Abstract. Introduction RESEARCH PAPER. Francxois Brun 1,Céline Richard-Molard 2, Loïc Pagès 3, Michaël Chelle 2 and Bertrand Ney 1, *

Transcription

1 Journal of Experimental Botany, Vol. 61, No. 8, pp , 2010 doi: /jxb/erq090 Advance Access publication 16 April, 2010 RESEARCH PAPER To what extent may changes in the root system architecture of Arabidopsis thaliana grown under contrasted homogenous nitrogen regimes be explained by changes in carbon supply? A modelling approach Francxois Brun 1,Céline Richard-Molard 2, Loïc Pagès 3, Michaël Chelle 2 and Bertrand Ney 1, * 1 AgroParisTech, UMR1091 INRA AgroParisTech Environnement et Grandes Cultures, F Thiverval-Grignon, France 2 INRA, UMR1091 INRA AgroParisTech Environnement et Grandes Cultures, F Thiverval-Grignon, France 3 INRA, UR1155 Plantes et Systèmes de culture Horticoles, Domaine Saint-Paul, Site Agroparc, F Avignon Cedex 9, France * To whom correspondence should be addressed. ney@agroparistech.fr Received 9 October 2009; Revised 18 March 2010; Accepted 19 March 2010 Abstract Root system architecture adapts to low nitrogen (N) nutrition. Some adaptations may be mediated by modifications of carbon (C) fluxes. The objective of this study was to test the hypothesis that changes in root system architecture under different N regimes may be accounted for by using simple hypotheses of C allocation within the root system of Arabidopsis thaliana. With that purpose, a model during vegetative growth was developed that predicted the main traits of root system architecture (total root length, lateral root number, and specific root length). Different experimental data sets crossing three C levels and two N homogenous nutrition levels were generated. Parameters were estimated from an experiment carried out under medium C and high N conditions. They were then checked under other C3N conditions. It was found that the model was able to simulate correctly C effects on root architecture in both high and low N nutrition conditions, with the same parameter values. It was concluded that C flux modifications explained the major part of root system adaptation to N supply, even if they were not sufficient to simulate some changes, such as specific root length. Key words: Assimilate partitioning, carbon allocation dynamics, C flux, modelling, N supply, rhizotron, root system morphogenesis, root system development, source/sink balance. Introduction The root system architecture determines the essential part of the nitrogen (N) uptake capacity by root exchange area and exploitation potential (Fitter et al., 2002). A set of morphogenetic processes, such as growth and branching, leads to the development of the root system architecture. These processes are highly organized in both space and time. Fundamental cellular mechanisms of axial growth (Beemster and Baskin, 1998; Beemster et al., 2002) or new root formation (Dubrovsky et al., 2000, 2006; Casimiro et al., 2003) have been described for Arabidopsis thaliana. However, quantitative expression of these processes remains unclear as they depend on internal signals and environmental conditions (Malamy and Ryan, 2001; Malamy, 2005). Several studies have shown that the axial growth of the root and the emergence of new roots are highly sensitive to carbon (C) availability. Changing experimental C conditions through the CO 2 level, light, leaf pruning, or sugar in the centre of the root on a short or long time scale has confirmed the key role of sugar as a nutrient or signal mediator (Bingham and Stevenson, 1993; Thaler and Pagès, 1996; Muller et al., 1998; Freixes et al., 2002; Willaume and Pagès, 2006). Moreover, the mineral environment, such as N availability, influences the root system architecture (Hodge, 2004). Mechanisms underlying morphogenetic changes in the root system have been separated into local and long-range ª The Author [2010]. Published by Oxford University Press [on behalf of the Society for Experimental Biology]. All rights reserved. For Permissions, please journals.permissions@oxfordjournals.org

2 2158 Brun et al. signals. Local N effects of root morphogenesis have been evidenced with split root experiments (Drew and Saker, 1975; Robinson, 1994; Zhang et al., 1999; Linkohr et al., 2002). Some authors have put forward the hypothesis that long-range signals are N specific (Zhang et al., 1999; Forde, 2002a, b; Remans et al., 2006). However, some signals could be mediated by changes in C fluxes. Indeed, reduction of shoot growth (Grindlay, 1997; Lemaire and Millard, 1999) and photosynthesis (Evans, 1983; Sinclair and Horie, 1989; Fahl et al., 1994) induces changes in C fluxes to roots (Scheible et al., 1997; Anandacoomaraswamy et al., 2002) when N is limiting. Consequently, there is a need to better distinguish specific N effects from effects mediated by induced changes in C supply. Plant responses to environmental stimuli are complex and entangled because of dynamic interactions between processes. Integration of these corresponding processes using a modelling approach could help to better understand the development of the root system. The first architectural models for the root system were designed to mimic as closely as possible the morphogenetic programme of the root system using fixed rules (Diggle, 1988; Pagès and Aries, 1988). Architectural models are useful for spatial representation of area of water (Doussan et al., 1998) or mineral uptake. However, they were not predictive under variable environmental conditions and did not take into account carbon availability. Other models include effects of the local environment such as temperature or soil mechanical properties on individual roots without taking into account the whole root system (Lynch et al., 1997). Somma et al. (1998) proposed a model taking into account the effect of soil N availability on global plant growth, but plant growth was related to water transfer and not directly to nutrient uptake. More recently, several source sink models, comparing C availability and C demand using a sink strength function for partitioning, have been proposed. In the model of Bidel et al. (2000) carbon partitioning among root sinks was based on the transport model of Minchin et al. (1993). Pagès (2000) has also suggested using a simple indicator of the overall availability of C for modelling purposes: the ratio total supply/total demand. Moreover, Thaler and Pagès (1998) have defined the sink strength (seen as potential growth) of any individual root from the size of its apex. They have also considered a feedback effect of carbohydrate supply on this root apex size. Based on the same rules, integration