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

A mechanistic model of photosynthetic protein turnover explains leaf acclimation to light and nitrogen availabilities and suggests that suboptimal photosynthetic nitrogen partitioning is due to daily light fluctuations.

Abstract

Plants continually adjust the photosynthetic functions in their leaves to fluctuating light, thereby optimizing the use of photosynthetic nitrogen (N_ph) 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 N_ph distribution along canopy depth or N_ph partitioning between functional pools. Our analyses suggest that N_ph distribution is close to optimum and N_ph reallocation is more important under low nitrogen. N_ph 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 N_ph 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 et al., 2010). To maximize canopy carbon gain, dynamic modifications of photosynthetic traits to track heterogeneous light distribution within the canopy are crucial (Retkute et al., 2015), especially for herbaceous species with a continuously leaf-forming nature (Niinemets et al., 2015). One of the most important strategies in photoacclimation is to maintain efficient utilization of limited resources in the photosynthetic apparatus, e.g. 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 nitrogen distribution in response to light has been intensively studied (Hirose and Werger, 1987; Werger and Hirose, 1991; Anten et al., 1995; Dreccer et al., 2000; Moreau et al., 2012; Hikosaka et al., 2016). Nitrogen distribution was reported to closely follow the light gradient and thus approach its optimum in wheat stands (Dreccer et al., 2000). However, this relationship has not been found in other studies (Moreau et al., 2012; Hikosaka et al., 2016). 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 et al., 1997; Meir et al., 2002; Wright et al., 2006; Hikosaka, 2016). This discrepancy between optimum and reality could be explained by physiological limitations and the cost of nitrogen reallocation (Hikosaka, 2016; Kitao et al., 2018) or might result from incorrect predictions. In some cases (e.g. Hikosaka, 2014; Kitao et al., 2018), 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 et al., 2015; 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 carbon gain by enhancing photosynthetic nitrogen use efficiency (PNUE; Zhu et al., 2010). Photosynthetic rate is determined by the limited rate of ribulose 1,5-bisphosphate (RuBP) carboxylation and RuBP regeneration in the photosynthetic machinery (Farquhar et al., 1980). 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 et al., 2010; Trouwborst et al., 2011; Vialet-Chabrand et al., 2017). 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 et al., 2011). Recently, with a modelling approach, it was predicted that a decreasing investment in the light harvesting function can increase canopy PNUE (Song et al., 2017). 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 et al., 2006) 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 et al. (2012) proposed an empirical model describing the combined effects of leaf age and light on leaf nitrogen economics for a grapevine canopy and demonstrated that the mean daily light integral over the previous 10 d explained 73% of the variation in nitrogen per unit leaf area. Since environmental acclimation and developmental (genetic control of leaf ageing) acclimation are regulated distinctively (Athanasiou et al., 2010), 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 et al., 2017). In growing leaves, photosynthetic proteins account for the highest cost in protein turnover (Li et al., 2017). At the expense of energy, protein turnover is necessary for adjusting protein levels in line with external triggers. It was experimentally shown that leaf Rubisco content increased with light (Yamori et al., 2010) and nitrogen supply level (Yamori et al., 2011a) and exhibited an evolution with leaf age that could be interpreted by Rubisco turnover (Suzuki et al., 2001; Ishimaru et al., 2001; 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 nitrogen (N_ph, mmol N m⁻²) is defined as biologically active nitrogen in the proteins involved in photosynthetic functions, i.e. carboxylation, electron transport and light harvesting. Leaf N_ph is calculated as the sum of nitrogen in the carboxylation pool (N_V), electron transport pool (N_J) and light harvesting pool (N_C, Trouwborst et al., 2011):

$$N_{\text{ph}}=N_{\text{V}}+N_{\text{J}}+N_{\text{C}}$$ (1)

