CN-Wheat, a functional–structural model of carbon and nitrogen metabolism in wheat culms after anthesis. II. Model evaluation

Abstract

Background and Aims Simulating resource allocation in crops requires an integrated view of plant functioning and the formalization of interactions between carbon (C) and nitrogen (N) metabolisms. This study evaluates the functional–structural model CN-Wheat developed for winter wheat after anthesis.

Methods In CN-Wheat the acquisition and allocation of resources between photosynthetic organs, roots and grains are emergent properties of sink and source activities and transfers of mobile metabolites. CN-Wheat was calibrated for field plants under three N fertilizations at anthesis. Model parameters were taken from the literature or calibrated on the experimental data.

Key Results The model was able to predict the temporal variations and the distribution of resources in the culm. Thus, CN-Wheat accurately predicted the post-anthesis kinetics of dry masses and N content of photosynthetic organs and grains in response to N fertilization. In our simulations, when soil nitrates were non-limiting, N in grains was ultimately determined by availability of C for root activity. Dry matter accumulation in grains was mostly affected by photosynthetic organ lifespan, which was regulated by protein turnover and C-regulated root activity.

Conclusions The present study illustrates that the hypotheses implemented in the model were able to predict realistic dynamics and spatial patterns of C and N. CN-Wheat provided insights into the interplay of C and N metabolism and how the depletion of mobile metabolites due to grain filling ultimately results in the cessation of resource capture. This enabled us to identify processes that limit grain mass and protein content and are potential targets for plant breeding.

INTRODUCTION

For monocarpic species, such as winter wheat (Triticum aestivum), the post-anthesis period is a crucial stage when complex interactions occur among vegetative organs and the growing grains. Aerial vegetative organs are the main source of carbon (C) due to their photosynthetic activity, in particular laminae and chaffs (Araus et al., 1993), and also through the constitution of reserve pools, e.g. fructans accumulated in stems (Schnyder, 1993). Besides, phloem C is necessary to maintain root activity, in particular regarding nitrate uptake (Simpson et al., 1983; Thornley and Cannell, 2000). Post-anthesis nitrate uptake can contribute 5–40 % of final grain nitrogen (N) according to environmental conditions and genotypes (Kichey et al., 2007; Bogard et al., 2010). Nevertheless, the mechanisms involved in the decrease of uptake capacity after anthesis (Oscarson et al., 1995) and the signal of N satiety (Taulemesse et al., 2015) still constitute areas of current research. Whole-plant behaviour results from trade-offs in the allocation of resources between roots, leaves, stems and grains. These trade-offs raise some crucial issues for plant scientists. How is the allocation of resources among shoot and roots regulated? This plastic trait is involved in the ability of plants to compete for above- and below-ground resources. What determines the balance between the maintenance of vegetative activity (photosynthesis and N uptake) and the growth of reproductive organs (grain filling)? On one hand, the availability of C and N for grain growth determines their biomass (crop production) and protein content. On the other hand, C is also needed to maintain root activity, which will affect the amount of N in photosynthetic organs, thus determining their activity and thereby sugar synthesis. This trade-off is under environmental control but also depends on the genotype, as illustrated by the stay-green behaviour of some crop cultivars. These are characterized by their ability to maintain significant areas of vegetative tissues that are still photosynthetic at maturity (Benbella and Paulsen, 1998; Borrell et al., 2001), but the underlying mechanisms remain unclear.

The trade-offs cited above result from the balance among several physiological processes, and the genetic determinants regulating these processes constitute crucial targets for agronomists and breeders. The diversity of the underlying processes and their genotypic and environmental regulation make it difficult to associate genetic parameters with specific plant traits. It therefore appears that an integrated view of plant functioning is necessary to unravel the partitioning rules of resources, their environmental variability and their impact on measurable traits (White et al., 2015). Functional–structural plant models that account for interactions between plant structure, functioning and environment (Godin and Sinoquet, 2005; DeJong et al., 2011) therefore represent a candidate framework to address these questions.

In a companion paper, we described CN-Wheat, a comprehensive process-based model accounting for C and N metabolism within wheat plants after anthesis. CN-Wheat is defined at culm scale and is decomposed into botanical modules. These modules include structural, storage and mobile materials and are connected to a common pool representing the phloem, which allows the circulation of mobile metabolites through the culm. The main physiological processes accounted for are related to (1) photosynthesis and transpiration, (2) nitrate uptake and their distribution in photosynthetic organs, (3) respiration, (4) C and N exudation by roots, (5) synthesis of storage and mobile metabolites, (6) turnover of proteins in photosynthetic organs, regulated by (7) an exploratory sub-model of cytokinins, and finally (8) tissue death and its consequences for resource capture and turnover. The major feature of the model is that physiological processes that drive C and N fluxes are regulated by local concentrations of metabolites. This allows the expression of complex feedbacks between C and N metabolisms and interactions among organs without using predefined allocation ratios or teleonomic rules.

The aim of this study was to evaluate CN-Wheat for its capacity to simulate the dynamics of C and N acquisition and distribution among organs, grain N and dry mass as well as tissue death. CN-Wheat predictions were evaluated against a field experiment conducted on wheat under three N fertilizations applied at anthesis. Some information was, however, missing from the dataset used (e.g. root biomass, soil N at anthesis, photosynthesis measurements), which led us to make some assumptions and to adapt the parameterization. Consequently, some aspects of the model were evaluated for their ability to reproduce realistic dynamics and spatial patterns of resources rather than for predicting their absolute values. The model was also used to understand how the trade-offs between the physiological processes have led to the observed partitioning of resources.

MATERIALS AND METHODS

Experimental datasets

CN-Wheat was calibrated on an experiment conducted on winter wheat at Clermont-Ferrand (France) in 1994 (Triboï et al., 2003; Martre et al., 2003). We used the results obtained for cultivar ‘Thésée’ sown at 300 seeds m⁻² with high N fertilization before anthesis and which received N at 0 (H0), 3 (H3) or 15 g m⁻² (H15) in the form of ammonium nitrate at anthesis. For each treatment, N and dry masses of each lamina, stem (sheaths, internodes and peduncle pooled), chaff and grains were measured as well as lamina green areas. Total areas and dry and N masses of individual sheaths, internodes and peduncles were obtained by using the method and complementary experiment described in Bertheloot et al. (2011b).

Environmental conditions and light interception

The CN-Wheat model was run with an hourly time step requiring hourly meteorological data for incident photosynthetically active radiation (PAR), air temperature, humidity, wind and CO₂. Only daily averaged meteorological data are available for Clermont-Ferrand in 1994, whereas hourly meteorological data have been available since 2005. For each simulated day of the year 1994 we selected in the 2005–14 database the same calendar day having the smallest differences in mean daily temperature and incident PAR, and used these hourly values in the simulation (Supplementary Data SI 1).

Light interception by photosynthetic organs was estimated by multiplying a relative PAR interception set for each organ (Bertheloot et al. 2011b), by the hourly incident PAR.

