Environmental triggers for photosynthetic protein turnover determine the optimal nitrogen distribution and partitioning in the canopy.

Plants continually adjust the photosynthetic functions in their leaves to fluctuating light, thereby optimizing the use of photosynthetic nitrogen (Nph) at the canopy level. To investigate the complex interplay between external signals during the acclimation processes, a mechanistic model based on the concept of protein turnover (synthesis and degradation) was proposed and parameterized using cucumber grown under nine combinations of nitrogen and light in growth chambers. Integrating this dynamic model into a multi-layer canopy model provided accurate predictions of photosynthetic acclimation of greenhouse cucumber canopies grown under high and low nitrogen supply in combination with day-to-day fluctuations in light at two different levels. This allowed us to quantify the degree of optimality in canopy nitrogen use for maximizing canopy carbon assimilation, which was influenced by Nph distribution along canopy depth or Nph partitioning between functional pools. Our analyses suggest that Nph distribution is close to optimum and Nph reallocation is more important under low nitrogen. Nph partitioning is only optimal under a light level similar to the average light intensity during acclimation, meaning that day-to-day light fluctuations inevitably result in suboptimal Nph partitioning. Our results provide insights into photoacclimation and can be applied to crop model improvement.

Introduction

Acclimation of leaf traits to fluctuating environments is a key mechanism to maximize fitness (Walters, 2005; Athanasiou ). To maximize canopy n class="Chemical">carbon gainpan>, dynpan>amic modificationpan>s of photosynpan>thetic traits to track heterogenpan>eous light distributionpan> withinpan> the canpan>opy are crucial (Retkute ), especially for herbaceous species with a conpan>tinpan>uously leaf-forminpan>g nature (Niinpan>emets ). One of the most importanpan>t strategies inpan> photoacclimationpan> is to mainpan>tainpan> efficienpan>t utilizationpan> of limited resources inpan> the photosynpan>thetic apparatus, e.g. pan> class="Chemical">nitrogen, by continuous modifications of (i) between-leaf distribution along the canopy depth and (ii) within-leaf partitioning between photosynthetic functions according to local light availability (Evans, 1989).

Vertical n class="Chemical">nitrogen distributionpan> inpan> responpan>se to light has beenpan> inpan>tenpan>sively studied (Hirose anpan>d Werger, 1987; Werger anpan>d Hirose, 1991; Antenpan> ; Dreccer ; Moreau ; Hikosaka ). pan> class="Chemical">Nitrogen distribution was reported to closely follow the light gradient and thus approach its optimum in wheat stands (Dreccer ). However, this relationship has not been found in other studies (Moreau ; Hikosaka ). In fact, many studies demonstrated that nitrogen distribution failed to track the within-canopy light gradient optimally due to a delay in nitrogen reallocation in the lower canopy layer and an underinvestment in the upper layer (Field, 1983; Evans, 1993; Hollinger, 1996; Hirose ; Meir ; Wright ; Hikosaka, 2016). This discrepancy between optimum and reality could be explained by physiological limitations and the cost of nitrogen reallocation (Hikosaka, 2016; Kitao ) or might result from incorrect predictions. In some cases (e.g. Hikosaka, 2014; Kitao ), the optimal nitrogen distribution that followed the within-canopy light gradient estimated by the Beer–Lambert law was predicted to be extremely high in the upper canopy, which might not be biologically reachable. This could result from the oversimplification of models in three aspects: (i) neglecting the effects of variations in the structural characteristics, e.g. leaf elevation angle (Falster and Westoby, 2003), on light interception of the leaves; (ii) neglecting age-dependent modifications and limitations during leaf development and ageing (Niinemets ; Niinemets, 2016); and (iii) assuming a linear relationship between photosynthetic capacity and photosynthetic nitrogen per unit leaf area instead of considering photoacclimation in functional nitrogen partitioning.

Optimizing functional partitioning within the leaf is of great importance because it improves n class="Chemical">carbon gainpan> by enpan>hanpan>cinpan>g photosynpan>thetic pan> class="Chemical">nitrogen use efficiency (PNUE; Zhu ). Photosynthetic rate is determined by the limited rate of ribulose 1,5-bisphosphate (RuBP) carboxylation and RuBP regeneration in the photosynthetic machinery (Farquhar ). Besides driving photosynthesis, light also triggers fine adjustments in nitrogen investment between (i) RuBP carboxylation (Rubisco), (ii) RuBP regeneration (electron transport), and (iii) light harvesting functions (Yamori ; Trouwborst ; Vialet-Chabrand ). The capability and significance of photoacclimation in functional nitrogen partitioning were empirically addressed in both light-demanding and shade-tolerant species (Evans, 1993; Hikosaka and Terashima, 1996; Pons and Anten, 2004; Hikosaka, 2005; Trouwborst ). Recently, with a modelling approach, it was predicted that a decreasing investment in the light harvesting function can increase canopy PNUE (Song ). However, genetic and physiological controls of photoacclimatory processes by environmental triggers are still not described mechanistically.

The degree of acclimation under a given environment is limited by the previous environmental conditions (Walters, 2005; Niinemets ) along with continuous age-dependent modifications in physiological traits (Niinemets, 2016). This emphasizes that static models, which do not consider the dynamics of plant growth and environmental fluctuations, may not be sufficiently precise in predicting acclimation behavior. Prieto proposed an empirical model describing the combined effects of leaf age and light on leaf n class="Chemical">nitrogen econpan>omics for a grapevinpan>e canpan>opy anpan>d demonpan>strated that the meanpan> daily light inpan>tegral over the previous 10 d explainpan>ed 73% of the variationpan> inpan> pan> class="Chemical">nitrogen per unit leaf area. Since environmental acclimation and developmental (genetic control of leaf ageing) acclimation are regulated distinctively (Athanasiou ), it is possible to integrate internal (age) and external (environment) triggers into a mechanistic model for better understanding of the developmental and environmental effects on photosynthetic acclimation.

Acclimation processes in leaf functioning are regulated by constant updates of protein content as a result of protein turnover, driven by the concurrent actions of degradation and synthesis (Li ). In growing leaves, photosynthetic proteins account for the highest cost in protein turnover (Li ). At the expense of energy, protein turnover is necessary for adjusting protein levels in line with external triggers. It was experimentally shown that leaf n class="Gene">Rubisco conpan>tenpan>t inpan>creased with light (Yamori ) anpan>d pan> class="Chemical">nitrogen supply level (Yamori ) and exhibited an evolution with leaf age that could be interpreted by Rubisco turnover (Suzuki ; Ishimaru ; Irving and Robinson, 2006). Based on the concept of protein turnover, Thornley (1998) proposed a mechanistic model predicting reasonable dynamics of photosynthetic acclimation at the leaf level. We refined this model to describe the dynamics of different photosynthetic nitrogen pools and to quantify the developmental and environmental effects of light and nitrogen availabilities on leaf acclimation. The optimality of nitrogen distribution and partitioning at the canopy scale was evaluated by integrating this model into a multi-layer model considering the structural characteristics of a cucumber canopy. This aims (i) to test whether the protein turnover can be a mechanistic explanation of the photosynthetic acclimation under dynamic environmental conditions; and (ii) to understand the regulatory mechanism of environmental triggers on the degree of optimality at the canopy level in terms of maximizing PNUE and canopy carbon assimilation, which can be considered as an indicator of the general fitness of the plants.