where N_V includes only Rubisco and represents the nitrogen investment in carboxylation capacity, N_J includes the electron transport chain, photosystem II core and Calvin cycle enzymes other than Rubisco, and N_C includes the photosystem I core and light harvesting complexes I and II. Functional pools N_V, N_J, and N_C are estimated from the maximum carboxylation rate (V_cmax, μmol CO₂ m⁻² s⁻¹), maximum electron transport (J_max, μmol e⁻ m⁻² s⁻¹) and leaf chlorophyll (Chl, mmol Chl m⁻²), respectively (Buckley et al., 2013):

$$N_{\text{V}}=V_{\text{cmax}}/{\chi }_{\text{V}}$$ (2a)

$$N_{\text{J}}=J_{\text{max}}/{\chi }_{\text{J}}$$ (2b)

$$N_{\text{C}}=\left(Chl-N_{\text{J}}\times {\chi }_{\text{CJ}}\right)/{\chi }_{\text{C}}$$ (2c)

where χ_V (μmol CO₂ mmol⁻¹ N s⁻¹) is the carboxylation capacity per unit Rubisco nitrogen, and χ_J (μmol e⁻ mmol⁻¹ N s⁻¹) is the electron transport capacity per unit electron transport nitrogen. χ_CJ (mmol Chl mmol⁻¹ N) and χ_C (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_X) is determined as the ratio of nitrogen in the pool X (N_X, mmol N m⁻²) to N_ph:

$$p_X=N_X/N_{\text{ph}}$$ (3)

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

$$\text{d}{N}_X/\text{d}t=S_X\left(t\right)-D_X\left(t\right)$$ (4)

Protein synthesis as an age-dependent and zero-order process (Li et al., 2017) is described by a logistic function and independent of the current N_X state:

$$S_X\left(t\right)=2S_{\text{max},X}/\left[1+\text{exp}\left(t\times t_{\text{d},X}\right)\right]$$ (5)

where S_max,X (mmol N m⁻² °Cd⁻¹) is the maximum protein synthesis rate of N_X that occurs at the early stage of leaf development (Supplementary Fig. S1 at JXB online). The constant t_d,X (°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/t_d,X, S_X reduces to 53.8% of S_max,X.

Table 1.

List of coefficients used in the protein turnover model for photosynthetic nitrogen pools, carboxylation pool N_V, electron transport pool N_J, and light harvesting pool N_C

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.

The degradation rate D_X is governed by first-order kinetics (Verkroost and Wassen, 2005; Li et al., 2017) with a degradation constant D_r,X (°Cd⁻¹):

$$D_X\left(t\right)=D_{r,X}\times N_X\left(t\right)$$ (6)

The variable S_max,X in Eq. (5) is a function of daily light interception (I_Ld, mol photons m⁻² d⁻¹):

$$S_{\text{max},X}=\left[S_{\text{mm},X}\times k_{\text{I},X}\times I_{\text{Ld}}/\left(S_{\text{mm},X}+k_{\text{I},X}\times I_{\text{Ld}}\right)\right]\times r_{\text{N},X}$$ (7)

where S_mm,X (mmol N m⁻² °Cd⁻¹) is the potential maximum protein synthesis rate and k_I,X is the rate constant describing the increase of S_max,X with I_Ld. The factor r_N,X increases with nitrogen level in the nutrient solution (N_S, mM) by a Michaelis–Menten constant, k_N,X (mM):

$$r_{\text{N},X}=N_{\text{S}}/\left(k_{\text{N},X}+N_{\text{S}}\right)$$ (8)