Parameter estimation

CN-Wheat includes ∼60 parameters and their estimation constituted a complex issue. We did not use numerical solvers to fit model parameters to experimental measurements, and therefore the set of parameters presented in this paper may not be optimum. Nevertheless, the purpose of this study was to evaluate whether a single set of parameters was able to account for the observed plant behaviour among contrasted N treatments. Except for the threshold of tissue death ($d_{tp,\hspace{0.17em}i}$), we assumed similar parameters for all photosynthetic organs, whatever their type and position along the culm. Three complementary methods, denoted ‘a’, ‘b’ and ‘c’, were used to estimate model parameters (Table 1): (a) the parameter was taken from the literature; (b) the parameter was estimated from experimental data in the literature (which made it possible to formalize a regulation rule and/or which provided usual metabolite concentrations and fluxes among organs); and (c) the parameter was calibrated on the experimental N treatments described above. Finally, some parameters were derived from the literature but slightly adapted to the experimental data used to calibrate CN-Wheat [denoted (b) and (c) in Table 1].

Table 1.

Description of model parameters, values and units. Methods for parameter estimation were as follows: (a) taken from literature; (b) recalculated, adapted or calibrated from literature; (c) calibrated on experimental data

Parameter	Description	Value	Unit	References
Root uptake of nitrates and N mineralization
$K_{roots}^{N,nitHATS}$	Affinity coefficient of nitrate uptake for HATS	Table 2	µmol N g−1	(b) Siddiqi et al. (1989, 1990)
${Vmax}_{roots}^{N,nitHATS}$	Maximum rate of nitrate uptake for HATS	Table 2	µmol N g−1 s−1	(b) Siddiqi et al. (1989, 1990)
$K_{roots}^{N,nitLATS}$	Rate of nitrate uptake for LATS	Table 2	m3 g−1 s−1	(b) Siddiqi et al. (1989, 1990)
$K_{roots}^{C,CHO}$	Regulation of nitrate uptake by carbohydrate concentration in roots	4000	µmol C g−1	(b) Siddiqi et al. (1989, 1990)
$r_{influx:netuptake}$	Ratio of nitrate influx to net uptake	0·6	Dimensionless	(b) Devienne et al. (1994)
${Miner}_{soil}^{N,nit}\left(t\right)$	Rate of N mineralization in soil	2·05 × 10−5	µmol N m−3 s−1	P. Martre (INRA, France)
Syntheses
$K_{roots}^{{S\hspace{0.5em}N,org}_{CHO\hspace{0.5em}}}$	Affinity coefficient for organic N synthesis according to root carbohydrates	350	µmol C g−1	(c)
$K_{roots}^{S\hspace{0.5em}{N,org}_{nit}}$	Affinity coefficient for organic N synthesis according to root nitrates	3	µmol N g−1	(c)
${Smax}_{roots}^{N,org}$	Maximum rate of organic N synthesis in roots	0·001	µmol N g−1 s−1	(c)
$K_{roots}^{CHO,cytok}$	Affinity coefficient for cytokinin synthesis according to root carbohydrates	1250	µmol C g−1	(c)
$n_{CHO}$	Parameter for the regulation of cytokinin synthesis by carbohydrates in roots	10	Dimensionless	(c)
$K_{roots}^{nit,cytok}$	Affinity coefficient for cytokinin synthesis according to root nitrates	200	µmol N g−1	(c)
$n_{nit}$	Parameter for the regulation of cytokinin synthesis by nitrates in roots	0·7	Dimensionless	(c)
${Smax}_{roots}^{cytok}$	Maximum rate of cytokinin synthesis in roots	4·5 × 10−4	AU g−1 s−1	(c)
$K_{tp,i}^{C,star}$	Affinity coefficient for starch synthesis in (tp,i)	20	µmol C g−1	(b, c) Trevanion (2002)
${Smax}_{tp,i}^{C,star}$	Maximum rate of starch synthesis in (tp,i)	2	µmol C g−1 s−1	(b, c) Trevanion (2002)
${Ks}_{tp,i}^{C,fruc}$	Affinity coefficient for fructan synthesis in (tp,i)	5000	µmol C g−1	(b, c) Bancal et al. (2012)
${Smax\_pot}_{tp,i}^{C,fruc}$	Potential maximum rate of fructan synthesis in (tp,i)	0·015	µmol C g−1 s−1	(b, c) Bancal et al. (2012)
${Kl}_{tp,i}^{C,fruc}$	Affinity coefficient for fructan synthesis inhibition by sucrose loading in (tp,i)	0·001	µmol C g−1	(c)
$n_{fruc}$	Parameter for inhibition of fructan synthesis by sucrose loading	3	Dimensionless	(c)
$K_{tp,i}^{C,suc}$	Affinity coefficient for sucrose synthesis in (tp,i)	0·66	µmol C g−1	(b, c) Trevanion (2002)
${Smax}_{tp,i}^{C,suc}$	Maximum rate of sucrose synthesis in (tp,i)	1	µmol C g−1 s−1	(b, c) Trevanion (2002)
$K_{tp,i}^{{S\hspace{0.5em}N,AA}_{triosesP\hspace{0.5em}}}$	Affinity coefficient for amino acid synthesis according to photosynthetic triose phosphates in (tp,i)	0·2	µmol C g−1	(c)
$K_{tp,i}^{S\hspace{0.5em}{N,AA}_{nit}}$	Affinity coefficient for amino acid synthesis according to photosynthetic organ nitrates in (tp,i)	3	µmol N g−1	(c)
${Smax}_{tp,i}^{N,AA}$	Maximum rate of amino acid synthesis in (tp,i)	1	µmol N g−1 s−1	(c)
$K_{\hspace{0.5em}tp,i}^{N,prot}$	Affinity coefficient for protein synthesis in (tp,i)	100	µmol N g−1	(b, c) Bertheloot et al. (2011b)
${Smax}_{tp,i}^{N,prot}$	Maximum rate of protein synthesis in (tp,i)	0·0015	µmol N g−1 s−1	(b, c) Bertheloot et al. (2011b)
Degradations
${\delta }_{tp,i}^{C,star}$	Relative rate of starch degradation in (tp,i)	0·0001	s−1	(a) Daudet et al. (2002)
${Kd}_{tp,i}^{C,fruc}$	Affinity coefficient for fructan degradation in (tp,i)	100	µmol C g−1	(b, c) Bancal & Soltani (2002)
${Dmax}_{tp,i}^{C,fruc}$	Maximum rate of fructan degradation in (tp,i )	0·035	µmol C g−1 s−1	(b, c) Bancal & Soltani (2002)
${\delta max}_{tp,i}^{N,prot}$	Maximum rate of protein degradation in (tp,i)	2·5 × 10−6	s−1	(b, c) Bertheloot et al. (2011b)
${Kd}_{tp,i}^{N,prot}$	Affinity coefficient for inhibition of protein degradation by cytokinins in (tp,i)	50	AU cytokinins g−1	(c)
$n_{cytok}$	Parameter for inhibition of protein degradation by cytokinins	2·1	Dimensionless	(c)
${\delta }_{tp,i}^{cytok}$	Rate of cytokinin degradation in (tp,i)	$3\times {10}^{-0}$	s−1	(c)
Inter-organ fluxes
$K_{roots}^{U\hspace{0.5em}C,suc}$	Affinity coefficient for sucrose unloading to roots	1000	µmol C g−1	(b, c) Simpson et al. (1983)
${Umax}_{phloem\to roots}^{C,suc}$	Maximum rate of sucrose unloading to roots	0·03	µmol C g−1 s−1	(b, c) Simpson et al. (1983)
$K_{roots}^{N,nitexport}$	Relative rate of nitrate export from roots	1$\times \hspace{0.5em}{10}^{-0}$	s−1	(b, c) Devienne et al. (1994)
$K_{roots}^{N,AAexport}$	Relative rate of amino acids export from roots	3$\hspace{0.5em}\times {10}^{-0}$	s−1	(c)
$K_{roots}^{cytokexport}$	Relative rate of cytokinin export from roots	2$\hspace{0.5em}\times {10}^{-0}$	s−1	(c)
$K_{roots}^{Tr}$	Parameter for the regulation of root exportations by culm transpiration	1	mmol water m−2 s−1	(c)
$r_{roots}^{C,exud}$	Proportion of C sucrose unloaded exuded by roots	0·20	Dimensionless	(a) Keith et al. (1986)
${\mathrm{\sigma }}^{C,suc}$	Conductivity for sucrose in (tp,i)	1·8$\hspace{0.5em}\times {10}^{-0}$	g2 µmol−1 m−2 s−1	(c)
${\mathrm{\sigma }}^{N,AA}$	Conductivity for amino acids in (tp,i)	1$\mathrm{\hspace{0.5em}}\times {10}^{-0}$	g2 µmol−1 m−2 s−1	(c)
${\beta }_{tp,i}$	Scale factor to estimate the section of (tp,i) with the phloem	1	${\left(g\hspace{0.5em}{m}^{-3}\right)}^{\raisebox{1ex}{$-2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	(c)
Growth of roots and grains
$K_{roots}^{C,mstruct}$	Affinity coefficient for root structural growth	1250	µmol C g−1	(c)
${Gmax}_{roots}^{C,mstruct}$	Maximum rate of root structural growth	0·015	µmol C g−1 s−1	(c)
$K_{grains}^{C,mstruct}$	Affinity coefficient for grain structural growth	300	µmol C	(c)
${Smax}_{grains}^{C,mstruct}$	Maximum rate of grain structural growth	1·5$\times {10}^{-0}$	s−1	(c)
$K_{grains}^{C,star}$	Affinity coefficient for starch synthesis in grains	400	µmol C g−1	(c)
${Smax}_{grains}^{C,star}$	Maximum rate of starch synthesis in grains	0·35	µmol C g−1 s−1	(c)
$t_{grains}^{init\hspace{0.5em}filling}$	Beginning of the period of grain filling	360	Hours from anthesis	(a) Bertheloot et al. (2011b)
$t_{grains}^{stop\hspace{0.5em}filling}$	End of the period of grain filling	900	Hours from anthesis	(a) Bertheloot et al. (2011b)
Tissue death
${\delta }_{roots}^{mstruct}$	Death rate of root structural mass at 20 °C	3·5$\hspace{0.5em}\times {10}^{-0}$	s−1	(a) Johnson and Thornley (1985)
$d_{tp,i}$	Fraction of maximum protein concentration below which laminae and stem organs die, respectively	0·5, 0·425	Dimensionless	(b) Bertheloot et al. (2011b)
${rate\_death}_{tp,i}^{area}$	Rate of tissue death in (tp,i)	0·2$\mathrm{\hspace{0.5em}}\times {10}^{-0}$	m2 s−1	(c)
Conversion factors
${MM}_C$	Molar mass of C	12	g mol−1	–
${MM}_N$	Molar mass of N	14	g mol−1	–
${conv}_{units}^{Nstruct}$	Conversion factor from µmol of N to g of structural N	1·43$·\hspace{0.5em}{10}^3$	g mol−1 10−1$·{10}^{-6}$	–
${conv}_{units}^{mstruct}$	Conversion factor from µmol of C to g of structural dry mass	3·13$·\hspace{0.5em}{10}^{-0}$	g mol−1 10−1$·{10}^{-6}$	–
$r_{C:mstruct}$	Mean contribution of C to structural dry mass	0·384	g C g−1	–
$r_{N:mstruct}$	Mean contribution of N to structural dry mass	0·02	g N g−1	–