at the whole maize plant scale has shown that such models can predict root system behaviour related to shoot growth and functioning (Drouet and Pagès, 2003). However, the analysis of specific N effects on root system architecture remains challenging, as N availability also affects shoot growth and, consequently, C supply to the root. The objective of this study was to test the hypothesis that changes in root system architecture under different homogenous N regimes may be accounted for using simple hypotheses of C allocation within the root system. With that purpose, a root system model of C partitioning for A. thaliana was built and then different experimental data sets crossing various C and N nutritional conditions were generated. This led to differing levels of growth and architecture of A. thaliana plants. The chosen strategy was then to keep the same parameter values in the model for all the C3N treatments and to check model simulation quality, considering that a good prediction ability would validate the underlying hypothesis of the model; that is, that the main adaptation of the root system resulted from induced changes of C flux. The model and its parameterization with the medium C3high N combination is described first. Then, simulations corresponding to the other C and N combination were used to evaluate the role of C supply changes on the morphogenesis of the root system under different homogeneous N regimes. Materials and methods Experiments Plant material: All experiments were conducted with the Wassilevskija (WS) ecotype (N1602 in the Nottingham Arabidopsis Stock Center or CS1602 in the Arabidopsis Biological Resource Center catalogue) of A. thaliana (L.) Heynh. Culture conditions: Isolated A. thaliana plants were grown as described in Devienne-Barret et al. (2006) in root observation boxes (rhizotrons) containing an organic greenhouse mix, provided with no added fertilizers (BASIC SUBSTRAT II, Stender GmbH, Germany). Plants were placed in a growth chamber (Strader, France), equipped with HPI-T PLUS lamps (400 W, Philips, The Netherlands) providing photosynthetically active radiation (PAR) from 245 lmol m 2 s 1 to 450 lmol m 2 s 1 depending on the shade curtain used. Plants were grown for up to 25 d (vegetative growth period) under short-day conditions to extend the vegetative stage, with an air temperature of 19 C, a relative humidity fluctuating between 60% and 70 %, and an 8/16 h day/ night photoperiod. Individual experiments: Three independent experiments were carried out with various light conditions. Plants were grown with a PAR of 250 lmol m 2 s 1 (C1), 300 lmol m 2 s 1 (C2), or 450 lmol m 2 s 1 (C3). The various PAR levels were obtained by using various shade curtains placed above the plants. The CO 2 concentrations during the light period were measured with an infrared gas analyser (ADC 225-Mk3, Analytical Development Company, Hoddesdon, UK). In each experiment, two N regimes were applied using nutrient solutions differing only in their nitrate concentration (2 mm and 10 mm for the N and the N+ treatment, respectively). Irrigation procedures and solution composition are described in Devienne-Barret et al. (2006). Irrigation took place once per day and ensured a relatively constant and homogeneous N availability in the soil, as shown in Devienne- Barret et al. (2006). Measurements: Five plants for each C3N treatment were harvested at 20 (C2), 22 (C1 and C3), and 25 (C1, C2 and C3) days after sowing (DAS). Shoots and roots were separated, lyophilized, and weighed on a microbalance (Sartorius Germany) to obtain shoot and root dry weights (SDW and RDW, respectively). The root system was recorded daily by tracing new root elongation on a transparent plastic sheet with coloured pens. Due to the 20 inclination of the rhizotron and the 3 mm soil thickness, almost all roots were growing against the transparent front sheet of the rhizotron and were therefore visible for measurements. After scanning the transparent plastic sheet, the

3 Modelling the root system of Arabidopsis thaliana 2159 root system architecture (length of the colour segments, coordinates, and relationship between two segments) was analysed with ImageJ (Abramoff et al., 2004) and a home-made plug-in designed for this purpose. The root apical diameter was directly measured in the zone where it becomes cylindrical on the observation boxes with a binocular magnifying glass (Hirox KH1000, Japan) and used as an estimator of the meristem size (Pagès, 1995). About 60 diameters were measured from 11 to 18 DAS in the C2 treatment. Modelling General overview: The root system is defined here as a link-based topological system (Fitter et al., 2002) in which root segments represent links. It is described as a repetitive structure involving a main axis with secondary axes, which may bear third-order axes, etc. (Fig. 1A). An axis is made up of 0 to n successive segments and a final meristem. It corresponds to an individual root. The root is split into segments at each foreseeable branching point. A meristem is a primordium before root emergence and is a mature meristem thereafter, capable of elongation and branching. The model, object oriented, similar to that of Drouet and Pagès (2003), was based on the balance between C supply and C demand with a root system using an explicit description of the root architecture. The general framework of the model is summarized in Fig. 1B. C supply to root (CS) was derived from the flux of accumulated RDW, which was estimated from experiments. C demand (CD) was calculated in terms of biomass for each root according to its apex diameter. The apex diameter of a young emerging root depended on the diameter of the parent segment on which it was borne. When CS was higher than the sum of CD (RCD, i.e. the sum of all individual biomass demand), all apices grew at their Fig. 1. (A) Schematic diagram of the root system and of relationship between source and sink. The root system is considered as a main axis (taproot), with a meristem and segments. Each segment bears an axis, with a primordium or with a mature meristem and segments. The supply is an input variable corresponding to the accumulation of dry weight in the root system. The demand is computed as the sum of the individual demands in dry weight of all the sinks (dir, distance between two adjacent ramifications; DW, dry weight; E m and E m,pot, segment m elongation, effective and potential, respectively; N, number of segments; U m and U min, apex diameter of segment m and minimum apex diameter for the elongation of the corresponding segment). (B) General framework of the model.