Materials and methods

Modelling the dynamics of photosynthetic protein turnover

Photosynthetic n class="Chemical">nitrogen (Nph, mmol N m−2) is definpan>ed as biologically active n class="Chemical">nitrogen in the proteins involved in photosynthetic functions, i.e. carboxylation, electron transport and light harvesting. Leaf Nph is calculated as the sum of nitrogen in the carboxylation pool (NV), electron transport pool (NJ) and light harvesting pool (NC, Trouwborst ):

where NV includes only n class="Gene">Rubisco anpan>d represenpan>ts the pan> class="Chemical">nitrogen investment in carboxylation capacity, NJ includes the electron transport chain, photosystem II core and Calvin cycle enzymes other than Rubisco, and NC includes the photosystem I core and light harvesting complexes I and II. Functional pools NV, NJ, and NC are estimated from the maximum carboxylation rate (Vcmax, μmol CO2 m−2 s−1), maximum electron transport (Jmax, μmol e− m−2 s−1) and leaf chlorophyll (Chl, mmol Chl m−2), respectively (Buckley ):

where χV (μmol n class="Chemical">CO2 mmol−1 N s−1) is the carboxylation capacity per unit n class="Gene">Rubisco nitrogen, and χJ (μmol e− mmol−1 N s−1) is the electron transport capacity per unit electron transport nitrogen. χCJ (mmol Chl mmol−1 N) and χC (mmol Chl mmol−1 N) are the conversion coefficients for chlorophyll per electron transport nitrogen and per light harvesting component nitrogen, respectively. Photosynthetic nitrogen partitioning fraction of a pool X (p) is determined as the ratio of nitrogen in the pool X (N, mmol N m−2) to Nph:

The rate of change of N is determined by the instantaneous protein synthesis rate [S(t), mmol N m−2 °Cd−1] and degradation rate [D(t), mmol N m−2 °Cd−1] of the corresponding enzymes and protein complexes at a given leaf age (t, °Cd):

Protein synthesis as an age-dependent and zero-order process (Li ) is described by a logistic function and independent of the current N state:

where n class="Chemical">Smax, (mmol N m−2 °n class="Chemical">Cd−1) is the maximum protein synthesis rate of N that occurs at the early stage of leaf development (Supplementary Fig. S1 at JXB online). The constant td, (°Cd−1) describes the relative decreasing rate of the protein synthesis over time (see Table 1 for the coefficients used in the protein turnover model). At age of 1/td,, S reduces to 53.8% of Smax,.

Table 1.

List of coefficients used in the protein turnover model for photosynthetic nitrogen pools, carboxylation pool NV, electron transport pool NJ, and light harvesting pool NC

Description	Coefficient	Unit	Pool NV	Pool NJ	Pool NC
Degradation constant [Eq. (6)]	D r	°Cd−1	0.0195	0.0195	0.0091
Increase rate constant of Smax with ILd [Eq. (7)]	k I	mmol N m2 ground d m−2 LA °Cd−1 mol−1 photon	0.173	0.130	0.234
Michaelis–Menten constant relating NS to Smax [Eq. (8)]	k N	mM	0.536	0.420	0.316
Potential maximum synthesis rate [Eq. (7)]	S mm	mmol N m−2 °Cd−1	1.122	0.852	0.248
Decreasing constant of synthesis rate [Eq. (5)]	t d	°Cd−1	0.001	0.002	0.001

The coefficients were estimated from the growth chamber experiment. Model variables and other coefficients are listed in Tables 2 and 3.

List of coefficients used in the protein turnover model for photosynthetic n class="Chemical">nitrogen pools, carboxylation pool NV, electron transport pool NJ, and light harvestinpan>g pool NC

Table 2.

List of model input and output variables

Description	Variable	Unit	Equation	Type
Net photosynthetic rate	A	μmol CO2 m−2 s−1	9a	Output
RuBP carboxylation-limited A	A c	μmol CO2 m−2 s−1	9b	Output
RuBP regeneration-limited A	A j	μmol CO2 m−2 s−1	9c	Output
Leaf absorptance	α	—	13	Output
Atmospheric CO2 concentration	C a	μmol CO2 mol−1	—	Input
Chloroplastic CO2 concentration	C c	μmol CO2 mol−1	14	Output
Leaf chlorophyll per unit area	Chl	mmol m−2	2c	Output
Leaf-to-air vapor pressure deficit	D	kPa	—	Input
Protein degradation rate of N pool X	D X	°Cd−1	6	Output
Factor for creating variation in N distribution	f d	—	18	Input
Factor for creating variation in N partitioning	f p	—	19	Input
Mesophyll conductance to CO2	g m	mol CO2 m−2 s−1	16	Output
Maximum gm	g mmax	mol CO2 m−2 s−1	17	Output
Stomatal conductance to CO2	g sc	mol CO2 m−2 s−1	15	Output
PPFD at leaf	I Lc	μmol photons m−2 s−1	—	Input
Daily photosynthetic photon integral at leaf	I Ld	mol photons m−2 d−1	—	Input
Mean ILd during the last 4 d	I Ld4d	mol photons m−2 d−1	—	Input
Electron transport rate	J	μmol e− m−2 s−1	12	Output
Maximum electron transport rate	J max	μmol e− m−2 s−1	2b	Output
Leaf area	LA	m2	—	Input
Total leaf photosynthetic N content in the canopy	N canopy	mmol N	—	Output
Leaf photosynthetic N content	N leaf	mmol N	—	Output
Leaf photosynthetic N per unit area	N ph	mmol N m−2	1	Output
N concentration of nutrient solution	N s	mM	—	Input
Concentration of N pool X	N X	mmol N m−2	4	Output
Concentration of N pool of light harvesting	N C	mmol N m−2	4	Output
Concentration of N pool of electron transport	N J	mmol N m−2	4	Output
Concentration of N pool of carboxylation	N V	mmol N m−2	4	Output
Partitioning fraction of N pool X	p X	—	3	Output
Daytime respiration rate in the absence of photorespiration	R d	μmol CO2 m−2 s−1	10	Output
Reduction factor of protein synthesis depending on N availability	r N	—	8	Output
Maximum protein synthesis rate	S max	mmol N m−2 °Cd−1	7	Output
Protein synthesis rate of N pool X	S X	mmol N m−2 °Cd−1	5	Output
Leaf age	t	°Cd	—	Input
Carboxylation rate	V c	μmol CO2 m−2 s−1	11	Output
Maximum carboxylation rate	V cmax	μmol CO2 m−2 s−1	2a	Output

Table 3.

List of model coefficients

Description	Coefficient	Unit	Value (SE)	Reference
Conversion coefficient of chlorophyll per light harvesting N	χC	mmol Chl mmol−1 N	0.03384	Buckley et al. (2013)
Conversion coefficient of chlorophyll per electron transport N	χCJ	mmol Chl mmol−1 N	4.64 × 10–4	Buckley et al. (2013)
Conversion coefficient of electron transport capacity per electron transport N	χJ	μmol e− mmol−1 N s−1	9.48	Buckley et al. (2013)
Conversion coefficient of carboxylation capacity per Rubisco N	χV	μmol CO2 mmol−1 N s−1	4.49	Buckley et al. (2013)
Minimum gsc	g 0	mol CO2 m−2 s−1	0.009	Chen et al. (2014)
Species-specific coefficient of gsc	g 1	—	3.51	Chen et al. (2014)
CO2 compensation point in the absence of dark respiration	Γ*	μmol CO2 mol−1	43.02	Singsaas et al. (2004)
Michaelis–Menten constant of Rubisco for CO2	K c	μmol CO2 mol−1	404	Chen et al. (2014)
Michaelis–Menten constant of Rubisco for O2	K o	mmol O2 mol−1	278	Chen et al. (2014)
O2 concentration at the site of carboxylation	O	mmol O2 mol−1	210	Chen et al. (2014)
Coefficient relating Nph to gmmax	r gm	mol CO2 mmol−1 N s−1	1.64 × 10–3 (5.27 × 10–4)	—
Minimum gmmax	r gm0	mol CO2 m−2 s−1	0.140 (0.0345)	—
Coefficient related to the decrease in Rd by growth respiration	R g	m2 d °Cd−1 mol−1 photon	4.16 × 10–4 (4.52 × 10–5)	—
Coefficient related to the increase in Rd by maintenance respiration	R m	μmol CO2 d °Cd−1 mol−1 photons s−1	1.88 × 10–4 (1.61 × 10–5)	—
Coefficient relating ILd to maximum Rd	R max	μmol CO2 μmol−1 photons s−1	0.308 (0.028)	—
Conversion efficiency of photons to J	ϕ	µmol e– µmol−1 photons	0.340 (2.5 × 10–3)	—
Convexity coefficient	θ	—	0.7	Chen et al. (2014)
Leaf age when gmmax occurs	t gm	°Cd	121 (8.1)	—
Standard deviation of the dependence of gm–t curve	v gm	—	0.860 (0.063)	—

Standard errors (SE) are indicated in parentheses.