Modelling leaf photosynthesis

Photosynthetic parameters V_cmax, J_max, and Chl were estimated from functional nitrogen pools N_V, N_J, and N_C, using Eq. (2a–c). The net photosynthetic rate (A, μmol CO₂ m⁻² s⁻¹) is defined as the minimum of RuBP carboxylation-limited (A_c, mmol CO₂ m⁻² s⁻¹) and RuBP regeneration-limited (A_j, mmol CO₂ m⁻² s⁻¹) net photosynthetic rate (Farquhar et al., 1980):

$$A=\text{min} \left(A_{\text{c}},A_{\text{j}}\right)$$ (9a)

$$A_{\text{c}}=V_{\text{c}}\times \left(C_{\text{c}}-{\Gamma }^{\text{*}}\right)/\left[C_{\text{c}}+K_{\text{c}}\left(1+O/K_{\text{o}}\right)\right]-R_{\text{d}}$$ (9b)

$$A_{\text{j}}=J\times \left(C_{\text{c}}-{\Gamma }^{\text{*}}\right)/\left(4C_{\text{c}}+8{\Gamma }^{\text{*}}\right)-R_{\text{d}}$$ (9c)

where C_c (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, K_c (μmol CO₂ mol⁻¹) and K_o (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, V_c (μmol CO₂ m⁻² s⁻¹) is carboxylation rate, and J (μmol e⁻ m⁻² s⁻¹) is electron transport rate. Daytime respiration rate R_d (μmol CO₂ m⁻² s⁻¹) is assumed to vary with t and the mean I_Ld during the previous 4 d (I_Ld4d):

$$R_{\text{d}}\left(t\right)=R_{\text{max}}\times I_{\text{Ld}4\text{d}}\times \text{exp}\left(-R_{\text{g}}\times I_{\text{Ld}4\text{d}}\times t\right)+R_{\text{m}}\times I_{\text{Ld}4\text{d}}\times t$$ (10)

where R_max (μmol CO₂ d mol⁻¹ photons s⁻¹) relates I_Ld4d to the maximum R_d, R_g (m² d °Cd⁻¹ mol⁻¹ photons) influences the decrease in the growth respiration, and R_m (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 V_cmax and J_max, respectively, depending on the photosynthetic photon flux density (PPFD) incident on the leaf (I_Lc, µmol photons m^–2 s^–1) according to Qian et al. (2012) and Ögren and Evans (1993), respectively:

$$V_{\text{c}}=V_{\text{cmax}}\left\{0.31+\frac{0.69}{1+\text{exp}\left[-0.009\times \left(I_{\text{Lc}}-500\right)\right]}\right\}$$ (11)

$$J=\left\{\varphi \times \alpha \times I_{\text{Lc}}+J_{\text{max}}-{\left[\begin{array}{l}{\left(\varphi \times \alpha \times I_{\text{Lc}}+J_{\text{max}}\right)}^2\\ -4\theta \times J_{\text{max}}\times \varphi \times \alpha \times I_{\text{Lc}}\end{array}\right]}^{0.5}\right\}/\left(2\theta \right)$$ (12)

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 I_Lc. Leaf absorptance (α, unitless) is related to Chl (Evans, 1993):

$$\alpha =Chl/\left(Chl+0.076\right)$$ (13)

Chloroplastic CO₂ concentration depends on the steady-state of stomatal conductance (g_sc, mol CO₂ m⁻² s⁻¹) and mesophyll conductance (g_m, mol CO₂ m⁻² s⁻¹) to CO₂:

$$C_{\text{c}}=C_{\text{a}}-A\times \left[\left(g_{\text{sc}}+g_{\text{m}}\right)/\left(g_{\text{sc}}\times g_{\text{m}}\right)\right]$$ (14)

where C_a (μmol CO₂ mol⁻¹) is atmospheric CO₂ concentration, and g_sc is calculated with species-specific constants of stomatal conductance, g₀ and g₁ (Chen et al., 2014), and leaf-to-air vapor pressure deficit (D, kPa, Medlyn et al., 2011):

$$g_{\text{sc}}=g_0+\left(1+g_1/\sqrt{D}\right)\times A/C_{\text{a}}$$ (15)

