The Coordination of Leaf Photosynthesis Links C and N Fluxes in C3 Plant Species

Vincent Maire; Pierre Martre; Jens Kattge; François Gastal; Gerd Esser; Sébastien Fontaine; Jean-François Soussana

doi:10.1371/journal.pone.0038345

Abstract

Photosynthetic capacity is one of the most sensitive parameters in vegetation models and its relationship to leaf nitrogen content links the carbon and nitrogen cycles. Process understanding for reliably predicting photosynthetic capacity is still missing. To advance this understanding we have tested across C₃ plant species the coordination hypothesis, which assumes nitrogen allocation to photosynthetic processes such that photosynthesis tends to be co-limited by ribulose-1,5-bisphosphate (RuBP) carboxylation and regeneration. The coordination hypothesis yields an analytical solution to predict photosynthetic capacity and calculate area-based leaf nitrogen content (N_a). The resulting model linking leaf photosynthesis, stomata conductance and nitrogen investment provides testable hypotheses about the physiological regulation of these processes. Based on a dataset of 293 observations for 31 species grown under a range of environmental conditions, we confirm the coordination hypothesis: under mean environmental conditions experienced by leaves during the preceding month, RuBP carboxylation equals RuBP regeneration. We identify three key parameters for photosynthetic coordination: specific leaf area and two photosynthetic traits (k₃, which modulates N investment and is the ratio of RuBP carboxylation/oxygenation capacity () to leaf photosynthetic N content (N_pa); and J_fac, which modulates photosynthesis for a given k₃ and is the ratio of RuBP regeneration capacity (J_max) to). With species-specific parameter values of SLA, k₃ and J_fac, our leaf photosynthesis coordination model accounts for 93% of the total variance in N_a across species and environmental conditions. A calibration by plant functional type of k₃ and J_fac still leads to accurate model prediction of N_a, while SLA calibration is essentially required at species level. Observed variations in k₃ and J_fac are partly explained by environmental and phylogenetic constraints, while SLA variation is partly explained by phylogeny. These results open a new avenue for predicting photosynthetic capacity and leaf nitrogen content in vegetation models.

Citation: Maire V, Martre P, Kattge J, Gastal F, Esser G, Fontaine S, et al. (2012) The Coordination of Leaf Photosynthesis Links C and N Fluxes in C₃ Plant Species. PLoS ONE 7(6): e38345. https://doi.org/10.1371/journal.pone.0038345

Editor: Ben Bond-Lamberty, DOE Pacific Northwest National Laboratory, United States of America

Received: December 27, 2011; Accepted: May 3, 2012; Published: June 7, 2012

Copyright: © 2012 Maire et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This study contributes to the French ANR DISCOVER project (ANR-05-BDIV-010-01). VM was funded by a PhD grant of the French research ministry (MENRT). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

The response of leaf net photosynthesis to variations in light, temperature and CO₂ concentration has been successfully represented by the biochemical model of C₃ photosynthesis proposed by Farquhar, von Caemmerer and Berry [1]. This model has pioneered the mechanistic representation of the main biochemical processes of leaf photosynthesis, based on the assumption that photosynthesis is limited by either the carboxylation/oxygenation of ribulose-1,5-bisphosphate (RuBP) by the enzyme ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco; W_c), or the regeneration of RuBP by the electron transport chain (W_j). Maximum rates of these two processes are determined by carboxylation capacity () and electron transport capacity (J_max). A strong correlation linearly links the variations of and J_max across species (e.g. [2]) and environmental conditions during plant growth (e.g. [3], [4]). Since both capacities are measured independently, this result suggests that CO₂ assimilation is regulated in a coordinated manner by these two processes [5].

The variations of net photosynthesis with growth condition, season and species, are related to concurrent changes in leaf nitrogen content (N_a) and to the allocation of nitrogen between different protein pools [6]. and J_max linearly correlate with N_a at both intra-and-interspecific levels [3], [4], [7]. Nevertheless, so far the relationship between and J_max and their link to N_a are empirical correlations, their scatter is substantial, and a predictive process understanding C–N coupling at the leaf scale is still missing. As photosynthetic capacity is among the most influential parameters in current vegetation models [8], such an understanding is essential to predict photosynthesis at leaf, plant, stand and ecosystem scales under changing environmental conditions.