The degradation rate D is governed by first-order kinetics (Verkroost and Wassen, 2005; Li ) with a degradation constant Dr, (°n class="Chemical">Cd−1):

The variable n class="Chemical">Smax, inpan> Eq. (5) is a function of daily light inpan>terception (ILd, mol photons m−2 d−1):

where Smm, (mmol N m−2 °n class="Chemical">Cd−1) is the potenpan>tial maximum proteinpan> synthesis rate and kI, is the rate constant describinpan>g the inpan>crease of n class="Chemical">Smax, with ILd. The factor rN, increases with nitrogen level in the nutrient solution (NS, mM) by a Michaelis–Menten constant, kN, (mM):

Modelling leaf photosynthesis

Photosynthetic parameters Vcmax, Jmax, and Chl were estimated from functional n class="Chemical">nitrogen pools NV, NJ, anpan>d NC, usinpan>g Eq. (2a–c). The net photosynpan>thetic rate (A, μmol pan> class="Chemical">CO2 m−2 s−1) is defined as the minimum of RuBP carboxylation-limited (Ac, mmol CO2 m−2 s−1) and RuBP regeneration-limited (Aj, mmol CO2 m−2 s−1) net photosynthetic rate (Farquhar ):

where Cc (μmol CO2 mol−1) is the chloroplastic CO2 concentration, Γ* (μmol CO2 mol−1) is the CO2 compensation point in the absence of dark respiration, Kc (μmol CO2 mol−1) and Ko (mmol O2 mol−1) are Michaelis–Menten constants of Rubisco for CO2 and O2, respectively, O (mmol O2 mol−1) is the O2 concentration at the site of carboxylation, Vc (μmol CO2 m−2 s−1) is carboxylation rate, and J (μmol e− m−2 s−1) is electron transport rate. Daytime respiration rate Rd (μmol CO2 m−2 s−1) is assumed to vary with t and the mean ILd during the previous 4 d (ILd4d):

where Rmax (μmol CO2 d mol−1 photons s−1) relates ILd4d to the maximum Rd, Rg (m2 d °Cd−1 mol−1 photons) influences the decrease in the growth respiration, and Rm (μmol CO2 d °Cd−1 mol−1 photons s−1) affects the increase in the maintenance respiration with t.

V c and J are calculated from Vcmax and Jmax, respectively, depending on the photosynthetic photon flux density (PPFD) incident on the leaf (ILc, µmol photons m–2 s–1) according to Qian and Ögren and Evans (1993), respectively:

where ϕ (µmol e– µmol photons−1) is the conversion efficiency of photons to J, and θ (unitless) is a constant convexity factor describing the response of J to ILc. Leaf absorptance (α, unitless) is related to Chl (Evans, 1993):

Chloroplastic CO2 concenpan>tration depenpan>ds on the steady-state of stomatal conductance (gsc, mol CO2 m−2 s−1) and mesophyll conductance (gm, mol CO2 m−2 s−1) to CO2:

where Ca (μmol n class="Chemical">CO2 mol−1) is atmospheric n class="Chemical">CO2 concentration, and gsc is calculated with species-specific constants of stomatal conductance, g0 and g1 (Chen ), and leaf-to-air vapor pressure deficit (D, kPa, Medlyn ):

Mesophyll conductance is expressed as a log-normal function of t (Chen ), where n class="Chemical">gm first inpan>creases durinpan>g leaf developmenpan>t and decreases durinpan>g ageinpan>g (Flexas ):

where tn class="Chemical">gm is the t whenpan> the maximum n class="Chemical">gm (gmmax, mol CO2 m−2 s−1) occurs and vgm is the standard deviation of the curve; gmmax is linearly related to Nph, since a similar relationship has been reported for C3 plants (e.g. Yamori ):

where rn class="Chemical">gm (mol n class="Chemical">CO2 mmol−1 N s−1) describes the rate of increase of gmmax in relation to Nph, and rgm0 (mol CO2 m−2 s−1) is the minimum gmmax.

The steady-state Ac was solved analytically with Eqs (9b), (14), and (15), and Aj with Eqs (9c), (14), and (15), following Moualeu‐Ngangue . Model variables and coefficients are listed in Tables 1–3.

Growth chamber experiment to investigate the dynamics of photosynthetic protein turnover

n class="Species">Cucumber (pan> class="Species">Cucumis sativus ‘Aramon’, Rijk Zwaan, De Lier, The Netherlands) plants were grown in two experiments at the Institute of Horticultural Production Systems, Leibniz Universität Hannover, Germany (latitude 52.4°N).

One growth chamber experiment was conducted from 21 October n class="Species">to 9 December 2016 with factorial combinpan>ationpan>s of three light anpan>d three pan> class="Chemical">nitrogen supply levels to parameterize the photosynthetic protein turnover model (see below). Cucumber seeds were sown in rock-wool cubes (36 × 36 × 40 mm) on 5 October. Eight days later, seedlings were transplanted to larger rock-wool cubes (10 × 10 × 6.2 cm) for another 8 d until the second true leaves appeared (leaf length ≥3 cm). Plants were transferred into 25 litre plastic containers (one plant per container) on 21 October and cultivated hydroponically with a 12 h light period and 24 °C day/20 °C night air temperature. Three nitrogen levels, 9.6, 4.6 and 2.3 mM, were supplied using Ca(NO3)2 and Ferty Basisdünger 1 (Planta GmbH, Regenstauf, Germany, 5.2 mM K, 1.3 mM P, 0.82 mM Mg in working solution). Nutrient solution was replaced weekly and adjusted to pH 6.0–6.5 two times a week. Three constant light conditions with daily photosynthetic photon integrals (DPI) of 28.9, 14.2, and 4.4 mol photons m−2 d−1 were provided using metal halide lamps. Four plants were grown under each treatment combination. Three leaves per plant (between leaf ranks four to eight, counted acropetally) were maintained horizontally and well exposed to incoming light using custom-made leaf holders, while the rest of the shoot was trained downward to avoid mutual shading. Gas exchange (see below) and relative chlorophyll content (SPAD-502; Minolta Camera, Japan) were measured at different thermal ages of the leaves, ranging from 45 °Cd to 558 °Cd, calculated by subtracting a base temperature of 10 °C (Savvides ) from mean daily air temperature around the leaf. Air temperature was recorded continuously using data loggers (Tinytag; Gemini Data Loggers, Chichester, UK). After gas exchange measurements, leaves were harvested for leaf area and nitrogen analyses.

Greenhouse experiment to evaluate optimality of nitrogen distribution and partitioning

One greenhouse experiment was carried out from 4 April to 12 May 2017 under two light regimes and two n class="Chemical">nitrogen supply levels to evaluate the model performanpan>ce anpan>d to collect inpan>put data for optimality anpan>alyses. Seeds were sown onpan> 14 March anpan>d tranpan>splanpan>ted to larger rock-wool cubes onpan> 22 March. After the third true leaves had appeared, planpan>ts were tranpan>sferred onpan>to rock-wool slabs onpan> 4 April with planpan>t denpan>sity of 1.33 planpan>ts m−2 anpan>d supplied with two pan> class="Chemical">nitrogen concentrations, 10 mM (high nitrogen, HN) and 2.5 mM (low nitrogen, LN), by drip irrigation using the same fertilizers as described in the growth chamber experiment. During the experimental period, average nitrogen supply was calculated from the nitrogen concentration in the nutrient supply and rock-wool slabs, which was 8.2 and 2.0 mM for HN and LN, respectively. Plants were grown under either high light (HL) or low light (LL) regimes. The southern half of the greenhouse was unshaded as the HL regime. The LL regime was created in the northern half of the greenhouse by shading nets to reduce incoming light from top and sides, where PPFD was reduced on average to ca. 40% of that under HL (38 ± 1.3% under sunny and 42 ± 0.2% under cloudy condition). Average DPI above the canopy was 21.4 and 8.5 mol photons m−2 d−1 for HL and LL, respectively, during the experimental period. DPI during the experimental period was recorded by the weather station located above the greenhouse. An average light transmittance of 49.8% through the greenhouse structure was applied (39.2% on a sunny day and 60.4% on a cloudy day). Air temperature in the middle canopy was recorded continuously using data loggers and was significantly higher under HL (0.5 °Cd per day). Gas exchange measurements and harvests were conducted at four time points on 21 April, 28 April, 5 May, and 12 May at two different canopy layers with two replications. Leaf age at measurement ranged from 77 to 414 °Cd. Leaf elevation angle was obtained by a 3D digitizer (Fastrak; Polhemus, Colchester, VT, USA) according to Chen . Leaves were harvested after gas exchange measurements to determine leaf area index (LAI, m2 m−2).