HATS, High Affinity Transport System; LATS, Low Affinity Transport System; AU, Arbitrary Units.

To simplify their estimation, parameters were grouped into meta-processes that reflect the calculation order in CN-Wheat and thus increasing dependency: (1) PAR interception, photosynthesis and respiration; (2) root N uptake; (3) synthesis and degradation of metabolites; (4) C and N distribution within the culm; and (5) tissue growth and death. Each group of meta-processes was successively and iteratively parameterized. Parameters related to the first group were described in the previous section for PAR interception and in the companion paper for the sub-models of photosynthesis and respiration. Two adjustments were required to improve model predictions: (1) grain respiration was calibrated using method ‘c’ in order to have realistic dry masses; and (2) the photosynthesis of stem and chaff as calculated by the Farquhar-based sub-model (Farquhar et al., 1980) was pragmatically lowered by 22 %. Indeed, the photosynthetic efficiency of stem and chaff is poorly documented, but Araus and Tapia (1987) have shown that the stomatal conductance was 3-fold lower in sheaths than in laminae, which would have required a specific parameterization of the photosynthesis model for stem organs. The methods and references used to estimate the parameters belonging to the next groups of meta-processes are summarized in Tables 1 and 2. In the end, about 60 % of the parameters were estimated using method (c) and 25 % by combining methods (b) and (c).

Table 2.

Parameters related to the dependence function of nitrate uptake on the concentration of nitrates in roots

Parameter	A (dimensionless)	λ
${Vmax}_{roots}^{N,\mathrm{\hspace{0.5em}}nitrates\mathrm{\hspace{0.5em}}HATS}$	0·1333	0·0025 (s−1)
$K_{roots}^{N,\mathrm{\hspace{0.5em}}nitrates\mathrm{\hspace{0.5em}}HATS}$	211812	0·0018 (g m−3)
$K_{roots}^{N,\mathrm{\hspace{0.5em}}nitrates\mathrm{\hspace{0.5em}}LATS}$	4·614$\mathrm{\hspace{0.5em}}\times {10}^{-0}$	1·6517$\mathrm{\hspace{0.5em}}\times {10}^{-0}$ (m3 µmol−1 s−1)

Initialization of model variables at anthesis

The culm at anthesis was represented as a single root compartment, four vegetative phytomers (each composed of a lamina, sheath and internode, numbered acropetally), a peduncle, a chaff and the whole grains (Fig. 1 in companion paper). Internodes 2 and 3 were completely enclosed in their previous sheaths, while internode 1 and the peduncle were partially exposed to light. These latter organs were therefore divided into an enclosed and an exposed part. Light interception of enclosed parts was estimated assuming that 10  % of the light was transmitted by sheaths.