Mesophyll conductance is expressed as a log-normal function of t (Chen et al., 2014), where g_m first increases during leaf development and decreases during ageing (Flexas et al., 2008):

$$g_{\text{m}}=g_{\text{mmax}}\times \text{exp}\left\{-0.5\times {\left[\text{ln}\left(t/t_{\text{gm}}\right)/v_{\text{gm}}\right]}^2\right\}$$ (16)

where t_gm is the t when the maximum g_m (g_mmax, mol CO₂ m⁻² s⁻¹) occurs and v_gm is the standard deviation of the curve; g_mmax is linearly related to N_ph, since a similar relationship has been reported for C₃ plants (e.g. Yamori et al., 2011a):

$$g_{\text{mmax}}=r_{\text{gm}}\times N_{\text{ph}}+r_{\text{gm}0}$$ (17)

where r_gm (mol CO₂ mmol⁻¹ N s⁻¹) describes the rate of increase of g_mmax in relation to N_ph, and r_gm0 (mol CO₂ m⁻² s⁻¹) is the minimum g_mmax.

The steady-state A_c was solved analytically with Eqs (9b), (14), and (15), and A_j with Eqs (9c), (14), and (15), following Moualeu‐Ngangue et al. (2016). Model variables and coefficients are listed in Tables 1–3.

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.

Growth chamber experiment to investigate the dynamics of photosynthetic protein turnover

Cucumber (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 to 9 December 2016 with factorial combinations of three light and three 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 et al., 2016) 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 nitrogen supply levels to evaluate the model performance and to collect input data for optimality analyses. Seeds were sown on 14 March and transplanted to larger rock-wool cubes on 22 March. After the third true leaves had appeared, plants were transferred onto rock-wool slabs on 4 April with plant density of 1.33 plants m⁻² and supplied with two 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 et al. (2014). 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 CO₂ m⁻² s⁻¹) and light response curves were measured using a portable photosynthesis system (LI-6400XT; Li-Cor Inc., Lincoln, NE, USA). All measurements were carried out under sample CO₂ 400 µmol mol⁻¹, leaf temperature 25 °C and relative humidity 55–65%. R_d was estimated from the linear portion of the light response curve (Kok, 1948). V_cmax was estimated using the one-point method (Wilson et al., 2000; De Kauwe et al., 2016), and J_max 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 et al., 1992). Chlorophyll fluorescence was measured using the multiphase flash approach (Loriaux et al., 2013) 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 nitrogen analyses. Total leaf 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. D_r,X and t_d,X were first quantified for each pool using data of all treatments. With the determined values of D_r,X and t_d,X, S_max,X was then quantified for each treatment. S_mm,X, k_I,X, and k_N,X were determined from S_max,X [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 I_Ld on R_d [Eq. (10)] and g_m [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 nitrogen per unit leaf area (N_ph, mmol N m⁻²), photosynthetic nitrogen per leaf (N_leaf, mmol N) and total leaf photosynthetic nitrogen content of the canopy (N_canopy, 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 I_Ld 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, N_ph, and p_X predictions following Kahlen and Stützel (2011).

Simulating daily canopy carbon assimilation

Daily canopy carbon assimilation during daytime (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 C_a 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 N_ph on DCA, a distribution factor f_d was introduced into Eq. (5) to create variations in the rate of protein synthesis, and a partitioning factor f_p,X was introduced into Eq. (7) to create variations in the maximum protein synthesis rate of different functional pools:

$$S_X\left(t\right)=2S_{\text{max},X}/\left[1+\text{exp}\left(t\times t_{\text{d},X}\times f_{\text{d}}\right)\right]$$ (18)

$$S_{\text{max},X}=\left[\begin{array}{l}{S}_{\text{mm},X}\times f_{\text{p},X}\times k_{\text{I},X}\times I_{\text{Ld}}\\ /\left(S_{\text{mm},X}\times f_{\text{p},X}+k_{\text{I},X}\times I_{\text{Ld}}\right)\end{array}\right]\times r_{\text{N},X}$$ (19)

