newphytologist.com

Feedback regulation of DXS adjusts the flux to substrate supply Next we used the model to explore the impact of overexpressing DXS on the MEP pathway flux. The model predicts that threefold increase of DXS mRNA concentrations results in only a 1.9fold increase of steady-state flux through the MEP pathway (Fig. 5b). The increase of the flux is more pronounced in the absence of the feedback regulation (Fig. 5c), with allosteric regulation mainly affecting the flux in the morning and PTR affecting the flux at all times during the day (Fig. 5c). Therefore, the model suggests that the feedback regulation of DXS protein activity and abundance provides a mechanism which restricts MEP pathway flux under conditions when supply of isoprenoid precursors is higher than demand, in agreement with data (Ghirardo et al., 2014). This might help plants to avoid an excessive accumulation of certain MEP pathway intermediates or products (Keetman et al., 2002). For example, an accumulation of methylerythritol cyclodiphoshate (MEcPP) could be interpreted as a signal of oxidative or biotic stress (Bitok & Meyers, 2012; Xiao et al., 2012; Zhou et al., 2012; Banerjee & Sharkey, 2014; Wright et al., 2014). In addition to affecting the flux, the presence of allosteric regulation of DXS protein causes a striking increase in the content and oscillation of DXS protein in both wild-type plants (Fig. S5) and, most dramatically, in the simulated DXS-overexpressing line (Fig. 5a). This is related to accumulation of nonactive complexes of DXS during the day (Fig. 5d), when MEP pathway flux is high (Fig. 5b). Therefore, an excess of IPP and DMAPP acts as a buffer that reduces DXS concentrations and activity under conditions when the supply of MEP substrate is higher than demand of prenyl diphosphates for plastidial isoprenoid biosynthesis. Experimentally testing the model with DXS-overexpressing transgenic plants In order to verify model predictions about oscillations in DXS protein concentrations under increased concentrations of DXS mRNA, we used the DXS-overexpressing A. thaliana lines 35S: DXS (Carretero-Paulet et al., 2006) and 35S:DXS-GFP (Pulido Ó 2015 The Authors New Phytologist Ó 2015 New Phytologist Trust

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Fig. 7 Modulation of the diurnal kinetics of the 2-C-methyl-D-erythritol 4-phosphate (MEP) pathway by demand of its isopentenyl diphosphate (IPP)/ dimethylallyl diphosphate (DMAPP) products in the model. (a) Simulated diurnal kinetics of the MEP pathway flux under three-fold changes in the rates of prenyl diphosphate consumption are shown. Solid, dashed and dotted lines correspond to normal, three-fold decreased, or three-fold increased rates of DMAPP and IPP consumption, respectively. The consumption rate was varied by changes in parameter km_cons. (b) Dependence of the peak value of diurnal flux on the consumption rate for model simulations with or without post-transcriptional regulation of an abundance of 1-deoxy-D-xylulose 5phosphate (DXP) synthase (DXS) protein are shown by solid and dashed lines, respectively.

et al., 2013). In particular, transgenic plants were selected which showed concentrations of DXS-encoding transcripts about threefold higher than those detected in the morning in untransformed plants (Fig. 6a). As predicted by the model (Fig. 5a), Western blot estimations of DXS protein concentrations in these transgenic lines showed an increase of total DXS and, in the case of the 35S:DXS-GFP line, DXS-GFP protein concentrations at the end of the day (at 12 h) compared with the end of the night (at 0 h), whereas no changes were observed for the endogenous DXR protein (Fig. 6b). By contrast, DXS mRNA concentrations remained constantly high throughout the day (Fig. 6a), supporting the model prediction that oscillations of DXS protein in DXS-overexpressing lines mainly result from post-transcriptional events (Figs 5, S5). Oppositely, DXS protein concentrations show only modest changes despite pronounced oscillations of DXS-encoding transcripts in wild-type plants (Figs 3a, 6a), again supporting our conclusion that feedback events provide the main regulation of the abundance of DXS protein. Altogether, our data suggest that allosteric inactivation of DXS by IPP and DMAPP might be responsible for the diurnal oscillations of the total concentration of DXS protein under increased stimulation of MEP pathway flux in DXS-overexpressing lines. This further confirms that allosteric regulation of DXS provides a fast regulatory mechanism of limiting MEP pathway flux by end-products in plants.