4 2160 Brun et al. potential. When this was not the case, each apex was supplied proportionally to the ratio CS/SCD. C2N+ treatment was used to parameterize the model. The model is able to simulate root elongation, meristem diameter, and ramifications on a daily time step. Variable abbreviations are summarized in Table 1. C supply and potential C demand: Dry biomass flux supplied to roots, DRDW (mg DW d 1 ), was estimated using an exponential growth model fitted on the observed RDW. This variable was considered as the only input variable. The root system potential dry matter demand DRDW pot (mg DW d 1 ) was calculated as the sum of the demand of n growing roots, calculated as potential growth rates, DRDW pot Z+ mzn mz1 DW m; pot ð1þ Root elongation, calculated in terms of length (E), needed conversion into dry matter to relate it to supply/demand calculation. The potential and effective dry weights of the root segment m were evaluated from its volume as: DW m Zq3E m 3p3U 2 m =4 DW m;pot Zq3E m;pot 3p3U 2 m =4 where q is the meristem volumic mass (mg mm 3 ). The satisfaction coefficient A was then calculated as: ð2aþ ð2bþ AZDRDW=DRDW pot Branching and growth rules for each individual root: Root potential and effective elongations. Many authors have shown for various species (Wilcox, 1962; Hackett, 1973; Coutts, 1987; Cahn et al., 1989) a close relationship between meristem apical diameter and elongation rate. In maize, apical diameter has been proved to be a good indicator of the number of cells in the meristem (Barlow and Pilet, 1984). Pagès (1995) has proposed considerering apical diameter as an estimator of growth potential. Following Thaler and Pagès (1998) in their model, the relationship between apical diameter and potentiel elongation was used, and was validated in A. thaliana (Fig. 2). A potential elongation rate E pot (mm d 1 ) for a given apical diameter U (mm) is supposed to be reached when there is no C limitation. The envelope curve (Fig. 2) is given by the following function: ifu m >U min then E m;pot Za3 1 exp b3 U m U min =a ð4þ else E m;pot Z0 Effective elongation E m (mm d 1 ) depends on the C availability ratio A (Equation 3): E m ZE m;pot 3A Table 1. (A) Abbreviation, unit, and short description of all the variables used in the model. (B) Abbreviation, value, unit, short description, and method of estimation of all the parameters used in the model (A) Variable Value Unit Description TDW mg DW Plant dry weight at day d SDW mg DW Shoot dry weight at day d RDW mg DW Root dry weight at day d DRDW mg DW d 1 DW supplied to root system per day (input variable) DRDW pot mg DW d 1 Total DW demand of roots E m, pot mm d 1 Potential elongation E m mm d 1 Effective elongation DW m mg DW d 1 DW used by the meristem m DW m, pot mg DW d 1 DW demand of the meristem m A Satisfaction coefficient U m, U p mm Diameter of apex or primordium U pr mm Diameter of parent segment bearing the root U lr mm Threshold diameter when primordium becomes meristem (B) Parameter Value Unit Description q mg DW cm 3 Meristem volumic mass (estimated from global calibration on data C2N+) U min mm Minimum diameter (estimated from individual root elongation data, C2N+) a 28.5 mm d 1 Maximum potential (estimated from individual root elongation data, C2N+) b d 1 Initial slope for potential elongation function (estimated from individual root elongation data, C2N+) dir 3 mm Constant distance between two adjacent ramifications (Estimated from minimum distance data, C2N+) a b h p, min h m, min h p, max h m, max Parameters of the relationship between the diameters of the lateral root and the root segment bearing it (estimated from individual root diameter data, C2N+) Minimum and maximum variations of primordium or meristem diameter (estimated from global calibration on data C2N+) ð3þ ð5þ

5 Modelling the root system of Arabidopsis thaliana 2161 Branching. Root branching has been formulated as a two-step process entailing initiation and emergence stages (Casimiro et al., 2003). A new lateral primordium appears when a new segment is formed by root elongation. Arabidopsis thaliana has an acropetal pattern and a relatively simple vascular system with only two xylem poles and two initiation files (Dubrovsky et al., 2000, 2006; Turner and Sieburth, 2002). Therefore, it was hypothesized that formation of a new root segment exclusively depended on a constant distance between two adjacent ramifications estimated from the minimum distance observed to be dirz3 mm (data not shown). This value was similar