Fig. 1.

Culm photosynthetic projected area (A), dry mass (B) and N mass (C) during the post-anthesis period for treatments H0, H3 and H15. Model predictions are in solid lines while experimental data are represented by squares (vertical bars represent ± s.d.). The contribution of each organ is also detailed in the key: $\sum (tp,i)$ accounts for the sum of all photosynthetic organs, and ‘stem’ accounts for the sum of sheaths, internodes and the peduncle. The vertical dashed line represents the beginning of the rapid filling stage of grains.

Initialization of CN-Wheat requires state variables related to organ masses, dimensions and metabolite amounts at anthesis (Table 3). Initial values of structural N and dry masses of roots, photosynthetic organs and grains were adapted from Bertheloot et al. (2011b), as were photosynthetic organ areas. For internode 1 and the peduncle, state variables were partitioned among enclosed and exposed parts according to their area ratio. In contrast, the variables described below were not taken from Bertheloot et al. (2011b) and were therefore calculated for the present work.

Table 3.

Initialization of state variables at anthesis: definitions, symbols and values

Definition	Symbol			Unit		Value					Definition						Symbol					Unit			Value
Density of culms	–			Culms m−2		410					(c) Roots
(a) Soil											Structural dry mass						$M_{roots}^{struct}$					g			0·50
Nitrate concentration1	$\left[N_{soil}^{nit}\right]$			g m−3		1·50					Structural N mass						$N_{roots}^{struct}$					g			0·01
Temperature	$T_{soil}$			°C		15					Carbohydrates						${\text{C}}_{\text{roots}}^{CHO\hspace{0.5em}}$					µmol C			740
(b) Grains											Nitrates						$N_{roots}^{nit}$					µmol N			250
Structural mass2	$M_{grains}^{struct}$			mg		75					Organic N						$N_{roots}^{org}$					µmol N			60
Starch C mass	$C_{grains}^{star}$			µmol		0					Cytokinins						${cytok}_{roots}^{}$					AU			2·50
Protein N mass3	$N_{grains}^{prot}$			mg		1·5					(d) Phloem
											Sucrose						$\left[{\text{C}}_{\text{phloem}}^{suc}\right]$					µmol C			831
											Amino acids						$\left[N_{phloem}^{AA}\right]$					µmol N			161
(e) Photosynthetic organs
					Lamina					Sheath					Internode								Peduncle			Chaff
Definition		Symbol	Unit		n		n-1	n-2	n-3	n		n-1	n-2	n-3	nexp			nenc	n-1	n-2	n-3		Exposed	Enclosed
Width/diameter4		$w_{tp,i}$	cm		2·50		1·90	1·40	1·10	0·40		0·40	0·30	0·20	0·30			0·30	0·30	0·30	0·20		0·3	0·3		1·2
Total area5		$A_{tp,i}^{Total}$	cm−2		34·60		34	22·80	16	6		5	4	2	0·80			4	4	2·50	1		2·70	5		15
Height4		$z_{tp,i}$	cm		60		41	28	17	52		34	22	12	41			34	21	11	3		65	52		74
Structural dry mass3		$M_{tp,i}^{struct}$	mg		140		90	50	40	123		95	73	58	32			160	152	109	74		58	106		210
Structural N mass3		$N_{tp,i}^{struct}$	mg		0·97		0·77	0·47	0·34	0·6		0·28	0·28	0·43	0·09			0·43	0·32	0·26	0·31		0·28	0·51		1·01
Triose phosphates		$C_{tp,i}^{triosesP}$	µmol C
Starch		$C_{tp,i}^{star}$	µmol C
Fructans		$C_{tp,i}^{fruct}$	µmol C
Sucrose		$C_{tp,i}^{suc}$	µmol C		750		481	120	0	672		517	398	319	177			875	828	594	406		315	582		726
Nitrates		$N_{tp,i}^{nit}$	µmol N
Amino acids		$N_{tp,i}^{AA}$	µmol N		34		19	8	1	5		4	3	3	1			7	7	5	3		2	5		24
Proteins		$N_{tp,i}^{prot}$	µmol N		343		193	80	10	53		41	32	25	14			69	66	47	32		25	46		243
Cytokinins		${cytok}_{tp,i}^{}$	AU		15		8	3·50	2·50	0·50		0·20	0·15	1·50	0·5			0·5	0·15	0·1	0·1		0·85	0·7		15
Relative PAR		${PAR}_{tp,i}^{relative}$	–		0·346		0·085	0·025	0·013	0·08		0·015	0·007	0·006	0·03			0·001	0·001	0·001	0·001		0·168	0·009		0·482

Unit for model use: ¹ µmol m⁻³; ² µmol N; ³ g; ⁴ m; ⁵ m².

Lamina widths and diameters of sheaths, internodes, peduncle and chaff were needed to calculate organ temperature (Supplementary Data SI 2 in companion paper). These variables were estimated from their lengths and projected areas using an allometric relation for laminae and assuming cylindrical shapes for stem organs. Organ lengths and projected areas were adapted from Bertheloot et al. (2011b). Initialization of non-structural N in photosynthetic organs was calculated as the difference between total N content at anthesis and structural N. We assumed that proteins represented 80 % of this non-structural N, the remaining 20 % being amino acids assigned to the considered organ (10 %) and the phloem (10 %). Similarly, we calculated the amount of non-structural C, which was considered to be sucrose, allocated to the organ (90 %) and the phloem (10 %). Fructan content is usually low at anthesis (Gebbing, 2003) and our simulations have shown that nitrates and starch contribute <0·5 % of the total non-structural N and C, respectively. Consequently, nitrates, fructans and starch were initialized at 0. Cytokinin contents of culm organs do not contribute significantly to the mass balance and were initialized at their respective steady states. We considered that laminae n−1, n−2 and n−3 had reached their maximum protein concentration before anthesis, which was therefore set to the protein concentration of lamina n at anthesis.

Model initialization was similar for the three N treatments (H0, H3 and H15) since plants had grown in the same conditions until anthesis. Culm density was 410 culms m⁻². Soil nitrate concentration at anthesis was set to 1·5 g N m⁻³ for all N treatments. Then, 0, 3 or 15 g N m⁻³ was added to the soil for treatments H0, H3 and H15, respectively.

Model time steps

Simulations were performed for 1200 h (50 d) from the commencement of anthesis. Different time steps were chosen according to the most appropriate frequency of calculation for each sub-model. Photosynthesis and tissue death sub-models were run every 2 h in order to reduce computational time. In contrast, differential equations related to the variations in the amounts of metabolites in each organ were solved with an hourly time step.

RESULTS

In the figures, the predicted amounts of C and N contained in the phloem are shown in specific graphs in order to illustrate model behaviour. However, as the phloem is histologically distributed in the whole plant, the figures also show the contribution of the phloem to the C and N contents of each organ. Phloem C and N were first allocated between shoot and roots according to their structural mass, then among photosynthetic organs according to their area.