Gas exchange measurements and estimation of photosynthetic parameters

Light-saturated net photosynthetic rate under PPFD of 1300 µmol photons m−2 s−1 (A1300, μmol n class="Chemical">CO2 m−2 s−1) anpan>d light responpan>se curves were measured usinpan>g a portable photosynpan>thesis system (LI-6400XT; Li-Cor Inpan>c., Linpan>colnpan>, NE, USA). All measuremenpan>ts were carried out under sample pan> class="Chemical">CO2 400 µmol mol−1, leaf temperature 25 °C and relative humidity 55–65%. Rd was estimated from the linear portion of the light response curve (Kok, 1948). Vcmax was estimated using the one-point method (Wilson ; De Kauwe ), and Jmax and ϕ by least squares fitting to a non-rectangular hyperbola (Ögren and Evans, 1993). Mesophyll conductance was estimated using the variable J method (Harley ). Chlorophyll fluorescence was measured using the multiphase flash approach (Loriaux ) following Moualeu‐Ngangue et al. (2017).

Nitrogen analyses and photosynthetic nitrogen partitioning estimation

Leaf samples obtained in the growth chamber experiment were freeze-dried and ground into a fine powder for n class="Chemical">nitrogen anpan>alyses. Total leaf pan> class="Chemical">nitrogen was analysed using the Kjeldahl method (Nelson and Sommers, 1980). Leaf chlorophyll was extracted with 96% ethanol and analysed colorimetrically (Lichtenthaler, 1987). Relationships between relative chlorophyll content (SPAD) and Chl were determined (Supplementary Fig. S2) for estimating Chl in the greenhouse experiment.

Model parameterization

The differential equations (4)–(6) were solved and the coefficients were quantified using R (version 3.3.0; R Foundation for Statistical Computing, Vienna, Austria) by using the packages ‘deSolve’ and ‘DEoptim’, which minimizes the sums of squares of the residuals between observations and simulations. The data obtained in the growth chamber experiment were used for the parameterization. Dr, and td, were first quantified for each pool using data of all treatments. With the determined values of Dr, and td,, n class="Chemical">Smax, was thenpan> quanpan>tified for each treatmenpan>t. Smm,, kI,, anpan>d kN, were determinpan>ed from pan> class="Chemical">Smax, [Eqs (7) and (8)] by least squares fitting in SigmaPlot (version 11.0, Systat software GmbH, Erkrath, Germany) as well as the influences of t and ILd on Rd [Eq. (10)] and gm [Eqs (16) and (17)].

Dynamic leaf photosynthetic nitrogen simulation and model evaluation

Daily environmental information during the experimental period (Supplementary Fig. S3) and the canopy information obtained at the four harvests, including age and area of each leaf, were used as input to simulate photosynthetic n class="Chemical">nitrogen per unit leaf area (Nph, mmol N m−2), photosynpan>thetic pan> class="Chemical">nitrogen per leaf (Nleaf, mmol N) and total leaf photosynthetic nitrogen content of the canopy (Ncanopy, mmol N). First, leaf elevation angle of each leaf and LAI were simulated empirically depending on t (Supplementary Fig. S4). Second, for each time step, the daily light interception ILd at the leaf was calculated and used in Eq. (7) to simulate protein turnover. Light interception was calculated by the Beer–Lambert law (Monsi and Saeki, 1953) with a light extinction coefficient of 0.695 and adjusted by the cosine of leaf elevation angle. For model evaluation, root mean squared deviation (RMSD) and accuracy (%) were determined for photosynthetic parameters, Nph, and p predictions following Kahlen and Stützel (2011).

Simulating daily canopy carbon assimilation

Daily canopy n class="Chemical">carbon assimilationpan> durinpan>g daytime (pan> class="Chemical">DCA, mol CO2 d−1) was simulated using greenhouse canopy characteristics obtained at the last harvest as input (Supplementary Table S1; Supplementary Fig. S5). Leaf-to-air vapor pressure deficit (D) 1.2 kPa and Ca 400 μmol CO2 mol−1 were used in all simulations, similar to the environmental conditions during the gas exchange measurements. Scenarios with different DPI levels were defined for simulating DCA. Up to six DPI levels were taken as relative to the average DPI during acclimation (aDPI) to simulate the influence of day-to-day DPI fluctuation on DCA. To simulate DCA, diurnal PPFD above the canopy was simulated for a given DPI level with a time step of 0.1 h by a simple cosine bell function (Kimball and Bellamy, 1986) with 14.4 h day length.

Modifying photosynthetic nitrogen distribution and partitioning

To evaluate the effects of between-leaf distribution and within-leaf partitioning of Nph on n class="Chemical">DCA, a distribution factor fd was inpan>troduced inpan>to Eq. (5) to create variations inpan> the rate of proteinpan> synthesis, and a partitioninpan>g factor fp, was inpan>troduced inpan>to Eq. (7) to create variations inpan> the maximum proteinpan> synthesis rate of differenpan>t functional pools:

A control condition was defined with fd=1 and fp,=1, when all coefficients in the synthesis process (Table 1) remained unmodified. Increasing fd accelerates the decrease in the rate of protein synthesis and enhances n class="Disease">acropetal Nph reallocation. An inpan>crease inpan> fp, results inpan> a higher rate of synpan>thesis of N anpan>d inpan>creases the partitionpan>inpan>g to pool X. A modified partitionpan>inpan>g patternpan> that maximized pan> class="Chemical">DCA was identified as optimal for several DPI levels, and the optimal values of fp, were determined using the package ‘DEoptim’ in R. The change in DCA caused by modified distribution or optimal partitioning of Nph was compared with the control conditions. The ratios between optimal and control partitioning fractions of each pool X, as well as the contributions of daily leaf carbon assimilation (DLA) to the DCA increase were calculated along the canopy depth.

Results

Mechanistic model aims to quantify the environmental effects of light and nitrogen availabilities and developmental effects on photosynthetic protein turnover

In the model, we assume that photosynthetic protein turnover is under genetic and environmental control. The genetic control is characterized by the potential maximum protein synthesis rate Smm, coefficient td, and protein degradation constant, Dr. The coefficient td affects the decrease in the rate of synthesis, and Dr contributes to the degradation rate, which together influence the developmental effect on protein turnover dynamics. The low value of td (0.001–0.002 °n class="Chemical">Cd−1, Table 1) suggests that the inpan>fluenpan>ce of ageinpan>g appears rather late inpan> the leaf lifespanpan> under a conpan>stanpan>t light enpan>vironpan>menpan>t. The coefficienpan>t Dr was found to be the same for the carboxylationpan> pool (NV) anpan>d the electronpan> tranpan>sport pool (NJ), while the light harvestinpan>g pool (NC) had a lower Dr (Table 1). The genpan>otypic senpan>sitivities to light anpan>d pan> class="Chemical">nitrogen availabilities are characterized by kI and kN, respectively. Collectively, Smm, kI, and kN determine the maximum protein synthesis rate Smax in Eq. (7). When light was increased 2.5-fold (from LL to HL), Smax increased by 50% in NV and NJ, and by 10% in NC, while nitrogen level had less influence on Smax (<10%), which only occurred under low nitrogen concentration (<3.5 mM) and the higher light intensity (Fig. 1), showing that light had a major control of Smax. NC had the highest kI (Table 1); consequently, Smax,C approached saturation at lower light intensity than Smax,V and Smax,J (Fig. 1). Smax,V and Smax,J were well coordinated in response to light and nitrogen level (Fig. 1A, B), but the higher kI and kN of NV (Table 1) suggested that NV synthesis is more sensitive to the variation in light and nitrogen availabilities than NJ.

Fig. 1.

Simulated effects of daily light interception (ILd, mol photons m−2 d−1) and nitrogen supply level in the nutrient solution (NS, mM) on maximum protein synthesis rate (Smax,) in Eq. (7) using coefficients from Table 1, of (A) the carboxylation, (B) the electron transport and (C) the light harvesting pools. The colors denote the normalized maximum protein synthesis rate, which is Smax, normalized by the potential maximum protein synthesis rate (Smm,) in Eq. (7). The data obtained in the growth chamber experiment were used for the parameterization. The arrows above and beside the figures indicate the corresponding average environmental conditions in the greenhouse experiment: high light (HL) 21.4 mol photons m−2 d−1; low light (LL) 8.5 mol photons m−2 d−1; high nitrogen (HN) 8.2 mM; low nitrogen (LN) 2.0 mM.