A control condition was defined with f_d=1 and f_p,X=1, when all coefficients in the synthesis process (Table 1) remained unmodified. Increasing f_d accelerates the decrease in the rate of protein synthesis and enhances acropetal N_ph reallocation. An increase in f_p,X results in a higher rate of synthesis of N_X and increases the partitioning to pool X. A modified partitioning pattern that maximized DCA was identified as optimal for several DPI levels, and the optimal values of f_p,X were determined using the package ‘DEoptim’ in R. The change in DCA caused by modified distribution or optimal partitioning of N_ph 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 S_mm, coefficient t_d, and protein degradation constant, D_r. The coefficient t_d affects the decrease in the rate of synthesis, and D_r contributes to the degradation rate, which together influence the developmental effect on protein turnover dynamics. The low value of t_d (0.001–0.002 °Cd⁻¹, Table 1) suggests that the influence of ageing appears rather late in the leaf lifespan under a constant light environment. The coefficient D_r was found to be the same for the carboxylation pool (N_V) and the electron transport pool (N_J), while the light harvesting pool (N_C) had a lower D_r (Table 1). The genotypic sensitivities to light and nitrogen availabilities are characterized by k_I and k_N, respectively. Collectively, S_mm, k_I, and k_N determine the maximum protein synthesis rate S_max in Eq. (7). When light was increased 2.5-fold (from LL to HL), S_max increased by 50% in N_V and N_J, and by 10% in N_C, while nitrogen level had less influence on S_max (<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 S_max. N_C had the highest k_I (Table 1); consequently, S_max,C approached saturation at lower light intensity than S_max,V and S_max,J (Fig. 1). S_max,V and S_max,J were well coordinated in response to light and nitrogen level (Fig. 1A, B), but the higher k_I and k_N of N_V (Table 1) suggested that N_V synthesis is more sensitive to the variation in light and nitrogen availabilities than N_J.

Fig. 1.

Simulated effects of daily light interception (I_Ld, mol photons m⁻² d⁻¹) and nitrogen supply level in the nutrient solution (N_S, mM) on maximum protein synthesis rate (S_max,X) 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 S_max,X normalized by the potential maximum protein synthesis rate (S_mm,X) 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 in two canopy layers weekly for four consecutive weeks. The model predicted leaf photosynthetic characteristics with high accuracy (70–91%, Fig. 2) and a trend of photosynthetic acclimation (Supplementary Fig. S6) similar to the experimental observations (Fig. 3), except for slight overestimations in photosynthetic nitrogen (N_ph, 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 (R_d, µmol CO₂ m⁻² s⁻¹); (C) leaf photosynthetic nitrogen (N_ph, mmol N m⁻²); (D) maximum carboxylation rate (V_cmax, µmol CO₂ m⁻² s⁻¹); (E) maximum electron transport rate (J_max, µmol e⁻ m⁻² s⁻¹); (F) chlorophyll (Chl, mmol Chl m⁻²); (G) partitioning fraction of the carboxylation pool (p_V); (H) partitioning fraction of the electron transport pool (p_J); and (I) partitioning fraction of the light harvesting pool (p_C). 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 (N_ph, mmol N m⁻²; A, B), partitioning fractions of the carboxylation pool (p_V; C, D), the electron transport pool (p_J; E, F), and the light harvesting pool (p_C; 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.