Haxeltine and Prentice [9] suggested a general model for the light-use efficiency of primary production, which links photosynthetic capacity and N_a. This model is based on the Farquhar’s model of photosynthesis and has been implemented in the global terrestrial vegetation model LPJ [10]. This approach does not account for N limitation and is based on the optimization theory that maximizes assimilation against incoming radiation. Until now, a clear understanding of leaf N variations along vegetative canopies as well as across species and environments has not been provided by the optimization theory [11], [12]. For instance, all reported studies observed N gradients less steep than predicted with the optimization theory, suggesting that it likely overestimates predicted C gain [13]–[18]. Moreover, there are several limitations in optimization theory calculations (for a detailed discussion, see [19]).

Chen et al. [20] proposed an alternative approach: the coordination hypothesis of leaf photosynthesis. The basic assumption of this approach is that and J_max are actively regulated by plants in response to environmental conditions such that for most representative conditions W_c equals W_j. The optimality criterion in this context is not maximum C gain (as proposed in [21]–[23]), but the balance of RuBP carboxylation and regeneration, providing a coordinated allocation of resources, i.e. nitrogen, to these two photosynthetic processes (Fig. S1). For vertical gradients within canopies the co-limiting N content was shown to increase with irradiance and to decline with temperature and with atmospheric CO₂ concentration [20]. In agreement with experimental studies, the coordination hypothesis showed that N distribution with canopy depth declines less than the light gradient [13]–[18].

However, so far this co-limitation and its link to N_a has been considered only for vertical gradients within plant canopies, and has not yet been studied and validated across plant species and environmental conditions. This is possibly due to a lack of appropriate data including environmental growth conditions and photosynthetic parameters for a range of C₃ plant species. In addition, a full test of this hypothesis requires extending the calculation of the co-limiting N content to account for the coupling between leaf photosynthesis and stomatal conductance [3] as well as ascribing leaf N to structural and metabolic pools [24], [25].

In this study, we evaluate for the first time the coordination hypothesis for sunlit leaves and its link to N_a for a large range of plant species grown under different environmental conditions. We use an extended version of the Farquhar model of C₃ photosynthesis, a stomatal conductance model and a leaf N model to couple C, N and water fluxes at the leaf scale (see equations and variables in Tables 1–2). We apply this model to a dataset that includes leaf and environmental characteristics during plant growth and gas exchange measurements for a total of 31 C₃ species (293 observations, Table S1). For each observation, plant characteristics included the specific leaf area (SLA, m² g⁻¹ DM), N_a (gN m⁻²), and and J_max (µmol m⁻² s⁻¹) at reference temperature and atmospheric CO₂ concentration. The dataset covers six plant functional types (PFTs) grown both under constant and outdoors environments at a range of N and water supplies and atmospheric CO₂ concentrations.

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Table 1. Equations of the photosynthesis - stomatal conductance models.

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Table 2. Parameters and variables of the photosynthesis - stomatal conductance models.

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In agreement with the half-life time of Rubisco [26], we assumed that photosynthetic coordination varies with the mean over one month of the environmental conditions during plant growth. We tested the coordination hypothesis: i) by comparing simulated W_c and W_j values for the measured N_a, and ii) by comparing simulated (N_ac) and measured (N_a) leaf N contents. Second, thanks to a statistical model, we distinguished the plant species and environmental conditions effects on leaf photosynthetic traits. Third, we tested the implications of our leaf photosynthesis coordination model for net C assimilation (A_n) and for photosynthetic N use efficiency (PNUE) by varying plant photosynthetic traits and environmental growth conditions. Based on these results, we discuss the applicability of the coordination hypothesis to predict photosynthetic capacity and N content of sunlit leaves at the ecosystem and global scales.