to the estimation of Dubrovsky et al. (2006). Thus the number of segments that are produced (n) was calculated as follows: Fig. 2. Relationship between elongation (E m ) and apical diameter (U m ) of meristems obtained from experimental data on A. thaliana plants grown in rhizotrons for up to 25 d (vegetative growth period) under the C2N+ treatment (PARZ300 lmol m 2 s 1,NO 3 concentrationz10 mm). The solid line corresponds to the envelope curve (if U m >U min then E m,pot Za3{1 exp[ b*(u m U min )/a]} else E m,pot Z0), which represents the potential elongation for a given apical diameter. This curve was used in the model to estimate the potential elongation of each meristem. Fig. 3. Relationship between emerged lateral root diameter and bearing root diameters. Experimental data were obtained from A. thaliana plants grown in rhizotrons for up to 25 d (vegetative growth period) under the C2N+ treatment (PARZ300 lmol m 2 s 1,NO 3 concentrationz10 mm). The solid line corresponds to the power function (U lr Za3U b rs ) used in the model to calculate the apical diameter of the emerged root. Fig. 4. Shoot and root dry weights at 20 (C2), 22 (C1 and C3), and 25 (C1, C2, and C3) days after sowing (DAS). Plants were grown in rhizotrons under short-day conditions and were submitted to two levels of N supply [2 mm (N ) or 10 mm (N+) NO 3 ] and to three levels of PAR [250 lmol m 2 s 1 (C1), 300 lmol m 2 s 1 (C2), or 450 lmol m 2 s 1 (C3)]. See Table 2 for statistics.

6 2162 Brun et al. nze m =dir Apical diameter of emerged root. Lecompte et al. (2005) have established a power function between the diameter of the bearing root segment and the diameters of its laterals in a wide range of species. Two periods of meristem development were distinguished: primordium (p) before emergence and true meristem (m) after. The primordium diameter (U p ) increases until it reaches the threshold diameter U lr as described in Equation 7, then the primordium becomes a meristem with a diameter denoted by U m. It was hypothesized and verified that the relationship between the Table 2. Statistics for shoot (SDW), root (RDW), and total (TDW) dry weights at 25 d after sowing An ANOVA procedure was carried out with the model YZC+N+C3N, with the aim of distinguishing a significant effect of C treatments, N treatments, and a potential interaction between C and N treatments on shoot, root, and total dry weight at 25 d after sowing. The corresponding data are presented in Fig 4. ANOVA Y[C+N+C3N C effect N effect N3C effect SDW NS *** NS RDW ** ** NS TDW ** ** NS **P <0.01; ***P <0.001; NS, non-significant. ð6þ threshold diameter U lr (mm) and the diameter of the segment bearing this root U rs (mm) followed a power function (Fig. 3): U lr Za3Urs b ð7þ Meristem diameter. C availability has been shown to affect apical diameter (Thaler and Pagès, 1996; Muller et al., 1998; Willaume and Pagès, 2006). It was considered that the apical diameter U varied according to a coefficient k p or k m, for primordium or meristem, respectively, when its diameter is >U min (see Equation 4). When the apical diameter is <U min, it was considered that the root stops elongating. Similar functions and parameters have been used for apical diameter in other root models (Drouet and Pagès, 2003): U p ðtþ1þzð1þk p Þ3U p ðtþ ð8aþ U m ðtþ1þzð1þk m Þ3U m ðtþ ð8bþ The relative variation of primordium (k p ) or meristem (k m ) diameter, respectively, varies linearly with C availability between a minimum (h p, min or h m, min ) which corresponds to a decrease and a maximum (h p, max or h m, max ). k p Zh p; min þa3 h p; max h p; min Þ k m Zh m; min þa3 h m; max h m; min Þ ð9aþ ð9bþ Model implementation, initial conditions, and discrepancies between model and data The object-oriented model was implemented in Python programming language ( with a database Fig. 5. Comparison of observed and simulated root system architecture for C2N+ (upper panel) and C2N (lower panel) treatments at the end of the experiment (25 DAS). (A) Pictures of root systems at 25 DAS. Arabidopsis thaliana plants were grown in rhizotrons under C2N+ or C2N treatments [PARZ300 lmol m 2 s 1,NO 3 concentrationz10 mm (N+) or 2 mm (N )]. The contrast of the images was maximized to improve root visualization. (B) Drawings of root system architecture at 25 DAS, carried out by tracing daily root elongation on a transparent plastic sheet with coloured pens. Colours correspond to the daily elongations recorded. (C) Simulations of root systems at 25 DAS for C2N+ and C2N treatments.