Simulated effects of daily light interception (ILd, mol photons m−2 d−1) and n class="Chemical">nitrogen supply level inpan> the nutrienpan>t solutionpan> (NS, mM) onpan> maximum proteinpan> synpan>thesis rate (pan> class="Chemical">Smax,) in Eq. (7) using coefficients from Table 1, of (A) the carboxylation, (B) the electron transport and (C) the light harvesting pools. The colors denote the normalized maximum protein synthesis rate, which is Smax, normalized by the potential maximum protein synthesis rate (Smm,) in Eq. (7). The data obtained in the growth chamber experiment were used for the parameterization. The arrows above and beside the figures indicate the corresponding average environmental conditions in the greenhouse experiment: high light (HL) 21.4 mol photons m−2 d−1; low light (LL) 8.5 mol photons m−2 d−1; high nitrogen (HN) 8.2 mM; low nitrogen (LN) 2.0 mM.

Effects of light and nitrogen availabilities on maximal protein synthesis rate explain the dynamics of photosynthetic acclimation

We evaluated the model using a greenhouse experiment, where leaves grown under combinations of two light regimes (HL and LL) and two nitrogen levels (HN and LN) were measured inpan> two canopy layers weekly for four consecutive weeks. The model predicted leaf photosynthetic characteristics with high accuracy (70–91%, Fig. 2) and a trenpan>d of photosynthetic acclimation (Supplemenpan>tary Fig. S6) similar to the experimenpan>tal observations (Fig. 3), except for slight overestimations inpan> photosynthetic nitrogen (Nph, Fig. 2C), carboxylation pool (Fig. 2D, G), and chlorophyll (Fig. 2F).

Fig. 2.

Comparisons between simulated and observed leaf photosynthetic parameters. (A) Light-saturated net photosynthetic rate under PPFD 1300 µmol photons m−2 s−1 (A1300, µmol CO2 m−2 s−1); (B) daytime respiration rate (Rd, µmol CO2 m−2 s−1); (C) leaf photosynthetic nitrogen (Nph, mmol N m−2); (D) maximum carboxylation rate (Vcmax, µmol CO2 m−2 s−1); (E) maximum electron transport rate (Jmax, µmol e− m−2 s−1); (F) chlorophyll (Chl, mmol Chl m−2); (G) partitioning fraction of the carboxylation pool (pV); (H) partitioning fraction of the electron transport pool (pJ); and (I) partitioning fraction of the light harvesting pool (pC). The observed data were obtained in the greenhouse experiment. The dotted grey lines are one-to-one lines. Root mean squared deviation (RMSD) and accuracy of the predictions are shown (see Materials and methods).

Fig. 3.

Comparisons of leaf photosynthetic nitrogen (Nph, mmol N m−2; A, B), partitioning fractions of the carboxylation pool (pV; C, D), the electron transport pool (pJ; E, F), and the light harvesting pool (pC; G, H) between high and low nitrogen supply (HN and LN, respectively; A, C, E, G) and between high and low light conditions (HL and LL, respectively; B, D, F, H). Each point represents the measurements in the greenhouse experiment obtained from a comparable canopy layer. The orange open circles indicate leaves grown under HL, the black closed circles indicate LL, the blue open squares indicate HN and the black closed squares indicate LN. The size of the circles increases with leaf age, ranging from 77 °Cd to 414 °Cd. The solid lines show the linear regression y=ax + b. The P values of the slope a are shown. The values of a are specified with 95% confidence intervals when they are significantly different from 1. The dotted grey lines are one-to-one lines.

Comparisons between simulated and observed leaf photosynthetic parameters. (A) Light-saturated net photosynthetic rate under PPFD 1300 µmol photons m−2 s−1 (A1300, µmol n class="Chemical">CO2 m−2 s−1); (B) daytime respirationpan> rate (Rd, µmol pan> class="Chemical">CO2 m−2 s−1); (C) leaf photosynthetic nitrogen (Nph, mmol N m−2); (D) maximum carboxylation rate (Vcmax, µmol CO2 m−2 s−1); (E) maximum electron transport rate (Jmax, µmol e− m−2 s−1); (F) chlorophyll (Chl, mmol Chl m−2); (G) partitioning fraction of the carboxylation pool (pV); (H) partitioning fraction of the electron transport pool (pJ); and (I) partitioning fraction of the light harvesting pool (pC). The observed data were obtained in the greenhouse experiment. The dotted grey lines are one-to-one lines. Root mean squared deviation (RMSD) and accuracy of the predictions are shown (see Materials and methods).

Comparisons of n class="Disease">leaf photosynthetic nitrogenpan> (Nph, mmol N m−2; A, B), partitionpan>inpan>g fractionpan>s of the carboxylationpan> pool (pV; C, D), the electronpan> tranpan>sport pool (pJ; E, F), anpan>d the light harvestinpan>g pool (pC; G, H) betweenpan> high anpan>d low pan> class="Chemical">nitrogen supply (HN and LN, respectively; A, C, E, G) and between high and low light conditions (HL and LL, respectively; B, D, F, H). Each point represents the measurements in the greenhouse experiment obtained from a comparable canopy layer. The orange open circles indicate leaves grown under HL, the black closed circles indicate LL, the blue open squares indicate HN and the black closed squares indicate LN. The size of the circles increases with leaf age, ranging from 77 °Cd to 414 °Cd. The solid lines show the linear regression y=ax + b. The P values of the slope a are shown. The values of a are specified with 95% confidence intervals when they are significantly different from 1. The dotted grey lines are one-to-one lines.

Photosynthetic acclimation in the greenhouse canopies as influenced by the interplay between light, n class="Chemical">nitrogen level anpan>d leaf age was examinpan>ed (Fig. 3). Light had positive effects onpan> Nph (Fig. 3A), the partitionpan>inpan>g fractionpan>s of NV (pV, Fig. 3C) anpan>d NJ (pJ, Fig. 3E) but negative effects onpan> the partitionpan>inpan>g fractionpan> of NC (pC, Fig. 3G). This negative effect of light onpan> pC canpan> be explainpan>ed by the high kI of NC (Table 1), which leads to anpan> saturationpan> of pan> class="Chemical">Smax,C under lower light (Fig. 1). The changes in Nph, pV, pJ, and pC with leaf age were similar to those with light (Fig. 3) due to the association in the gradients of age and light.

In comparison with HN, Nph under LN was significantly lower in the young leaves but similar in the old leaves (Fig. 3A). In the greenhouse, young leaves developed under high light intensity, which increased the sensitivity of n class="Chemical">Smax to pan> class="Chemical">nitrogen level (Fig. 1). During the simultaneous increase in leaf age and mutual shading, the effects of nitrogen supply on Smax became less prevalent (Fig. 1). Nitrogen level had less influence on functional partitioning (Fig. 3C, E, G) than light (Fig. 3D, F, H).

Photosynthetic nitrogen distribution is close to optimum and the effect of nitrogen reallocation is more prominent under limited nitrogen availability

The influence of Nph distribution pattern along the canopy depth on daily canopy n class="Chemical">carbon assimilationpan> (pan> class="Chemical">DCA, mol CO2 d−1) was evaluated by introducing a distribution factor fd to create variations in the rate of protein synthesis. In our model, protein synthesis and degradation rates determined simultaneously (i) total leaf photosynthetic nitrogen content of the canopy (Ncanopy, mmol N), (ii) Nph distribution in the canopy, and (iii) Nph partitioning fractions of pools X (p) in the leaf. Thus, it was impossible to modify single elements while maintaining the other two constant. Increasing fd led to a faster reduction of Nph during leaf ageing and more acropetal Nph reallocation. However, it also reduced Ncanopy and tended to increase pC (data not shown). Therefore, to obtain the leaf photosynthetic nitrogen content (Nleaf,, mmol N in leaf i) with comparable Ncanopy, simulated Nleaf, with fd=n (denoted as N′leaf,) was adjusted proportionally to the ratio between Ncanopy calculated with fd=1 and with fd=n:

p was set equal to the control value:

These adjustments assured the same amount of Ncanopy among the distribution patterns. The factor fd was varied between 0.5 and 5.0 at intervals of 0.5 in the simulation, which gave values of Nph comparable to those measured in n class="Species">cucumber leaves (22–135 mmol N m−2; Fig. 4). Canpan>opy Nph distributionpan>s with enpan>hanpan>ced pan> class="Chemical">acropetal reallocation were created by increasing fd (Fig. 4; Supplementary Fig. S7). In general, the distribution of Nph corresponded to the vertical light distribution except in the expanding leaves in the upper canopy, and the Nph distribution with light was steeper under LL (Supplementary Fig. S7).