Methods

A Model Coupling Leaf N with CO₂ and H₂O Fluxes

Several formulations and parameterizations of the original model by Farquhar et al. [1] have been described. Here, we refer to the formulation and parameterization used by Wohlfahrt et al. [3]. The net rate of C assimilation (A_n, µmol m⁻² s⁻¹) was limited either by carboxylase activity of Rubisco (W_c, µmolCO₂ m⁻² s⁻¹) or by electron flux through the chloroplast photosystems (W_j, µmolCO₂ m⁻² s⁻¹) (see Eqn 3–4, 7 in Table 1). Their respective capacity, and J_max, scaled with photosynthetic leaf N content (N_pa, gN m⁻²) (Eqn 6, 9). The relationship between the intracellular CO₂ concentration (C_i, Pa) and the stomatal conductance (g_s, mmol m⁻² s⁻¹) was modeled according to Falge et al. [27] (Eqn 14–17). g_s can limit A_n and thereby modify the linearity of the photosynthetic capacities vs N_pa relationship [28]. An analytical method was used to couple A_n and g_s, leading to the calculation of A_n through a system of five equations and five unknowns [29], [30] (Eqn 17). The daytime temperature dependence of and J_max was described following Medlyn et al. [31] (Eqn 12). Some studies have shown from a large dataset that the entropy terms of and J_max acclimate to the mean growth temperature (T_g, K) experienced by leaves over the preceding month [32]. The formalism and parameterization proposed by these authors [32] was used in this study to describe the acclimation of and J_max to T_g (Eqn 18–19). Similarly, Ainsworth and Long [33] have shown an acclimation of A_n to atmospheric CO₂ concentration during the preceding month (C_g, Pa). This was also taken into account (Eqn 20–21), by modifying the relationship of Vc_max and J_max at standard temperature (J_fac, dimensionless) and the relationship of Vc_max at standard temperature to N_pa (k₃, µmolCO₂ g⁻¹ N s⁻¹) according to a linear function of the difference between reference () and growth CO₂ concentrations (C_g).

A sensitivity analysis of the photosynthesis-stomatal conductance model was performed by analyzing the range of parameter variations in literature (Text S1, Table S2) and the sensitivity of the model outputs in response to a ±15% change in parameter values (Text S1, Fig. S2–S3). An index of sensitivity (IOS) was calculated as the ratio of output to parameter changes and was used to discuss on the model uncertainties linked to model calibration.

Coordinated N Content of Sunlit Leaves

Within leaves, N is partitioned between metabolic and structural pools [24], [25]. The coordinated leaf N content, N_ac (gN m⁻²) is calculated as the sum of structural leaf N and of photosynthetic leaf N (Np_ac, gN m⁻²). As leaf structures are highly dependent upon the biomass investment in dry matter (DM) [34], structural leaf N (f_ns, gN g⁻¹ DM) is expressed per unit DM. f_ns is assumed constant across species and independent of canopy depth and light intensity. f_ns value corresponds to the average value reported in the literature for a range of C₃ species (0.012 gN g⁻¹ DM, for a review see Lötscher et al. [25]). In contrast, metabolic leaf N associated with leaf photosynthesis is expressed per unit area since both light capture and CO₂ exchange with atmosphere are intrinsically area-based phenomena [3]. As a key measure of leaf morphology [6], SLA links dry matter-based structural N content (f_ns) to area-based photosynthetic N content (Np_ac):(1)

Under given environmental conditions, Np_ac is defined as the N_pa value at which A_n was co-limited by W_c and W_j (Fig. S1). Both and J_max are linear functions of Np_a and, for given environmental conditions, there is a single Np_ac value for which W_c equals W_j. At this co-limiting point, Np_ac equals (see Text S2 Eqn 2a-2d for details):(2)where α (molCO₂ mol⁻¹photon) is the apparent quantum yield of A_n at saturating CO₂, PPFD (µmol m⁻² s⁻¹) is the photosynthetic photon flux density, (µmol CO₂ g⁻¹N s⁻¹) is k₃ acclimated to C_g (Eqn 21), k₂ (Pa) is an intermediate variable synthesizing the Rubisco affinity for CO₂ (Eqn 5), Γ* (Pa) is the CO₂ compensation point in the absence of mitochondrial respiration, is J_fac acclimated to C_g and T_g (CO₂ air concentration and temperature during preceding month of plant growth, Eqn 19–20), and and (dimensionless) are the response functions of and J_max to temperature (Eqn 12). Overall, Np_ac integrates the sensitivity of photosynthetic machinery to T_g, PPFD, C_i and h_s.