Culm photosynthetic area, dry and N mass

Regardless of the N treatment, the overall predictions of culm photosynthetic area, dry mass and N mass were in good agreement with the experimental data (Fig. 1). Laminae, which constituted two-thirds of the total photosynthetic area at anthesis, showed an earlier decrease in green area for the low-N fertilization treatment H0 compared with H3 and H15 (Fig. 1A). The simulations for lamina green areas matched well with experiments, but with slight overestimation in H3 and H15 for the latter stages. A more detailed analysis revealed that this overestimation was mainly due to an overestimated lifespan of laminae n-2 and n-3, which should have little effect on C assimilation and thereby model predictions. CN-Wheat predicted a realistic dynamic of stem and chaff green areas, with complete death occurring earlier than for laminae, which cannot be confirmed from the experimental data. On average, measured aerial dry mass of culms increased by 1·12 g (Fig. 1B), with surprisingly little difference among N treatments. Here, the model predicted that the increase in total aerial dry mass would depend on the N treatment. This was related to the slight discrepancies for grain mass predictions, which increased from H0 to H15, as could be expected from the respective dynamics of photosynthetic areas. The model accurately reproduced the dynamic of photosynthetic organ dry mass, which started to decrease towards the structural dry masses from the beginning of grain filling, with slight differences among N treatments. Little information is available for roots, but the predicted decrease in their dry mass was also observed for wheat after anthesis by Asseng et al. (1997). Mobile C of the phloem reached 0·4 g averaged across H0, H3 and H15 and showed similar dynamics among the N treatments. Compared with total dry mass, measured N mass dynamics showed significant differences between the N treatments, which were well reproduced by the model (Fig. 1C). Simulated culm N mass increased by 0·85, 5·94 and 14·56 mg over the post-anthesis period for H0, H3 and H15, respectively. CN-Wheat accurately predicted the differences in grain N accumulation observed over the N treatments. In agreement with the observations, the model predicted an earlier and faster remobilization of N from photosynthetic organs in H0 compared with H15. Also, total N mass of roots at anthesis was ∼15 mg, which is close to the results reported by Devienne et al. (1994) for wheat plants grown hydroponically. A striking aspect observed in Fig. 1 is the coincidence between the beginning of the grain-filling stage and the depletion of the phloem, as well as an increase in C and N remobilization from photosynthetic organs and roots. For H0, N remobilization and the resulting death of photosynthetic organs began earlier than the grain filling stage due to the depletion of soil nitrates.

Photosynthesis and respiration

Simulated photosynthesis and respiration cannot be compared with the experimental data as these measurements were not performed. Nevertheless, the model allows analysis of the two processes and the contribution of each organ (Fig. 2). Simulated daily photosynthesis of the whole culm was similar among N treatments until the beginning of green tissue death (Fig. 2A). Cumulated gross photosynthesis of the culm represented assimilation of 0·94, 1·28 and 1.36 g of C for H0, H3 and H15, respectively. Most of the assimilated C came from the laminae and that of the flag leaf alone contributed 55 % of overall photosynthesis (averaged across N treatments). Simulations also showed a significant contribution of the chaff (20 %) to culm photosynthesis. The predominant contributions of the flag leaf and chaff to photosynthesis during post-anthesis stages is in agreement with several studies (Evans and Rawson, 1970; Gent and Kiyomoto, 1989; Araus et al., 1993). The contribution of chaff varied from 10 to 76 % according to genotype (presence or absence of awns) as well as experimental conditions and procedures, which may be affected by the recycling of respired CO₂ occurring in grains and bracts (Araus et al., 1993).

Fig. 2.

Daily gross photosynthesis of aerial organs (A) and culm respiration (B) over the post-anthesis period for treatments H0, H3 and H15. ‘Stem’ accounts for the sum of sheaths, internodes and the peduncle. Values for respiration related to phloem loading ($R_{}^{phloem}$), nitrate reduction ($R_{}^{Nnit,\hspace{0.5em}red}$) and uptake ($R_{}^{Nnit,\hspace{0.5em}upt}$) were pooled. The vertical dashed line represents the beginning of the rapid filling stage of grains.

Respiratory activities of the whole culm were similar among N treatments until the beginning of tissue death (Fig. 2B). Residual respiration was the main source of C loss until the beginning of grain filling and then declined, due to the reduction of C and N content in the culm (Fig. 1). Growth (in particular of grains) also represented a strong respiratory cost, which decreased faster for H0 than H3 and H15. Similarly, the other respiratory activities (phloem loading, N uptake and reduction) were also increased by N fertilization and represented 3·6, 4·5 and 17·3  % of the total culm respiration for H0, H3 and H15, respectively. Predicted respiration and the contributions of each process are in agreement with Thornley and Cannell’s paper (2000). Moreover, our tests (data not shown) indicated that the simulated residual respiration was close to the one that would have been calculated from (1) a maintenance respiration model depending on structural mass (McCree, 1970) and (2) the diurnal respiration derived from the Farquhar-based model of photosynthesis (SI 2).

Distribution and remobilization of non-structural C and N

Simulated distributions of non-structural C are shown in Fig. 3 for laminae, chaff and stem (including sheaths, internodes and peduncle), roots and phloem. Regardless of the organ, the overall pattern shows an early increase in non-structural C followed by a drastic decrease from the beginning of grain filling. A late and transient increase in non-structural C was also observed following the end of grain filling (900 h post-anthesis), in particular for H3 and H15, for which the remaining green tissues transiently maintained photosynthetic activity. A marked gradient of non-structural C was observed between laminae according to their vertical position (Fig. 3A), which could be expected from their respective size, irradiance and photosynthetic activity (this vertical gradient of non-structural C was also observed in a personal experiment). Non-structural C of laminae exhibited diurnal variations, in particular for laminae n and n-1. This was the consequence of their high irradiance, which causes C to accumulate during the day, while the night period was characterized by C loading into the phloem. Shaded organs exhibited smoother diurnal variations of non-structural C, which was nearly at equilibrium with the phloem. Taken together, stem and chaff accumulated up to 193 mg of C averaged across the N treatments (Fig. 3B). Non-structural C of the stem was mainly composed of fructans (see illustration in the next section), which were completely remobilized during grain filling. Little information is available in the literature about the kinetics of C content in roots of a single culm, but our simulations showed that roots accumulated up to ∼60 mg of carbohydrates at 400 h post-anthesis, which then dropped as grain filling began (Fig. 3C). During the simulations, mobile C contained in the phloem represented up to 150 mg of C (Fig. 3D) and followed a similar kinetic to culm organs. The dynamics of non-structural C in the culm showed little difference among the N treatments. Nevertheless, laminae in H3 and H15 maintained higher amounts of C during the later stages compared with H0, due to delayed senescence. Non-structural C in roots was also slightly lower in H3 and H15 than in H0. This was the result of the low amounts of nitrates in H0, which led to reduced consumption of C for organic N synthesis.

Fig. 3.