Photosynthetic acclimation in the greenhouse canopies as influenced by the interplay between light, nitrogen level and leaf age was examined (Fig. 3). Light had positive effects on N_ph (Fig. 3A), the partitioning fractions of N_V (p_V, Fig. 3C) and N_J (p_J, Fig. 3E) but negative effects on the partitioning fraction of N_C (p_C, Fig. 3G). This negative effect of light on p_C can be explained by the high k_I of N_C (Table 1), which leads to an saturation of S_max,C under lower light (Fig. 1). The changes in N_ph, p_V, p_J, and p_C 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, N_ph 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 S_max to nitrogen level (Fig. 1). During the simultaneous increase in leaf age and mutual shading, the effects of nitrogen supply on S_max 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 N_ph distribution pattern along the canopy depth on daily canopy carbon assimilation (DCA, mol CO₂ d⁻¹) was evaluated by introducing a distribution factor f_d 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 (N_canopy, mmol N), (ii) N_ph distribution in the canopy, and (iii) N_ph partitioning fractions of pools X (p_X) in the leaf. Thus, it was impossible to modify single elements while maintaining the other two constant. Increasing f_d led to a faster reduction of N_ph during leaf ageing and more acropetal N_ph reallocation. However, it also reduced N_canopy and tended to increase p_C (data not shown). Therefore, to obtain the leaf photosynthetic nitrogen content (N_leaf,i, mmol N in leaf i) with comparable N_canopy, simulated N_leaf,i with f_d=n (denoted as N′_leaf,i) was adjusted proportionally to the ratio between N_canopy calculated with f_d=1 and with f_d=n:

$$N_{\text{leaf},i}\left(f_{\text{d}}=n\right)=N{\text{'}}_{\text{leaf},i}\left(f_{\text{d}}=n\right)\times \left[N_{\text{canopy}}\left(f_{\text{d}}=1\right)/N_{\text{canopy}}\left(f_{\text{d}}=n\right)\right]$$ (20a)

p _X,i was set equal to the control value:

$$p_{X,i}=N_{X,i}\left(f_{\text{d}}=1\right)/N_{\text{ph},i}\left(f_{\text{d}}=1\right)$$ (20b)

These adjustments assured the same amount of N_canopy among the distribution patterns. The factor f_d was varied between 0.5 and 5.0 at intervals of 0.5 in the simulation, which gave values of N_ph comparable to those measured in cucumber leaves (22–135 mmol N m⁻²; Fig. 4). Canopy N_ph distributions with enhanced acropetal reallocation were created by increasing f_d (Fig. 4; Supplementary Fig. S7). In general, the distribution of N_ph corresponded to the vertical light distribution except in the expanding leaves in the upper canopy, and the N_ph distribution with light was steeper under LL (Supplementary Fig. S7).

Fig. 4.

Leaf photosynthetic nitrogen (N_ph, 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 f_d 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 N_ph distributions (f_d=1) are indicated by the green lines.

To simulate the natural fluctuations in light between days, three light levels representing 200% (aDPI₂₀₀), 100% (aDPI₁₀₀) and 50% (aDPI₅₀) of average DPI during acclimation (aDPI) were used in the DCA simulation. Under aDPI₁₀₀ and aDPI₅₀, enhancing acropetal N_ph reallocation did not significantly increase DCA (<5%), suggesting that N_ph distribution was optimal under constant and decreasing DPI (Fig. 5B, C). More acropetal reallocation did not improve the optimality in N_ph 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 N_ph reallocation resulted in an increase in DCA by 7% under LN at aDPI₂₀₀ (Fig. 5A), indicating that acropetal N_ph reallocation was more important under LN than HN.

Fig. 5.

Effects of photosynthetic nitrogen (N_ph) distributions with different values of f_d (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 N_ph reallocation increases with f_d. 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 N_ph distribution by the DCA obtained with the control N_ph distribution (f_d=1) under same DPI. A change within ±5% (grey shading) is considered insignificant.

It was observed that N_ph was more overestimated in the older leaves than in the younger ones (Fig. 2C), which indicated that our model tended to underestimate the acropetal N_ph reallocation when scaling up from leaf to canopy level. In order to maintain a constant light environment for the measured leaves in the growth chamber experiment, leaves younger than the sampled leaves were trained downward and their light interception, together with their nitrogen demand, was inevitably reduced; therefore, the model coefficients were obtained from the leaves with limited nitrogen reallocation. However, underestimating acropetal N_ph reallocation would not affect our result that N_ph distribution was close to optimum.