Dataset

A dataset was assembled from measurements and literature to associate leaf photosynthetic traits of mature sunlit leaves with environmental growth conditions (Dataset SI4). and J_max at reference temperature (T^r = 20°C), N_a, SLA, as well as T_g, PPFD, h_s and C_g during the month preceding leaf measurements were included. and J_max values were standardized using a consistent formulation and parameterization of Γ* and the Michaelis-Menten constants for carboxylase (K_c, Pa) and oxygenase (K_o, Pa) Rubisco activity [32], [35].

The dataset has 293 entries from 31 C₃ plant species covering six plant functional types (PFTs): temperate broadleaved and coniferous evergreen trees (PFT1), temperate broadleaved deciduous trees (PFT2), deciduous shrubs and herbs (PFT3), perennial C₃ grasses and forbs (PFT4), C₃ crops (wheat, PFT5) and N-fixing trees (PFT6). The final dataset covers a wide range of plant growth conditions: T_g (ranging from 7.1 to 21.0°C), PPFD (500 to 1170 µmol m⁻² s⁻¹), h_s (0.51 to 0.89) and C_g (36 and 60 Pa). However, data corresponding to severe drought and/or to very low N availability during growth were excluded from the dataset. Four categories of inorganic N availability (low, medium, high and very high), two categories of soil moisture and of atmospheric CO₂ concentration (ambient and elevated) and six categories of experimental set-up (climate chamber, sunlit climate chamber, botanical garden, natural vegetation, free air CO₂ enrichment (FACE) and open top chambers) were defined. The dataset has been made available via the TRY initiative on plant traits [36].

Data Analysis

Coordinated W_c and W_j.

The basic assumption of the coordination hypothesis is that under the environmental conditions to which a leaf is adapted, RuBP carboxylation equals RuBP regeneration (W_c = W_j). Here we tested this for the average daily plant growth conditions (excluding night values) during the last month preceding photosynthesis measurements. We used four environmental variables (C_g, PPFD, T_g and h_s) corresponding to the average plant growth conditions as model input, and and J_max derived from separate photosynthesis measurements on the same plants. A single set of values was used for all other 33 model parameters and was originated from Wohlfahrt’s calibration (Table 2) [3], [4]. W_c and W_j, both predicted for the average plant growth conditions for each observation (n = 293), were compared by least square linear regression. Regression residuals were analyzed using a general linear model (GLM) with T_g, h_s, C_g and with PFTs and N categories. PFTs and N levels were compared by the post ANOVA Tukey’s HSD method.

Prediction of the coordinated leaf N content.

N_ac was calculated for each observation (n = 293) using four environmental variables (C_g, PPFD, T_g and h_s) corresponding to the growth conditions of the past month and three leaf traits (k₃, J_fac and SLA). k₃ is calculated as the ratio between and Np_a, while J_fac is calculated as the ratio between J_max and . The prediction of N_ac was evaluated by the relative root mean squared error (RRMSE), which is the relative average of the squared differences between predicted and observed values [37]. RRMSE values lower than 0.2 indicates here acceptable errors. Systematic (RRMSE_S) and unsystematic (RRMSE_U) errors [37] specified the error source of RRMSE (Eq. I).(I)where E_i and M_i are the predicted and measured values of the observation i, is the average of M_i and is an estimate of E_i deriving from the linear regression between E_i and M_i.

Dependence of leaf photosynthetic parameters on plant functional type (PFT).

ANOVA followed by LSD method for mean comparison tests, were used to analyze the role of PFT for the estimation of leaf photosynthetic traits used in the test of the coordination hypothesis (, J_max, k₃, J_fac and SLA). In order to test if the calibration of leaf photosynthetic traits can be simplified to obtain a unique value or a value by PFT, we estimated independent values of k₃, J_fac and SLA traits minimizing the squared differences between N_a and N_ac (Newton’s optimization method). Mean and optimized values per PFT were then compared by linear regressions. The calibration of leaf traits by species was not tested since the number of observations per species was too variable in our dataset.

Dependence of leaf photosynthetic parameters on environmental growth conditions.

Multiple regression models were used to analyze the effects of environmental growth conditions (T_g, PPFD, h_s and C_g, N and soil moisture categories) on leaf traits (, J_max, k₃, J_fac and SLA). For regression models of k₃ and J_fac, the values of dependent variables were log-transformed and all residuals followed a normal distribution.