Fig. 4.

Leaf photosynthetic nitrogen (Nph, mmol N m−2) distributions along the canopy depth, characterized by leaf area index (LAI, m2 m−2). Variations in nitrogen distribution were created using a distribution factor fd ranging from 0.5 to 5.0 at intervals of 0.5 in Eq. (18) under different growth conditions. (A) High nitrogen and high light (HN+HL); (B) high nitrogen and low light (HN+LL); (C) low nitrogen and high light (LN+HL); (D) low nitrogen and low light (LN+LL). Simulated control Nph distributions (fd=1) are indicated by the green lines.

n class="Disease">Leaf photosynthetic nitrogenpan> (Nph, mmol N m−2) distributions along the canopy depth, characterized by leaf area inpan>dex (LAI, m2 m−2). Variations inpan> n class="Chemical">nitrogen distribution were created using a distribution factor fd ranging from 0.5 to 5.0 at intervals of 0.5 in Eq. (18) under different growth conditions. (A) High nitrogen and high light (HN+HL); (B) high nitrogen and low light (HN+LL); (C) low nitrogen and high light (LN+HL); (D) low nitrogen and low light (LN+LL). Simulated control Nph distributions (fd=1) are indicated by the green lines.

To simulate the natural fluctuations in light between days, three light levels representing 200% (n class="Chemical">aDPI200), 100% (pan> class="Chemical">aDPI100) and 50% (aDPI50) of average DPI during acclimation (aDPI) were used in the DCA simulation. Under aDPI100 and aDPI50, enhancing acropetal Nph reallocation did not significantly increase DCA (<5%), suggesting that Nph distribution was optimal under constant and decreasing DPI (Fig. 5B, C). More acropetal reallocation did not improve the optimality in Nph distribution in terms of maximizing DCA since a large proportion of leaf area was located in the middle-lower to lower canopy (Supplementary Fig. S5). However, enhancing Nph reallocation resulted in an increase in DCA by 7% under LN at aDPI200 (Fig. 5A), indicating that acropetal Nph reallocation was more important under LN than HN.

Fig. 5.

Effects of photosynthetic nitrogen (Nph) distributions with different values of fd (Fig. 4) on daily canopy carbon assimilation (DCA) under different daily photosynthetic photon integrals (DPI, mol photons m−2 d−1) relative to average DPI during acclimation (aDPI). (A) Two-fold aDPI (aDPI200); (B) aDPI (aDPI100); (C) half aDPI (aDPI200). Acropetal Nph reallocation increases with fd. Plants grown under high nitrogen and high light (HN+HL, orange open circles), under high nitrogen and low light (HN+LL, black closed circles), under low nitrogen and high light (LN+HL, orange open triangles), and under low nitrogen and low light (LN+LL, black closed triangles) are compared under given DPI. The relative change in DCA was calculated by dividing the DCA obtained with a given Nph distribution by the DCA obtained with the control Nph distribution (fd=1) under same DPI. A change within ±5% (grey shading) is considered insignificant.

Effects of photosynthetic n class="Chemical">nitrogen (Nph) distributionpan>s with differenpan>t values of fd (Fig. 4) onpan> daily canpan>opy pan> class="Chemical">carbon assimilation (DCA) under different daily photosynthetic photon integrals (DPI, mol photons m−2 d−1) relative to average DPI during acclimation (aDPI). (A) Two-fold aDPI (aDPI200); (B) aDPI (aDPI100); (C) half aDPI (aDPI200). Acropetal Nph reallocation increases with fd. Plants grown under high nitrogen and high light (HN+HL, orange open circles), under high nitrogen and low light (HN+LL, black closed circles), under low nitrogen and high light (LN+HL, orange open triangles), and under low nitrogen and low light (LN+LL, black closed triangles) are compared under given DPI. The relative change in DCA was calculated by dividing the DCA obtained with a given Nph distribution by the DCA obtained with the control Nph distribution (fd=1) under same DPI. A change within ±5% (grey shading) is considered insignificant.

It was observed that Nph was more overestimated in the older leaves than in the younger ones (Fig. 2C), which indicated that our model tended to underestimate the n class="Disease">acropetal Nph reallocation whenpan> scalinpan>g up from leaf to canpan>opy level. Inpan> order to mainpan>tainpan> a conpan>stanpan>t light enpan>vironpan>menpan>t for the measured leaves inpan> the growth chamber experimenpan>t, leaves younger thanpan> the sampled leaves were trainpan>ed downward anpan>d their light inpan>terceptionpan>, together with their pan> class="Chemical">nitrogen demand, was inevitably reduced; therefore, the model coefficients were obtained from the leaves with limited nitrogen reallocation. However, underestimating acropetal Nph reallocation would not affect our result that Nph distribution was close to optimum.

Suboptimal nitrogen partitioning is due to daily light fluctuation

To find the optimal within-leaf Nph partitioning between functions, the potential maximal protein synthesis rate for pool X was modified by a factor fp,, ranging from 0.2 to 2.0. Increasing fp, resulted in higher protein synthesis rates, but it also increased Ncanopy and the proportion of n class="Chemical">nitrogen distributed inpan> the upper canpan>opy. After simulatinpan>g pan> class="Chemical">nitrogen partitioning with a modified fp,, Nleaf of each leaf was re-assigned to their control values that were obtained with fp,=1. Partitioning patterns with maximal DCA at six DPI levels (25–400% aDPI) were identified as optimal and the maximal DCA was compared with control DCA (Fig. 6). The increase in DCA by optimal partitioning was insignificant (<5%) when DPI was close to aDPI (indicated by the arrows in Fig. 6). This suggested the ability of plants to maximize DCA by optimizing Nph partitioning to aDPI. Nph partitioning deviated further from optimum when DPI diverged from aDPI (Fig. 6). Therefore, strong day-to-day light fluctuation induced suboptimality in Nph partitioning and led to lower PNUE.

Fig. 6.

Increase in daily canopy carbon assimilation (DCA) by optimizing photosynthetic nitrogen (Nph) partitioning for different growth conditions under various daily photosynthetic photon integrals (DPI, mol photons m−2 d−1). The increase in DCA was the DCA with the optimal partitioning under a given DPI in comparison with the control partitioning [fp,=1 in Eq. (19)]. An increase less than 5% (grey shading) is considered insignificant. The average DPI during acclimation (aDPI) is indicated by the orange arrow for HL (21.4 mol photons m−2 d−1) and by the black arrow for LL (8.5 mol photons m−2 d−1). The asterisks indicate the scenarios compared in Figs 7, 8 and Table 4 with 50%, 100% and 200% aDPI. The symbols and colors used here are the same as those in Fig. 5.

Increase in daily canopy n class="Chemical">carbon assimilationpan> (pan> class="Chemical">DCA) by optimizing photosynthetic nitrogen (Nph) partitioning for different growth conditions under various daily photosynthetic photon integrals (DPI, mol photons m−2 d−1). The increase in DCA was the DCA with the optimal partitioning under a given DPI in comparison with the control partitioning [fp,=1 in Eq. (19)]. An increase less than 5% (grey shading) is considered insignificant. The average DPI during acclimation (aDPI) is indicated by the orange arrow for HL (21.4 mol photons m−2 d−1) and by the black arrow for LL (8.5 mol photons m−2 d−1). The asterisks indicate the scenarios compared in Figs 7, 8 and Table 4 with 50%, 100% and 200% aDPI. The symbols and colors used here are the same as those in Fig. 5.

Fig. 7.