Non-structural C distribution within the culm during the post-anthesis period for treatments H0, H3 and H15. Amounts of C are shown for each lamina (A), chaff and stem (sheaths, internodes and the peduncle) (B), roots (C) and phloem (D). As the phloem is botanically present in each organ, non-structural C shown in (A–C) includes the contribution from the phloem allocated to laminae, stem, chaff and roots according to their structural mass and area. The vertical dashed line represents the beginning of the rapid filling stage of grains.

The distribution of non-structural N showed contrasted dynamics among organs and N treatments (Fig. 4). The model was able to simulate the observed vertical gradient of N among laminae as well as the differences in the remobilization of non-structural N from laminae (Fig. 4A). Remobilization of N occurred earlier and faster for H0 compared with H3 and H15. The dynamics of non-structural N of the stem were also predicted correctly, although the model was not fully able to account for the higher accumulation of N in stems of H15 (Fig. 4B). Simulated dynamics of non-structural N in chaff were in agreement with the measurements and accounted for the differences among N treatments, but the model slightly overestimated N depletion from chaff during the late stages. Accumulation of non-structural N in roots (Fig. 4C) showed marked differences according to the N treatment and reached 6·4, 9·3 and 10·4 mg for H0, H3 and H15, respectively. The absence of N fertilization in H0 depleted root N at 600 h post-anthesis, while ∼4 mg of N was still present in roots of H15 at maturity. The concentration of nitrates in roots (data not shown) reached 710, 1100 and 1300 µmol g⁻¹ for H0, H3 and H15, respectively. These results are in the order of magnitude measured by Devienne et al. (1994). Mobile N contained in the phloem (Fig. 4D) showed a drastic decrease from the beginning of grain filling and was surprisingly slightly affected by the N treatment. Larger differences in phloem N may, however, arise with more contrasted N fertilizations applied during the pre-anthesis period, for instance. Non-structural N increased in the phloem from the end of grain filling, particularly for H15, for which the model predicted a resumption of N uptake (further explanations are given below).

Fig. 4.

Non-structural N distribution within the culm during the post-anthesis period for treatments H0, H3 and H15. Model predictions are shown as solid lines while experimental data are represented by squares (vertical bars represent ± s.d.). Amounts of N are shown for each lamina (A), chaff and stem (sheaths, internodes and the peduncle) (B), roots (C) and phloem (D). As the phloem is botanically present in each organ, non-structural N shown in (A–C) includes the contribution from the phloem allocated to laminae, stem, chaff and roots according to their structural mass and area. The vertical dashed line represents the beginning of the rapid filling stage of grains.

Investigation of metabolite distribution

In order to show the ability of CN-Wheat to simulate metabolite distribution and concentrations, detailed compositions of non-structural C and N are illustrated for two different photosynthetic organs of the H3 treatment. The first example relates to the exposed lamina of the flag leaf (Fig. 5A, B), which intercepts 40 % of the incident light, and the second is the enclosed part of the peduncle (Fig. 5C, D). In agreement with the literature (Schnyder, 1993), sucrose was the main form of C in the lamina compared with starch, triose phosphates and fructans (Fig. 5A). Sucrose concentration ranged from 100 to 600 µmol g⁻¹ and showed high diurnal variations (Caputo and Barneix, 1999). The simulated concentrations of sucrose appeared to be overestimated compared with the literature, where usual values in wheat leaves ranged from 200 to 400 µmol g⁻¹ (Judel and Mengel, 1982; Araus et al., 1987; Trevanion, 2000; Xue et al., 2008). This potential discrepancy could result from an overestimation of photosynthesis, but may also reflect that some metabolic pathways, which were neglected in the model, could affect sucrose concentration (e.g. competition for substrate, supplementary consumption). As expected (Schnyder, 1993; Trevanion, 2000, 2002), starch was a minor pool of C, which was depleted at the end of the night periods. Triose phosphates, which represent the net product of the Calvin cycle, were present at very low concentrations (0–0·15 µmol g⁻¹), as reported by Trevanion (2002), and also showed diurnal variations resulting from the balance between photosynthesis and their consumption for the synthesis of sucrose, starch and amino acids. In agreement with the predictions of the model, fructan content has been reported to be usually low in laminae of grass species (Borland and Farrar, 1985; Schnyder, 1993). Proteins were the major N metabolite in the lamina (Fig. 5B) and dropped from ∼2500 to 270 µmol g⁻¹, resulting in a massive remobilization of N usable for grain filling. Although proteins were not measured experimentally, the accuracy of the model in simulating the dynamics of non-structural N (Fig. 4A) indicates that the predicted protein concentrations were realistic. Amino acids were 10 times lower than proteins and ranged from ∼50 to 210 µmol g⁻¹, which is close to the results obtained by Caputo and Barneix (1999). Nitrates were present at low concentrations (<6 µmol g⁻¹) and showed diurnal peaks due to their import through the transpiration stream. We are not aware of studies with which the simulated nitrate concentrations can be directly compared; however, these results are very close to those obtained in a personal experiment conducted on wheat grown in field conditions (R. Barillot and B. Andrieu, unpubl. res.).

Fig. 5.

Detailed metabolite concentrations for C (left panels) and N (right panels) for two examples of photosynthetic organs: lamina n (A, B) and the enclosed (enc) part of the peduncle (C, D). Simulations are shown during the organ’s lifespan. The vertical dashed line represents the beginning of the rapid filling stage of grains.

The concentrations of sucrose (Fig. 5C) and amino acids (Fig. 5D) of the enclosed part of the peduncle were lower than in the lamina and exhibited smoother diurnal variations. Our simulations also showed that sucrose and amino acids were at equilibrium with the phloem. Indeed, the low irradiance and thus photosynthetic activity of the enclosed peduncle caused a nearly heterotrophic metabolism (Wardlaw, 1965; Gebbing, 2003). In contrast with the lamina, the enclosed peduncle accumulated a large amount of fructans (up to 1150 µmol g⁻¹) before the beginning of grain filling. After this stage, fructans were markedly remobilized until the end of grain filling. The level and kinetics of fructan concentration are consistent with observations published on wheat peduncles (Wardlaw and Willenbrink, 1994; Gebbing, 2003). In CN-Wheat, fructans are concomitantly subjected to synthesis and degradation, meaning that the balance between the two processes led to a net synthesis of fructans before the beginning of grain filling, which was then followed by net degradation. This may explain why some studies have reported an absence of fructan degradation during their accumulation (Winzeler et al., 1990). Besides, the absence of diurnal variations of fructans in our simulations consolidates the idea that fructans did not act as a source of C during the dark period of the diurnal cycle (Schnyder, 1993).

Fluxes of C and N in roots

Another interesting view that the model can bring is an estimate of the fluxes of C and N from and towards roots and their differences according to the N treatment (Fig. 6). Maximal nitrate uptake rates reached 10 µmol h⁻¹ at the beginning of the simulation (Fig. 6A), and were in the same order of magnitude as those reported in the literature for wheat in various experimental conditions (Rodgers and Barneix, 1988; Devienne et al., 1994; Taulemesse et al., 2015). The model also predicted that root N uptake would stop only after 150 h post-anthesis for H0, whereas it lasted for the whole of the simulation period for H15. For H0 and H3, the cessation of N uptake was clearly related to the depletion of soil nitrates (inset in Fig. 6A). For H15, N uptake dropped 100 h after the beginning of grain filling, which is explained by the decrease in C content in roots (Fig. 3C). Although a diminution in root C was also observed for H0 and H3, it did not impact N uptake because soil nitrates were the limiting factor. During the whole post-anthesis period, roots absorbed 3·70, 11·05 and 29·92 mg of N for H0, H3 and H15, respectively. Therefore, a positive correlation between root N uptake and final grain N emerged from the present model (data not shown).