Suboptimal nitrogen partitioning is due to daily light fluctuation

To find the optimal within-leaf N_ph partitioning between functions, the potential maximal protein synthesis rate for pool X was modified by a factor f_p,X, ranging from 0.2 to 2.0. Increasing f_p,X resulted in higher protein synthesis rates, but it also increased N_canopy and the proportion of nitrogen distributed in the upper canopy. After simulating nitrogen partitioning with a modified f_p,X, N_leaf of each leaf was re-assigned to their control values that were obtained with f_p,X=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 N_ph partitioning to aDPI. N_ph partitioning deviated further from optimum when DPI diverged from aDPI (Fig. 6). Therefore, strong day-to-day light fluctuation induced suboptimality in N_ph partitioning and led to lower PNUE.

Fig. 6.

Increase in daily canopy carbon assimilation (DCA) by optimizing photosynthetic nitrogen (N_ph) 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 [f_p,X=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.

By optimizing N_ph partitioning, DCA could be increased by nitrogen reinvestment in the limited functional pools. Under aDPI₂₀₀, N_ph partitioning was suboptimal under HL (Fig. 6), and this suboptimality was less under HN than under LN (Table 4). By reinvesting about half of N_C into N_V and N_J (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 N_ph partitioning (Table 4) due to an underinvestment in the light harvesting function. Reinvesting N_V into N_C in the middle or upper canopy (HL, Fig. 8A; LL, 8B, 8D) increased DCA by 7–25% (Table 4).

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.

Fig. 7.

Ratio between optimal and control partitioning fractions (optimal p_X/control p_X) of the carboxylation pool (p_V, orange circles), the electron transport pool (p_J, red triangles), the light harvesting pool (p_C, 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_X/control p_X), 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.

Discussion

This model is the first approach applying a dynamic protein turnover mechanism at the leaf level to assess the optimality and limitation in nitrogen use at the canopy level. Here, maximized canopy carbon assimilation is considered as a general indicator of maximizing fitness. The adaptation of the protein turnover mechanism gives reasonable predictions of optimal N_ph 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 nitrogen content (Anten et al., 1998), shows more plastic responses to light than to nutrient availability (Poorter et al., 2009; Poorter et al., 2010). Mechanistic models can be used to interpret measured biological data (Chen et al., 2015, 2018), as in our model here, providing a quantitative explanation of the different plastic responses in leaf nitrogen economics (e.g. photosynthetic nitrogen per unit leaf area, N_ph, and photosynthetic capacities) to light and to nitrogen by their effects on the maximum protein synthesis rate (S_max, Fig. 1). A 5-fold increase in light (4–20 mol photons m⁻² d⁻¹) doubled S_max of the carboxylation pool (N_V) and electron transport pool (N_J; Fig. 1A, B), which is similar to the published values (Niinemets et al., 2015). In contrast, increasing nitrogen supply from 2 to 10 mM increased S_max of N_V and N_J only by 20% and 16%, respectively. The effects of light on photosynthetic nitrogen can be quantitative (on N_ph) or qualitative (on nitrogen partitioning, p_X; Niinemets et al., 2006; Buckley et al., 2013), while nitrogen only affected N_ph by restricting S_max (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 et al., 2006, Chen et al., 2014). Therefore, leaf photosynthetic acclimation to light occurs together with leaf ageing, which is characterized by the protein degradation constant D_r and the constant t_d describing the decrease of protein synthesis rate in our model. The D_r values of N_V and N_J fall within the range of in vivo quantifications reported by Peterson et al. (1973) and Li et al. (2017). The low value of t_d (Table 1) explains the modest influence of ageing on leaf photosynthetic capacity observed under constant light conditions (Pettersen et al., 2010a).