flux in response to alterations in the consumption rate were less dramatic in the absence of PTR (Fig. 7b). The model suggests that PTR provides a relatively slow response of the MEP pathway to changes in the product demand or substrate supply. It takes several days for the system to reach new steady state after changes in the ratio of supply and demand of MEP pathway products, which corresponds to the experimental data on changes in DXS protein concentration when the MEP pathway flux is restricted by application of an inhibitor of the MEP pathway (Fig. 4a) (Guevara-Garcıa et al., 2005; Han et al., 2013). We therefore conclude that the post-transcriptional regulation of DXS protein abundance is crucial for the adjustment of the MEP pathway to persistent changes in environmental conditions, such as substrate supply or product demand. In conclusion, several layers of regulation shape the MEP pathway during the day. First, light strongly stimulates MEP pathway flux via the availability of GAP substrate, an effect that is especially pronounced in source tissues. Second, the circadian clock facilitates the flux during the daytime. And third, feedback regulation of DXS adjusts the flux through the MEP pathway accordingly to the demand of downstream products. The available model represents a useful tool for guiding future biotechnological strategies aimed to increase the concentrations of MEP-derived isoprenoids of interest as drugs, pigments, nutrients or biofuels in plants.

Feedback regulation of DXS adjusts the flux to the product demand

Acknowledgements

Next we used the model to analyse the diurnal response of the MEP pathway to alterations in the rate of consumption of prenyl diphosphates by downstream processes. Model simulations demonstrate that an increase of consumption upregulates the MEP pathway flux (Fig. 7a) through a decrease in IPP and DMAPP, which in turn leads to increased accumulation of DXS protein (Fig. 4). Similarly, a decreased rate of consumption results in the reduction of MEP pathway flux (Fig. 7a). These changes in the

We are very grateful to S. Mitra and L. P. Wright (MPICE, Jena, Germany) for critically reading and making valuable comments on the manuscript, and M. R. Rodrıguez-Goberna for excellent technical support. This work was mainly funded by the European Union FP7’s TiMet project (contract 245143). O.E. is supported by the Marie Curie ITN ‘AccliPhot’ (GA 316 427), funded by the European Union. P.P. was funded by the Spanish Direccion General de Investigacion (grant BIO2011-23680).

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Fig. S3 Dependence of MEP pathway kinetics on the supply of GAP in the model. Fig. S4 Experimental qPCR measurements of the diurnal time courses of DXS, HDR and PSY expression in the wild-type (Ws) and lhy-21/cca1-11 mutant under constant light conditions. Fig. S5 Effects of the feedback regulation of DXS on the diurnal kinetics of the MEP pathway in wild-type plants in the model. Table S1 Primers used in this work for qPCR analysis Table S2 Parameters of the MEP pathway submodel Table S3 Enzyme and metabolite concentrations in the MEP pathway submodel Table S4 Enzyme and metabolite concentrations in the full model Methods S1 Mathematical modelling of the MEP pathway.

Supporting Information Additional supporting information may be found in the online version of this article. Fig. S1 The proposed scheme for the feedback regulation of DXS protein in the model.

Methods S2 Model scripts in Matlab. Please note: Wiley Blackwell are not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing material) should be directed to the New Phytologist Central Office.

Fig. S2 Sensitivity of the model kinetics to parameter variations.

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Mathematical modelling of the diurnal regulation of the MEP pathway in Arabidopsis.

Isoprenoid molecules are essential elements of plant metabolism. Many important plant isoprenoids, such as chlorophylls, carotenoids, tocopherols, pre...
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