7 Modelling the root system of Arabidopsis thaliana 2163 Fig. 6. Dynamics of total root length in all C3N treatments. Filled diamonds represent experimental points and solid lines correspond to model simulations. TRL sim Za TRL obs +b is the equation of the regression line, RMSE, root mean square error. Arabidopsis thaliana plants were grown in rhizotrons under short-day conditions up to 25 DAS and were submitted to two levels of N supply [2 mm (N ) or 10 mm (N+) NO 3 ] and to three levels of PAR [250 lmol m 2 s 1 (C1), 300 lmol m 2 s 1 (C2), or 450 lmol m 2 s 1 (C3)]. interface (MySQL, to use the experimental data directly, and an R language (R Development Core Team, 2009) interface to compute the graphical and statistical outputs. The model structure was encoded similarly to that in Drouet and Pagès (2003). In order to compare simulations with experimental observations, it was decided to begin simulation at 7 DAS with the observed root system characteristics; that is, a 1.3 cm long taproot with an apical diameter of 0.10 mm and laterals.

8 2164 Brun et al. To evaluate the prediction quality of the model, predicted values were compared with observations using a linear model, Y mod Za- 3Y obs +b. The slope (a) and the intercept (b) were compared with 1 and 0, respectively, by performing a Student s test. The R 2 of the linear model represents the precision of the predictions. In addition, root mean square error (RMSE) was calculated for each treatment. Results Model parameters were estimated (see below) using only the data recorded for the C2N+ treatment. This treatment was chosen because it represented the medium C regime and no limitation in N nutrition. Then, the model was tested under the other C and N conditions using the same parameter values except for dry biomass fluxes supplied to roots, considered as an input variable. Root and shoot dry weights At 20 for C2, 22 for C1 and C3, or 25 DAS, whatever the C level, N limitation strongly affected SDW and slightly affected RDW (Fig. 4). The difference between N treatments increased with C levels. C effects were significant on RDW and TDW (total dry weight), and not on SDW. Conversely, N effects were highly significant on SDW and only just significant on RDW and TDW (Table 2). The interaction between N and C was not significant for the three variables. However, as expected, a contrasting data set showing large variations in C3N supply and demand was generated. Parameterization Parameters of Equation 4 were fitted to the envelope curve (Fig. 2) and were estimated as mm, 28.5 mm d 1,and d 1 for U min, a, andb, respectively. q of Equation 2 was estimated as mg DW cm 3. This value was similar to those used by Drouet and Pagès (2003) on maize. a and b of Equation 7 were estimated as and 0.761, respectively (Fig. 3). In the present experiments, the maximum relative diameter variation per day was measured for enlargement or reduction. Variation of taproot apical diameter from 5% to 10% in 1 d was observed, and these extreme values were considered for parameterization. h p, min and h p, max in Equation 9a were estimated as 0.06 and 0.15, respectively. h m, min and h m, max in Equation 9b were estimated as and 0.10, respectively. Parameter values and estimation methods are summarized in Table 1. The model simulated root system architectures close to that observed, as shown in Fig. 5 for C2N and C2N+ treatments. It was notably able to reproduce the higher root branching and lateral root length observed with N+ treatment in comparison with N treatment. Validation of the model under various C and N conditions Observed and simulated total root length (TRL, cm plant 1 ), lateral root number per plant (LRN), and specific root length (SRL, cm mg 1 ) were compared. These three global variables summarize the main architectural traits (growth, development, and distribution of dry weight). TRL was well predicted among treatments (Fig. 6) since whatever the treatment, R 2 was never lower than 0.94 and RMSEs were low. Figure 7A, which shows the comparison between observed and simulated TRL at the different sampling dates, indicates that the global quality of the model was good (slopez1.04, not significantly different from 1, R 2 Z0.94). However, when N regimes were analysed separately, it was observed that the model tended to underestimate TRL slightly in low N supply conditions (slopez0.94, significantly different from 1, R 2 Z0.96) and to overestimate TRL slightly in the case of high N regimes (slope Z 1.11, significantly different from 1, R 2 Z0.95). The same trend was observed for LRN (Fig. 8). The model tended to overestimate the number of lateral roots (Fig. 7B) (slopez1.14, significantly different from 1), Fig. 7. Comparison between observed and simulated data for (A) total root length and (B) lateral root number. Points correspond to experimental data from plants grown in rhizotrons under short-day conditions up to 25 DAS and were submitted to two levels of N supply [2 mm (N ) or 10 mm (N+) NO 3 ] and to three levels of PAR [250 lmol m 2 s 1 (C1), 300 lmol m 2 s 1 (C2), or 450 lmol m 2 s 1 (C3)]. Solid lines represent the linear regressions carried out between simulated and observed data. Dotted lines represent the equation xzy corresponding to a perfect match between simulated and observed data.