Fig. 6.

Rates of C and N fluxes in roots are shown for (A) nitrate uptake and (B) unloading from phloem, (C) structural dry mass growth and (D) death, and (E) C exudation and (F) N exudation. The vertical dotted line represents the beginning of the rapid filling stage of grains.

The decrease in root C is illustrated by the reduction in C unloading from phloem, which dropped from ∼40 µmol h⁻¹ before the period of grain filling to <15 µmol h^–1 regardless of the N treatment (Fig. 6B). Early rates of C unloading were similar among N treatments and consistent with studies conducted on wheat at post-anthesis (Simpson et al., 1983) and young barley plants (Farrar, 1985). Due to earlier death of green area tissues in H0 (Fig. 1A), C unloading to roots was lower than for H3 and H15 from 500 h post-anthesis.

The decrease in root structural dry mass began at anthesis (Fig. 1B), but became faster after the beginning of grain filling. This was related to the decrease in root growth (Fig. 6C), which then became lower than root death (Fig. 6D). The higher concentrations of root carbohydrates observed for H0 compared with H3 and H15 (Fig. 3C) resulted in higher root growth in this treatment.

Regardless of the N treatment, carbohydrates and organic N exudation ranged from 0 to 8·5 µmol h^–1 and from 0 to 0·7 µmol h^–1, respectively (Fig. 6E, F). These figures also show that the higher the N fertilization, the higher the root exudation. During the overall post-anthesis period, exudation represented a transfer of 105, 140 and 150 mg of C and 4, 5·33 and 12·2 mg of N to the soil, for H0, H3 and H15 respectively. Assuming 410 culms m^–2, root exudation represented from 430 to 615 kg ha^–1 of C and from 16 to 50 kg ha^–1 of N added to the soil during the post-anthesis period. The estimation of C exudation is in agreement with the study of Keith et al. (1986), showing exudation of 520 kg ha^–1 for wheat grown in field conditions. Janzen (1990) and Janzen and Bruinsma (1993) also observed that N exudation increased with higher fertilization. Rroço and Mengel (2000) reported that N rhizodeposition measured between ear emergence and maturity represented 12 % of total N captured by wheat plants. These values are reasonably close to our simulation for the post-anthesis period (12, 13 and 18 % in H0, H3 and H15, respectively). However, it is known that mechanisms for N rhizodeposition differs from those for C rhizodeposition (Jones et al., 2009) and the simple formalism taken in CN-Wheat will likely need to be further elaborated in the future. Another striking aspect of Fig. 6 is the transient resumption of root activities after the end of grain filling, in particular for H15. This is related to the unloading of C from the remaining green tissues, which then allowed the resumption of N uptake (if the soil was not empty), root growth and exudation.

DISCUSSION

In this study, the functional–structural plant model CN-Wheat was parameterized for winter wheat plants grown in field conditions under three N fertilizations applied at anthesis. Based on a realistic representation of the culm, CN-Wheat accounts for the main physiological processes involved in the regulation of C and N metabolisms: photosynthesis and respiration, nitrate uptake and distribution in photosynthetic organs, exudation by roots, synthesis of storage and mobile metabolites, protein turnover and tissue death. Using a single set of parameters, CN-Wheat was validated for its ability to predict the kinetics of N and dry masses in laminae, stem organs, chaff and grains as well as lamina green areas under contrasted N fertilizations. The main discrepancies observed are related to (1) the N dynamics in stems of the H15 treatment (and to a lesser extent of the chaff), which tended to decrease too early compared with measurements, and (2) the high amounts of sucrose in photosynthetic organs. Although it was beyond the scope of this paper, the accuracy of CN-Wheat would have been clearly enhanced by dedicated experiments and the use of numerical methods for parameter estimation and a sensitivity analysis. Some experimental uncertainties may also be mentioned: (1) variables for individual stem organs were estimated from a complementary experiment conducted on a different cultivar; (2) N and structural dry masses were roughly estimated from organ masses at maturity; (3) hourly meteorological data were rebuilt from different years; and (4) data related to soil nitrate concentration at anthesis were missing, as was the rate of N mineralization; we also assumed a 100 % recovery rate of the N fertilizer. Besides, CN-Wheat simulated a transient increase in root N uptake and in the C and N content of roots and photosynthetic organs after the end of grain filling. Such behaviour seems unlikely, meaning that some aspects were not accounted for in the model, such as the developmental processes involved in the monocarpic character of wheat (Lammer et al., 2004).

A major aspect of the model is that the physiological processes that drive the C and N fluxes are regulated by the local concentrations in metabolites. We believe this assumption is close to the actual functioning of plants while avoiding the use of teleonomic approaches, which are difficult to assess experimentally. The present study demonstrates that this paradigm has succeeded in simulating C and N distribution in a wheat culm, while using parameters and variables related to clearly identified processes. This makes it possible to conduct specific experiments in order to assess various parts of the model (photosynthesis, Michaelis–Menten functions for the synthesis of CN metabolites, etc.) and therefore estimate the related parameters and their genetic variability. Another important modelling choice is the identification of a common pool of C and N that represents the phloem. Although the phloem is histologically present inside each organ, with gradients of metabolites along the vasculature, the concept of a common pool used to share mobile metabolites among organs was also used by several authors (Cooper and Clarkson, 1989; Kull and Kruijt, 1999; Thornley, 2004; Bertheloot et al., 2011a). Without defining source/sink priorities, the present study demonstrates that the assumption of a common pool is able to account for the allocation of C and N among photosynthetic organs, roots and grains under three N fertilizations. The allocation of resources is an emergent property that resulted from a simplified transport-resistant rule driven by the concentrations in C and N and the parameters related to the loading and unloading functions. The modelling assumptions discussed above have led to the identification/formalization of the main physiological processes involved in C and N metabolism. Below we will discuss the benefits, limits and further improvements of the main types of processes implemented in CN-Wheat, with regard to the model evaluation that was performed.

The first point deals with the models of photosynthesis and respiration. The estimation of C assimilation and losses through respiration has led to realistic dry masses at the whole culm scale, as well as for individual organs. Both formalisms, the Farquhar-based model for photosynthesis (Farquhar et al., 1980) and a physiological approach for respiration (Thornley and Cannell, 2000), were pertinent with regard to our modelling framework, as they deal with regulations by local factors (PAR, temperature), activities (e.g. N uptake and reduction) and metabolite concentrations (e.g. N, carbohydrates). Although these models remain to be assessed on proper datasets, they have led to realistic estimations and they also have the added benefit of dealing with variables that could be measured experimentally. Besides, the respiration of grains is poorly documented to our knowledge; we therefore had to adjust this parameter pragmatically. Similarly, we assumed that photosynthesis was more efficient for laminae than for stem organs, for which we therefore decreased the estimate of C assimilation calculated from the Farquhar-based model.