Ratio between optimal and control partitioning fractions (optimal p/control p) of the carboxylation pool (pV, orange circles), the electron transport pool (pJ, red triangles), the light harvesting pool (pC, green squares), and contributions of daily leaf carbon assimilation (DLA) to the daily canopy carbon assimilation (DCA) increase by optimal partitioning (grey bars, right y-axis) along the canopy depth [leaf area index (LAI) m2 m−2] under 200% average daily photosynthetic photon integral during acclimation (aDPI200) for plants grown under (A) high nitrogen and high light (HN+HL), (B) high nitrogen and low light (HN+LL), (C) low nitrogen and high light (LN+HL), (D) low nitrogen and low light (LN+LL) conditions. Photosynthetic nitrogen partitioning is close to optimum for HN+LL and LN+LL under aDPI200, which corresponds to a DPI of 42.7 and 17.1 mol photons m−2 d−1 for HL and LL, respectively. See Table 4 for the increase in DCA by the optimal partitioning.

Fig. 8.

Ratio between optimal and control partitioning fractions (optimal p/control p), and contributions of daily leaf carbon assimilation (DLA) to the daily canopy carbon assimilation (DCA) increase by optimal partitioning (grey bars, right y-axis) along the canopy depth [leaf area index (LAI) m2 m−2] under 50% average daily photon integral during acclimation (aDPI50) for plants grown under (A) high nitrogen and high light (HN+HL), (B) high nitrogen and low light (HN+LL), (C) low nitrogen and high light (LN+HL), (D) low nitrogen and low light (LN+LL) conditions. Photosynthetic nitrogen partitioning is close to optimum for LN+HL under aDPI50, which corresponds to a DPI of 10.7 and 4.3 mol photons m−2 d−1 for HL and LL, respectively. The symbols and colors used here are the same as those in Fig. 7. See Table 4 for the increase in DCA by the optimal partitioning.

Table 4.

Increase in the daily canopy carbon assimilation (DCA) by optimized photosynthetic nitrogen distribution or partitioning under various daily photosynthetic photon integrals (DPI, mol photons m−2 d−1) for canopies grown under different conditions

Growth condition	Light level		Control DCA	Increase in DCA (%) by optimized
	aDPI level (%)	DPI	(mol CO2 d−1)	Distribution	Partitioning
HN+HL	200	42.7	0.5467	<5%	6.3%
	100	21.4	0.3217	<5%	<5%
	50	10.7	0.1368	<5%	7.1%
HN+LL	200	17.1	0.2554	<5%	<5%
	100	8.5	0.1195	<5%	<5%
	50	4.3	0.0259	<5%	23.6%
LN+HL	200	42.7	0.4011	7.0%	12.7%
	100	21.4	0.2653	<5%	<5%
	50	10.7	0.1221	<5%	<5%
LN+LL	200	17.1	0.2261	6.9%	<5%
	100	8.5	0.1108	<5%	<5%
	50	4.3	0.0215	<5%	25.0%

Average DPI during acclimation (100% aDPI), 200% and 50% aDPI were tested. The increase in DCA for plants grown under the combinations of high nitrogen (HN), high light (HL), low nitrogen (LN), and low light (LL) was calculated by comparing the DCA between optimal and control distribution or partitioning.

Increase in the daily canopy n class="Chemical">carbon assimilationpan> (pan> class="Chemical">DCA) by optimized photosynthetic nitrogen distribution or partitioning under various daily photosynthetic photon integrals (DPI, mol photons m−2 d−1) for canopies grown under different conditions

Average n class="Chemical">DPI durinpan>g acclimationpan> (100% pan> class="Chemical">aDPI), 200% and 50% aDPI were tested. The increase in DCA for plants grown under the combinations of high nitrogen (HN), high light (HL), low nitrogen (LN), and low light (LL) was calculated by comparing the DCA between optimal and control distribution or partitioning.

By optimizing Nph partitioning, n class="Chemical">DCA could be inpan>creased by pan> class="Chemical">nitrogen reinvestment in the limited functional pools. Under aDPI200, Nph partitioning was suboptimal under HL (Fig. 6), and this suboptimality was less under HN than under LN (Table 4). By reinvesting about half of NC into NV and NJ (Fig. 7A, C), DCA increased by 6% under HN and by 13% under LN (Table 4), as a result of increased carbon assimilation in the middle-lower canopy (Fig. 7A, C). Under aDPI50, HN did not reduce the suboptimality in Nph partitioning (Table 4) due to an underinvestment in the light harvesting function. Reinvesting NV into NC in the middle or upper canopy (HL, Fig. 8A; LL, 8B, 8D) increased DCA by 7–25% (Table 4).

Ratio between optimal and control partitioning fractions (optimal p/control p) of the carboxylation pool (pV, orange circles), the electron transport pool (pJ, red triangles), the light harvesting pool (pC, green squares), and contributions of daily leaf n class="Chemical">carbon assimilationpan> (DLA) to the daily canpan>opy pan> class="Chemical">carbon assimilation (DCA) increase by optimal partitioning (grey bars, right y-axis) along the canopy depth [leaf area index (LAI) m2 m−2] under 200% average daily photosynthetic photon integral during acclimation (aDPI200) for plants grown under (A) high nitrogen and high light (HN+HL), (B) high nitrogen and low light (HN+LL), (C) low nitrogen and high light (LN+HL), (D) low nitrogen and low light (LN+LL) conditions. Photosynthetic nitrogen partitioning is close to optimum for HN+LL and LN+LL under aDPI200, which corresponds to a DPI of 42.7 and 17.1 mol photons m−2 d−1 for HL and LL, respectively. See Table 4 for the increase in DCA by the optimal partitioning.

Ratio between optimal and control partitioning fractions (optimal p/control p), and contributions of daily leaf n class="Chemical">carbon assimilationpan> (DLA) to the daily canpan>opy pan> class="Chemical">carbon assimilation (DCA) increase by optimal partitioning (grey bars, right y-axis) along the canopy depth [leaf area index (LAI) m2 m−2] under 50% average daily photon integral during acclimation (aDPI50) for plants grown under (A) high nitrogen and high light (HN+HL), (B) high nitrogen and low light (HN+LL), (C) low nitrogen and high light (LN+HL), (D) low nitrogen and low light (LN+LL) conditions. Photosynthetic nitrogen partitioning is close to optimum for LN+HL under aDPI50, which corresponds to a DPI of 10.7 and 4.3 mol photons m−2 d−1 for HL and LL, respectively. The symbols and colors used here are the same as those in Fig. 7. See Table 4 for the increase in DCA by the optimal partitioning.

Discussion

This model is the first approach applying a dynamic protein turnover mechanism at the leaf level to assess the optimality and limitation in n class="Chemical">nitrogen use at the canpan>opy level. Here, maximized canpan>opy pan> class="Chemical">carbon assimilation is considered as a general indicator of maximizing fitness. The adaptation of the protein turnover mechanism gives reasonable predictions of optimal Nph and accurate predictions of leaf photosynthetic traits.

Mechanistic explanation of leaf nitrogen economics under a wide range of light and nitrogen availabilities

It is well documented that light has the major control of leaf economics. For example, specific leaf area, an integrative indicator of leaf structure that co-varies with leaf n class="Chemical">nitrogen conpan>tenpan>t (Antenpan> ), shows more plastic responpan>ses to light thanpan> to nutrienpan>t availability (Poorter ; Poorter ). Mechanpan>istic models canpan> be used to inpan>terpret measured biological data (Chenpan> , 2018), as inpan> our model here, providinpan>g a quanpan>titative explanpan>ationpan> of the differenpan>t plastic responpan>ses inpan> leaf pan> class="Chemical">nitrogen economics (e.g. photosynthetic nitrogen per unit leaf area, Nph, and photosynthetic capacities) to light and to nitrogen by their effects on the maximum protein synthesis rate (Smax, Fig. 1). A 5-fold increase in light (4–20 mol photons m−2 d−1) doubled Smax of the carboxylation pool (NV) and electron transport pool (NJ; Fig. 1A, B), which is similar to the published values (Niinemets ). In contrast, increasing nitrogen supply from 2 to 10 mM increased Smax of NV and NJ only by 20% and 16%, respectively. The effects of light on photosynthetic nitrogen can be quantitative (on Nph) or qualitative (on nitrogen partitioning, p; Niinemets ; Buckley ), while nitrogen only affected Nph by restricting Smax (Figs 1, 3). Similar effects of light and nitrogen availabilities on the partitioning between electron transport and light harvesting functions were observed in spinach (Terashima and Evans, 1988). Our model of protein turnover explains the photosynthetic acclimation to light and nitrogen supply and provides a mechanistic insight into leaf nitrogen economics.