9 Modelling the root system of Arabidopsis thaliana 2165 Fig. 8. Dynamics of lateral root number in all C3N tretreatments. Filled diamonds represent experimental points and solid lines correspond to model simulations. LRN sim Za LRN obs +b is the equation of the regression line, RMSE, root mean square error. Arabidopsis thaliana plants were grown in rhizotrons under short-day conditions up to 25 DAS and were submitted to two levels of N supply [2 mm (N ) or 10 mm (N+) NO 3 ] and to three levels of PAR [250 lmol m 2 s 1 (C1), 300 lmol m 2 s 1 (C2), or 450 lmol m 2 s 1 (C3)]. especially in the N+ regime [slopez1.22, significantly different from 1 (R 2 Z0.93) versus 1.02, not significantly different from 1, for N (R 2 Z0.92)]. Figure 9 shows that SRL decreased with time for observed and simulated data. SRL was higher in the N treatment compared with the N+ treatment in the three C

10 2166 Brun et al. regimes. In all C treatments, SRL was well simulated by the model only in the N+ condition, and better at 20 DAS (C2) or 22 DAS (C1 and C3) than at 25 DAS. SRL was greatly underestimated in the N condition. It was concluded that TRL as well as LRN variations were mainly driven by C fluxes and that an additional specific N effect may have to be considered in low N supply conditions, via SRL. Discussion A modelling approach was used to evaluate to what extent the effects of low N availability could be simulated as a consequence of induced effects of N to C balance at the whole-plant scale. As the main result, it was shown that C flux modifications when N was limited explained the main part of root system architecture adaptations. Observations of root system under C3N conditions and a C partitioning modelling approach were chosen to study C3N interaction effects on root system architecture The model was constructed on the same basis and with the same rules as other C-based models of root system architecture (Thaler and Pagès, 1998; Drouet and Pagès, 2003). An original feature of this modelling approach was to take into account a few processes of root growth and development that only depend on C availability and to consider that they were able to simulate C but also N effects. To limit the number of parameters, some simplifications were added, such as no root mortality and a constant potential branching density. Secondary radial growth wasnot taken into account because it was not considered as an important C sink. Nevertheless, some radial secondary growth of roots has been observed under the conditions used (data not shown). Another important choice was the absence of differences between root types for the parameterization. In most models, roots have different parameters depending on their types (see, for example, Drouet and Pagès. 2003). Thus, only 12 parameters were sufficient to characterize all the relationships used in the model. In comparison, 20 are listed in Drouet and Pagès (2003) for the root system and 25 in the generic model Root typ that summarized all root morphological features in one unique model (Pagès et al., 2004). The many simplifications chosen here led to a simple and specific model for A. thaliana covering the whole period of vegetative growth. Consequently, it is not claimed that a totally new and robust model has been constructed, but rather a tool forged for the evaluation of to what extent changes of C flux are sufficient Fig. 9. Dynamics of specific root length (cm mg 1 )ofa. thaliana plants grown in rhizotrons for up to 25 DAS under C1, C2, or C3 treatment (upper, middle, and lower panel, respectively). Open and filled triangles correspond to experimental points for N and N+ treatments, respectively. Solid and dotted lines represent model simulations for N+ and N treatments, respectively. Experimental treatments crossed two levels of N supply [2 mm (N ) or 10 mm (N+) NO 3 ] and three levels of PAR [250 lmol m 2 s 1 (C1), 300 lmol m 2 s 1 (C2), or 450 lmol m 2 s 1 (C3)].

11 Modelling the root system of Arabidopsis thaliana 2167 to explain the main adaptation of the root system for different C and N availabilities. The C supply/demand ratio was used as a coefficient of satisfaction of the demand. Although this formalism remains simple and does not purport to reflect the real functioning of the plant, it was considered as a quantitative indicator of the endogenous environment for C, as defined by Pagès (2000). In the present case, C supply was defined as the observed flux of accumulated RDW, which was easily calculated from the data as an entry variable and constituted an original approach. This choice was driven by the objective to study assimilate allocation amongst the root system architecture, without considering assimilate sharing between shoot and root parts of the plant, this last point still being subject to discussion (Farrar and Jones, 2000). Concerning the demand, it was calculated for each root and summed for the whole root system. The demand of each root was defined as the potential growth when C supply is not limited, which is one point of view among others to define demand (Farrar, 1993). The experimental design has only permitted two harvests for SDW, RDW, and TDW measurements late in the cycle, which could explain mismatches between simulated and observed results at the beginning of the simulation. The modelling approach showed the importance of changes in C supply induced by N limitation for root system architecture and allowed a potential specific N effect on root elongation process to be highlighted The model gave good predictions