Besides light and nitrogen availability, temperature has effects on photosynthetic nitrogen content and partitioning (Yamori et al., 2005; Kattge and Knorr, 2007; Yamori et al., 2009). Temperature dependency of developmental processes and biochemical reactions is often described by exponential or Arhenius-type functions (Parent et al., 2010; 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 et al., 2016).

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

Under sufficient nitrogen availability, Rubisco can function as a storage protein, which means that the amount of Rubisco can exceed the requirements to support photosynthesis (Carmo-Silva et al., 2015). The Rubisco pool has the highest value of k_N (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 V_cmax and J_max with nitrogen availability (Hikosaka, 2004; Yamori et al., 2011a), 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 et al., 1986; Kaiser et al., 2018), 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 [V_c=V_cmax in Eq. (9b)] in the DCA simulation resulted in a 4-fold above-optimum investment in N_V even under aDPI (data not shown). Since Rubisco is not an especially inefficient catalyst in comparison with other chemically related enzymes (Bathellier et al., 2018), 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 et al., 2013; Poorter et al., 2013). 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 Rubisco and electron transport (Ishimaru et al., 2001; Yamori et al., 2011b) should be increased under increasing light (Fig. 7), and a larger antenna size for light harvesting (Masuda et al., 2003) is required under decreasing light availability (Fig. 8). It is clear that the pattern of optimal 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 nitrogen use induced by light fluctuation. Since carbon assimilation is the rate-limiting step for yield production of cucumber plants due to the indeterminate production of vegetative and generative organs (Wiechers et al., 2011), 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 et al., 2016). 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 et al., 2010b; Trouwborst et al., 2010; Chen et al., 2014). These results provide a physiological explanation at canopy level for the observations of supplemental lighting experiments (Hovi et al., 2004; Hovi-Pekkanen and Tahvonen, 2008; Pettersen et al., 2010b; Trouwborst et al., 2010). 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 et al., 2017).

Light fluctuations occur particularly in the lower canopy layer, where sunflecks cause strong and frequent variations in light, thereby increasing variations of N_ph and p_X in the older leaves (Fig. 3). Interestingly, leaves under HL seemed to prioritize their nitrogen investment in N_J over N_C under LN with increasing leaf age (Fig. 3E), which might be explained by the reduced LAI development under LN+HL and, hence, the higher light interception of the older leaves (Figs S4C, S5). Since within-leaf and within-day light heterogeneity (e.g. sunflecks) were not described in the model, these variations observed in the greenhouse experiment could not be reproduced in the simulations (Supplementary Fig. S6). This can be improved by coupling the model with a 3D structural plant model and the use of shorter time steps in the simulations to capture more realistic response of photoacclimation.

Conclusions

We propose a mechanistic model to quantify the effects of leaf age, nitrogen and light availabilities on photosynthetic acclimation. The model predicts the observed photosynthetic acclimation under different combinations of 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 nitrogen turnover.

Fig. S2. Relationship between relative chlorophyll content and leaf 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 nitrogen traits between nitrogen supply levels and between light conditions.

Fig. S7. Leaf photosynthetic nitrogen distributions with the vertical light distribution.

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

Glossary

Abbreviations

aDPI

average daily photosynthetic photon integral during acclimation

Chl

chlorophyll per unit leaf area

DCA

daily canopy carbon assimilation

DPI

daily photosynthetic photon integral

HL

high light

HN

high nitrogen

J_max

maximum electron transport rate

LL

low light

LAI

leaf area index

LN

low nitrogen

N_C

light harvesting pool of photosynthetic nitrogen

N_J

electron transport pool of photosynthetic nitrogen

N_ph

photosynthetic nitrogen

N_V

carboxylation pool of photosynthetic nitrogen

PNUE

photosynthetic nitrogen use efficiency

PPFD

photosynthetic photon flux density

V_cmax

maximum carboxylation rate