The sub-model of N uptake by roots integrates the physiological knowledge described in the literature with regard to the regulation of N uptake by (1) nitrate concentrations in soil and roots (Siddiqi et al., 1990; Taulemesse et al., 2015) and (2) root carbohydrates (Masclaux-Daubresse et al., 2010), which were reported to stimulate expression of genes involved in nitrate uptake, translocation and assimilation (Lillo, 2008). Although this sub-model remains to be further calibrated and validated by specific experiments, a single set of parameters was able to account for the differences in N uptake and accumulation in the culm under contrasted N fertilizations. Our results also demonstrate that the formalisms used in CN-Wheat are able to predict a cessation of root N uptake during the grain-filling period, even for the H15 treatment, for which >5 g N m⁻² remained in the soil at the end of the simulation. The simulations suggest that, before the beginning of grain filling, root N uptake was not limited by the availability of carbohydrates (Figs 3C and 6B) but rather by the amount of N in the soil, particularly for H0 and H3. Moreover, the accumulation of nitrates in roots of H15 (Fig. 4C) resulted in a downregulation of N uptake. During the grain filling period, grains were strongly competing for phloem C, which depleted the pool of C in roots after 500 h (Figs 3C and 6B), leading to the drastic diminution of N uptake observed in H15 (Fig. 6A). To a lesser extent, the loss of root structural dry mass (Fig. 1B) was also involved in the cessation of nitrate uptake. While N uptake decreased, the model still allowed export of root nitrates and organic N to the photosynthetic organs through the transpiration stream. This allowed the remobilization of root N and C (Gebbing et al., 1998).

The formalisms used to account for the syntheses and degradations of metabolites were able to predict the differences in C and N content for the three N treatments, as well as their vertical distribution among the photosynthetic organs. The vertical gradient of N in the plant was an emergent property of CN-Wheat that did not require the use of concepts derived from optimization theory or a co-distribution with the light profile (Chen et al., 1993; Hirose, 2005; Prieto et al., 2012). In the present model, N input in photosynthetic organs is related to nitrate import through the transpiration stream, which depends on light absorption. Moreover, the accumulation of proteins is regulated by (1) the amount of amino acids, whose synthesis depends on nitrates and sucrose, and (2) the rate of degradation, which is down-regulated by cytokinins. Besides, the overall predicted concentrations of metabolites and their relative abundances are in good agreement with the literature. Nevertheless, the predicted concentrations of sucrose appeared to be significantly overestimated compared with published work on various wheat cultivars and growing conditions (Judel and Mengel, 1982; Araus et al., 1987; Trevanion, 2000; Xue et al., 2008). This discrepancy with the literature may result from: (1) an overestimation of C assimilation, in particular for stem and chaff, for which few data are available and which were not measured in the experiment used to calibrate the model; and (2) taking no account of pathways that also use triose phosphates as substrates and/or those related to sucrose consumption (lipid or secondary metabolism).

The last point of this discussion deals with the modelling of tissue death in CN-Wheat, probably the process for which we have the fewest clues from the literature. We therefore considered the idea that tissue death could be empirically related to the maximum concentration of proteins reached by the considered organ (Bertheloot et al., 2011a). Despite the uncertainties of estimating this latter variable at anthesis and for each organ, the predictions of lamina green areas were in good agreement with the experimental data in all N treatments. In order to improve model predictions for stem organs, we set a different fraction of the maximum protein concentration below which the stem tissue dies. Moreover, our preliminary tests did not allow identification of indicators other than the maximum protein concentration to trigger tissue death (e.g. amino acid or sucrose concentrations, photosynthesis:respiration ratios, residual respiration threshold). Therefore, the lifespan of green tissues in CN-Wheat is regulated by the processes involved in protein synthesis (amino acids) and degradation (cytokinins). An illustration of the simulated dynamics and distribution of cytokinins is available in Supplementary Data SI 3. Although the sub-model of cytokinins remains exploratory, it allows us to account for experimental evidence related to (1) the inhibition of tissue death by cytokinins (Mok and Mok, 1994) through (2) the down-regulation of protein degradation (Wingler et al., 1998; Criado et al., 2009; Koeslin-Findeklee et al., 2015), (3) the role of roots in shoot senescence through the synthesis of cytokinins that are exported by the transpiration stream (Badenoch-Jones et al., 1996; Pons et al., 2001) and (4) the regulation of cytokinin synthesis by root concentrations in carbohydrates and nitrates (Sakakibara et al., 2006). The dynamics of cytokinin concentration, by regulating the rate of protein degradation, played a pivotal role in determining the difference in organ death between treatments. The decrease in cytokinins in photosynthetic organs has enhanced the degradation of proteins and resulted from the decrease in cytokinin synthesis in roots. This was related to the diminution of root nitrates, e.g. when N soil was depleted (H0 and H3), and/or when root carbohydrates decreased, e.g. when grains were strongly competing for phloem C (H15). Obviously, the sub-model of cytokinins remains to be assessed and validated properly in a wide range of conditions. Nevertheless, we believe that the formalism in CN-Wheat may represent a starting point to study the regulation of senescence by cytokinins, while also taking into account the main plant processes involved in the metabolism of C and N.

To conclude, the present study demonstrates that the assumptions used in CN-Wheat are able to predict the behaviour of wheat plants under contrasted N fertilizations at anthesis. Using a single set of parameters, estimated from the literature or calibrated on data, consistent simulations were produced regarding resource acquisition and their distribution among photosynthetic organs, roots and grains for the three N treatments. Beyond its evaluation, CN-Wheat also provided original insights enabling analysis of how integrated responses at plant scale can emerge from local processes. Indeed, the model was able to account for the spatial distribution of resources within plant architecture. The model also illustrated how the rapid filling of grains decreased the availability of mobile metabolites which ultimately determined the dynamics of CN remobilization from vegetative organs. Besides, the genericity of the processes and formalisms should make the model able to represent the genotypic variability of wheat and adaptable for other species. Coupled to experimental studies (e.g. use of labelled C and N), the model may also help to refine our knowledge on plant functioning and target traits for breeding, like those involved in N efficiency or the negative relation between grain yield and protein content (Simmonds, 1995; Oury and Godin, 2007). Besides, agriculture has to face two major challenges: incentives for more sustainable practices, which tend to decrease the use of fertilizers and pesticides (Aubertot et al., 2007), and the adaptation of practices to the elevation of CO₂ and temperatures (Brisson and Levrault, 2010). In this context, CN-Wheat may contribute to the investigation of plant behaviour in response to new environmental conditions and agronomic practices.

SUPPLEMENTARY DATA

Supplementary data are available online at www.aob.oxfordjournals.org and consist of the following. SI 1: supplementary information for meteorological data. SI 2: supplementary information for comparison of respiration models. SI 3: supporting information for the cytokinin sub-model.