of TRL and LRN in all conditions, even if outputs underestimated TRL in N treatments and overestimated TRL and LRN in N+ treatments, when all data were taken into account. In fact, the model underestimated TRL and LRN near the middle of the experiment. The model showed the temporal decrease of SRL in accordance with the observations, albeit that they were done at the end of the experiments. During vegetative growth, the root system grew and meristem sizes increased. Consequently, with the same amount of allocated biomass, each meristem produced a relatively shorter root length; but, as a feedback, diameter will decrease (so this effect on SRL might be reduced). This observation is the outcome of both these opposite effects. However, this variable was well predicted only for the N+ regime and was greatly underestimated for N treatment. This underestimation of SRL in the N regime compared with simulation could explain the slightly underestimated simulated values observed for TLR and LRN in N regimes. Thus, whether or not C flux modifications explained the major part of root system adaptation, they were not sufficient to simulate some changes fully, such as SRL. It was therefore shown that root elongation processes might be affected by N availability, as the root presented a higher elongation rate for a given apex diameter under low N compared with high N nutrition. Cellular processes involved in that adaptation need to be studied further. An increased production of cells could be involved, as suggested by van der Weele et al. (2000) in the case of water deficiency. Moreover, in adding this specific N effect on potential root elongation to the model, it should be possible to improve the simulations in low N nutrition treatments, especially for SRL, which is an important adaptation process of the root system under low N conditions. Even if the molecular bases of local N signalling are now quite well established, the integration of both the local N effect and the long-range C flux effect is still misunderstood. Such a modelling approach could help to clarify the interactions between these two regulation pathways. Acknowledgements We thank Julie Rodrigues and Olivier Maury for help in the experiments and data analysis. Seeds were kindly provided by the NAP of INRA Versailles. The English text was improved by Suzette Tanis-Plant. This work was supported by grants from the Action Concertée Incitative Biologie du Développement et Physiologie Intégrative programme (INRA). References Abramoff M, Magelhaes P, Ram S Image processing with imagej. Biophotonics International 11, Anandacoomaraswamy A, De Costa W, Tennakoon PLK, Van Der Werf A The physiological basis of increased biomass partitioning to roots upon nitrogen deprivation in young clonal tea (Camellia sinensis (l.) o. kuntz). Plant and Soil 238, 1 9. Barlow P, Pilet P The effect of abscisic acid on cell growth, cell division and DNA synthesis in the maize root meristem. Physiologia Plantarum 62, Beemster GTS, Baskin TI Analysis of cell division and elongation underlying the developmental acceleration of root growth in Arabidopsis thaliana. Plant Physiology 116, Beemster G, DeVusser K, DeTavernier E, DeBock K, Inze D Variation in growth rate between Arabidopsis ecotypes is correlated with cell division and a-type cyclin-dependent kinase activity. Plant Physiology 129, Bidel LPR, Pagès L, Riviere LM, Pelloux G, Lorendeau JY MassFlowDyn I: a carbon transport and partitioning model for root system architecture. Annals of Botany 85, Bingham I, Stevenson E Control of root growth: effects of carbohydrates on the extension, branching and rate of respiration of different fractions of wheat roots. Physiologia Plantarum 88, Cahn M, Zobel R, Bouldin D Relationship between root elongation rate and diameter and duration of growth of lateral roots of maize. Plant and Soil 119, Casimiro I, Beeckman T, Graham N, Bhalerao R, Zhang HM, Casero P, Sandberg G, Bennett MJ Dissecting Arabidopsis lateral root development. Trends in Plant Science 8, Coutts M Developmental processes in tree root systems. Canadian Journal of Forestry Research 17, Devienne-Barret F, Richard-Molard C, Chelle M, Maury O, Ney B Ara-rhizotron: an effective culture system to study

12 2168 Brun et al. simultaneously root and shoot development of Arabidopsis thaliana. Plant and Soil 280, Diggle A Rootmap: a model in three-dimensional coordinates of the growth and structure of fibrous root systems. Plant and Soil 105, Doussan C, Vercambre G, PagèsL Modelling of the hydraulic architecture of root systems: an integrated approach to water absorption distribution of axial and radial conductances in maize. Annals of Botany 81, Drew M, Saker L Nutrient supply and the growth of the seminal root system in barley. II. Localized, compensatory increases in lateral root growth and rates of nitrate uptake when nitrate supply is restricted to only part of the root system. Journal of Experimental Botany 26, Drouet JL, PagèsL Graal: a model of growth, architecture and carbon allocation during the vegetative phase of the whole maize plant model description and parameterisation. Ecological Modelling 165, Dubrovsky JG, Doerner PW, Colon-Carmona A, Rost TL Pericycle cell proliferation and lateral root initiation in Arabidopsis. Plant Physiology 124, Dubrovsky JG, Gambetta GA, Hernandez-Barrera A, Shishkova S, Gonzalez I Lateral root initiation in Arabidopsis: developmental window, spatial patterning, density and predictability. Annals of Botany 97, Evans J Nitrogen and photosynthesis in the flag