In a growing canopy, leaf age is associated with decreasing light availability (Niinemets , Chen ). Therefore, leaf photosynthetic acclimation to light occurs together with leaf ageing, which is characterized by the protein degradation constant Dr and the constant td describing the decrease of protein synthesis rate in our model. The Dr values of NV and NJ fall within the range of in vivo quantifications reported by Peterson and Li . The low value of td (Table 1) explains the modest influence of ageing on leaf photosynthetic capacity observed under constant light conditions (Pettersen ).

Besides light and n class="Chemical">nitrogen availability, temperature has effects onpan> photosynpan>thetic pan> class="Chemical">nitrogen content and partitioning (Yamori ; Kattge and Knorr, 2007; Yamori ). Temperature dependency of developmental processes and biochemical reactions is often described by exponential or Arhenius-type functions (Parent ; Parent and Tardieu, 2012; Kahlen and Chen, 2015). In our model, temperature effects are considered partly by the temperature sum, which assumes a linear relationship between protein synthesis and leaf temperature. Since the exact temperature dependency of protein synthesis and degradation is unknown and our data are obtained from controlled environments with minimized temperature fluctuations, we apply the linear parsimonious approach to avoid speculation and overparameterization (Parent ).

Above-optimum Rubisco investment can be a mechanism to adapt canopy photosynthesis to short-term light fluctuations

Under sufficient n class="Chemical">nitrogen availability, pan> class="Gene">Rubisco can function as a storage protein, which means that the amount of Rubisco can exceed the requirements to support photosynthesis (Carmo-Silva ). The Rubisco pool has the highest value of kN (Table 1), indicating that Rubisco synthesis reacts with higher sensitivity to increasing nitrogen availability than the other two pools. This explains the increase in the ratio between Vcmax and Jmax with nitrogen availability (Hikosaka, 2004; Yamori ), especially under LL (Fig. 3C, E). Under HN, Rubisco storage is advantageous since light-induced Rubisco activation, having a time constant of 3–5 min (Portis ; Kaiser ), is much faster than Rubisco synthesis. Therefore, Rubisco storage can be a mechanism for quick adaptation to a sudden increase in light. This explains why the plants grown under HN have wider ranges of DPI, at which nitrogen partitioning is optimal, than those under LN (Fig. 6; Table 4). Furthermore, excluding Rubisco activation [Vc=Vcmax in Eq. (9b)] in the DCA simulation resulted in a 4-fold above-optimum investment in NV even under aDPI (data not shown). Since Rubisco is not an especially inefficient catalyst in comparison with other chemically related enzymes (Bathellier ), above-optimum Rubisco investment in the canopy can be rather a mechanism for adapting to short-term light fluctuation than a mechanism to overcome its enzymatic inefficiency.

Implications for crop model improvement and greenhouse management

Using plant models to understand crop performance requires knowledge of physiological mechanisms (Boote ; Poorter ). By integrating the known biological mechanism of protein turnover at the leaf level into a multi-layer model of canopy photosynthesis, we demonstrate the explanatory power of a mechanistic model for the measured biological data. Our simulations suggest that canopy photosynthesis can be increased by manipulating the functional pools related to photosynthesis. For example, investment in n class="Gene">Rubisco anpan>d electronpan> tranpan>sport (Ishimaru ; Yamori ) should be inpan>creased under inpan>creasinpan>g light (Fig. 7), anpan>d a larger anpan>tenpan>na size for light harvestinpan>g (Masuda ) is required under decreasinpan>g light availability (Fig. 8). It is clear that the patternpan> of optimal pan> class="Chemical">nitrogen partitioning depends strongly on light regime, and biosynthetic regulation is unlikely to keep up with daily light fluctuation (up to 4-fold difference; Supplementary Fig. S3).

In greenhouse cultivation, it is possible to achieve a more stable light environment using supplemental lighting. This can be a plausible solution to improve the vertical light distribution (Lu and Mitchell, 2016) and to minimize the suboptimality in n class="Chemical">nitrogen use inpan>duced by light fluctuationpan>. Sinpan>ce pan> class="Chemical">carbon assimilation is the rate-limiting step for yield production of cucumber plants due to the indeterminate production of vegetative and generative organs (Wiechers ), canopy carbon gain can be considered as an approximation for yield. Our simulation suggests that the suboptimal nitrogen partitioning induced by a 50% decrease in DPI can be compensated by reducing the light limitation of the shaded leaves using inter-row lighting during the high-light season (ca. 7% increase in DCA) and using top-lighting, possibly in combination with inter-lighting, during the low-light season (ca. 25% increase in DCA; Table 4; Fig. 8), similar to the reported increase in cucumber fruit yield (22%–31%) by inter-lighting in the winter season (Kumar ). In the summer season, suboptimal nitrogen partitioning induced by sudden doubling in DPI can be overcome by pre-treatment of increasing nitrogen supply and inter-lighting (ca. 6% increase in DCA; Table 4), which maintains the biochemical capacity and reduces the biochemical limitation of the shaded leaves (Pettersen ; Trouwborst ; Chen ). These results provide a physiological explanation at canopy level for the observations of supplemental lighting experiments (Hovi ; Hovi-Pekkanen and Tahvonen, 2008; Pettersen ; Trouwborst ). Furthermore, the relationship between protein synthesis rate and intercepted light intensity is non-linear in our model [Eq. (7)], which may offer an explanation why the photoacclimatory responses of a leaf grown under natural within-day light fluctuation differ from that under constant light, as shown in a recent experimental study (Vialet-Chabrand ).

Light fluctuations occur particularly in the lower canopy layer, where sunflecks cause strong and frequent variations in light, thereby increasing variations of Nph and p in the older leaves (Fig. 3). Interestingly, leaves under HL seemed to prioritize their n class="Chemical">nitrogen inpan>vestmenpan>t inpan> NJ over NC under LN with inpan>creasinpan>g leaf age (Fig. 3E), which might be explainpan>ed by the reduced LAI developmenpan>t under LN+HL and, henpan>ce, the higher light inpan>terception of the older leaves (Figs S4C, S5). Sinpan>ce withinpan>-leaf and withinpan>-day light heterogenpan>eity (e.g. sunflecks) were not described inpan> the model, these variations observed inpan> the greenpan>house experimenpan>t could not be reproduced inpan> the simulations (Supplemenpan>tary Fig. S6). This can be improved by couplinpan>g the model with a 3D structural plant model and the use of shorter time steps inpan> the simulations to capture more realistic response of photoacclimation.

Conclusions

We propose a mechanistic model to quantify the effects of leaf age, n class="Chemical">nitrogen anpan>d light availabilities onpan> photosynpan>thetic acclimationpan>. The model predicts the observed photosynpan>thetic acclimationpan> under differenpan>t combinpan>ationpan>s of pan> class="Chemical">nitrogen supply and light availability in the greenhouse. Model simulation indicates that photosynthetic nitrogen distribution is close to optimum and photosynthetic nitrogen partitioning can be optimal under constant light conditions. However, large fluctuation in light between days under natural conditions inevitably leads to suboptimal nitrogen partitioning. Our study provides insights into photosynthetic acclimation and the model can be used for crop model improvement and provides guidelines for greenhouse management.

Supplementary data

Supplementary data are available at JXB online.

Fig. S1. Schematic diagram of photosynthetic n class="Chemical">nitrogen turnover.

Fig. S2. Relationship between relative n class="Chemical">chlorophyll contenpan>t and leaf n class="Chemical">chlorophyll concentration.

Fig. S3. Environmental input for the model evaluation and simulation.

Fig. S4. Relationships between leaf angle, LAI, and age.

Fig. S5. Leaf area distribution used as input in the daily canopy assimilation simulation.

Fig. S6. Comparisons of simulated photosynthetic n class="Chemical">nitrogen traits betweenpan> n class="Chemical">nitrogen supply levels and between light conditions.

Fig. S7. n class="Disease">Leaf photosynthetic nitrogenpan> distributions with the vertical light distribution.

Table S1. Canopy characteristics used in the daily canopy assimilation simulation.

Click here for additional data file.