leaf of wheat (Triticum aestivum L.). Plant Physiology 72, Fahl J, Carelli M, Vega J, Magalhaes A Nitrogen and irradiance levels affecting net photosynthesis and growth of young coffee plants (Coffea arabica L.). Journal of Horticultural Science 69, Farrar JF Sink strength: what is it and how do we measure it? Introduction. Plant, Cell and Environment 16, Farrar JF, Jones DL The control of carbon acquisition by roots. New Phytologist 147, Fitter A An architectural approach to the comparative ecology of plant root systems. New Phytologist 106(Suppl.), Fitter A, Williamson L, Linkohr B, Leyser O Root system architecture determines fitness in an Arabidopsis mutant in competition for immobile phosphate ions but not for nitrate ions. Proceedings of the Royal Society B: Biological Sciences 269, Forde BG. 2002a. Local and long-range signaling pathways regulating plant responses to nitrate. Annual Review of Plant Biology 53, Forde BG. 2002b. The role of long-distance signalling in plant responses to nitrate and other nutrients. Journal of Experimental Botany 53, Freixes S, Thibaud MC, Tardieu F, Muller B Root elongation and branching is related to local hexose concentration in Arabidopsis thaliana seedlings. Plant, Cell and Environment 25, Grindlay D Towards an explanation of crop N demand based on the optimization of leaf N per unit leaf area. Journal of Agricultural Science 128, Hackett C A growth analysis of the young sorghum root system. Australian Journal of Biological Science 26, Hodge A Tansley review The plastic plant: root responses to heterogeneous supplies of nutrients. New Phytologist 162, Lecompte F, Pagès L, Ozier-Lafontaine H Patterns of variability in the diameter of lateral roots in the banana root system. New Phytologist 167, Lemaire G, Millard P An ecophysiological approach to modelling resource fluxes in competing plants. Journal of Experimental Botany 50, Linkohr BI, Williamson LC, Fitter AH, Leyser HM Nitrate and phosphate availability and distribution have different effects on root system architecture of Arabidopsis. The Plant Journal 29, Lynch JP, Nielsen KL, Davis RD, Jablokow AG Simroot: modelling and visualization of root systems. Plant and Soil 188, Malamy JE Intrinsic and environmental response pathways that regulate root system architecture. Plant, Cell and Environment 28, Malamy JE, Ryan KS Environmental regulation of lateral root initiation in Arabidopsis. Plant Physiology 127, Minchin P, Thorpe M, Farrar J A simple mechanistic model of phloem transport which explains sink priority. Journal of Experimental Botany 44, Muller B, Stosser M, Tardieu F Spatial distributions of tissue expansion and cell division rates are related to irradiance and to sugar content in the growing zone of maize roots. Plant, Cell and Environment 21, Pagès L Growth-patterns of the lateral roots of young oak (Quercus robur) tree seedlings relationship with apical diameter. New Phytologist 130, Pagès L How to include organ interactions in models of the root system architecture? The concept of endogenous environment. Annals of Forest Science 57, Pagès L, Aries F Sarah: modèle de simulation de la croissance, du développement et de l architecture des systèmes racinaires. Agronomie 8, 898. Pagès L, Vercambre G, Drouet J-L, Lecompte F, Collet C, Le Bot J Root typ: a generic model to depict and analyse the root system architecture. Plant and Soil 258, R Development Core Team A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. URL: Remans T, Nacry P, Pervent M, Girin T, Tillard P, Lepetit M, Gojon A A central role for the nitrate transporter nrt2.1 in the integrated morphological and physiological responses of the root system to nitrogen limitation in Arabidopsis. Plant Physiology 140, Robinson D Tansley review no.73. The response of plants to non-uniform supplies of nutrients. New Phytologist 127, Scheible WR, Gonzalez-Fontes A, Lauerer M, Muller-Rober B, Caboche M, Stitt M Nitrate acts as a signal to induce organic acid metabolism and repress starch metabolism in tobacco. The Plant Cell 9,

13 Modelling the root system of Arabidopsis thaliana 2169 Sinclair T, Horie T Leaf nitrogen, photosynthesis, and crop radiation use efficiency: a review. Crop Science 29, Somma F, Hopmans J, Clausnitzer V Transient threedimensional modeling of soil water and solute transport with simultaneous root growth, root water and nutrient uptake. Plant and Soil 202, Thaler P, PagèsL Root apical diameter and root elongation rate of rubber seedlings (Hevea brasiliensis) show parallel responses to photoassimilate availability. Physiologia Plantarum 97, Thaler P, Pagès L Modelling the influence of assimilate availability on root growth and architecture. Plant and Soil 201, Turner S, Sieburth LE Vascular patterning. In: Somerville CR, Meyerowitz EM, eds. The Arabidopsis Book. Rockville, MD: American Society of Plant Biologists, van der Weele CM, Spollen WG, Sharp RE, Baskin TI Growth of Arabidopsis thaliana seedlings under water deficit studied by control of water potential in nutrient-agar media. Journal of Experimental Botany 51, Wilcox H Growth studies of the root of incense cedar, Librocedrus decurrens II. Morphological features of the growth system and root behaviour. American Journal of Botany 49, Willaume M, PagèsL How periodic growth pattern and source/sink relations affect root growth in oak tree seedlings. Journal of Experimental Botany 57, Zhang H, Jennings A, Barlow PW, Forde BG Dual pathways for regulation of root branching by nitrate. Proceedings of the National Academy of Sciences, USA 96,