We tested if the prediction of leaf photosynthetic traits by environmental growth conditions was robust and validated likewise the coordination hypothesis. We conducted bootstrap analyses to predict W_c and W_j as a function of and J_max estimated by an independent regression model and environmental growth conditions. In the same way, bootstrap analyses were conducted to predict N_ac as a function of estimated k₃ and J_fac. To do so, two-thirds of the 293 observations were randomly used to parameterize the multiple regression models (20 random sets, Tables S3–S4). These models were used to predict the leaf photosynthetic parameters , J_max, k₃ and J_fac of the remaining observations from their environmental growth conditions. As SLA was not predictable from environmental growth conditions (see in result the low coefficient of determination in SLA regression model), experimental specific values were used. Finally, W_c, W_j and N_ac were calculated and the coordination hypothesis was evaluated again (Tables S5–S6).

We also attempted to falsify the testable hypothesis (W_c = W_j and N_a = N_ac) provided by the photosynthetic coordination hypothesis. To this end, we randomized environmental growth conditions among observations (permutation test) and tested the alternative hypothesis significant differences between W_c and W_j and between N_a and N_ac.

Prediction from our leaf photosynthesis coordination model.

The implications of the coordination hypothesis for N_ac, A_n and PNUE were tested by varying: i) the values of the leaf parameters k₃ and J_fac under mean environmental growth conditions (PPFD = 666 µmol m⁻² s⁻¹, T_g = 16.9°C, h_s = 0.74); ii) the values of the environmental growth parameters T_g and PPFD assuming mean leaf photosynthetic parameter values (k₃ = 59.1 µmol g⁻¹Np_a s⁻¹; J_fac = 2.45; SLA = 17.7 m² kg⁻¹ DM).

All statistical tests were performed using Statgraphics Plus (v. 4.1, Manugistics, USA).

Results

Leaf Photosynthesis Shows Co-limitation Under Mean Growth Conditions

We assessed the level of photosynthetic co-limitation by comparing dark (W_c) to light-driven (W_j) biochemical processes under growth conditions experienced by the leaves in the month prior to observations. W_c strongly correlated with W_j (Fig. 1A, n = 293, P<0.001, intercept not significantly different from zero) across species and growth environments (characterized by T_g, PPFD, h_s and C_g). An ANOVA on the regression residuals revealed a significant PFT effect (d.f. = 5, 283; P<0.001; data not shown). The calculated W_c/W_j ratio was not significantly different from one (t-test at P<0.05, n = 293). This ratio varied neither with species parameters, nor with environmental growth conditions.

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Figure 1. Tests of the coordination hypothesis using experimental values of leaf photosynthetic traits (Vc_max, J_max, J_fac, k₃ and SLA).

A) Relationship between the predicted rates of RuBP carboxylation/oxygenation (W_c) and RuBP regeneration (W_j) under plant growth conditions. B) Relationship between predicted (N_ac) and observed (N_a) leaf N content. N_a was calculated as the sum of the leaf photosynthetic and structural N contents. Leaf photosynthetic N content was predicted using Eqn 2 with the species-specific parameters k₃ and J_fac. C) Relationship between predicted (Np_ac) and observed (Np_a) photosynthetic leaf N content. D) Relationship between predicted and observed leaf C/N ratio. A common leaf structural N content was used (fns = 0.012 gN g⁻¹ DM). Solid lines are the regressions. Short-dashed and long-dashed lines indicate the confidence (at 95%) and prediction intervals, respectively. The insert in Fig. 1B shows the same relationship without the very high observed N_a values for the PFT1. ***, P<0.001.

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Predicted Coordinated Leaf N Content (N_ac) Matches Observed Leaf N Content (N_a)

Overall, predicted and observed N_a values were closely correlated with a slope not significantly different from one and an intercept not significantly different from zero (Fig. 1B, n = 293, P<0.001, RRMSE = 0.12). The breakdown of RRMSE into unsystematic and systematic error terms showed that the prediction error was mostly unsystematic and therefore associated to data and not to a systematic model error (RRMSEs = 0.012; RRMSEu = 0.108). An ANOVA on the residuals of the prediction showed weak but significant effects of PFTs, T_g and h_s (d.f. = 5, 1, 1, respectively; P<0.01; data not shown).

As f_ns was assumed constant across species [25], we calculated N_pa and N_pac by subtracting the ratio f_ns/SLA to N_a and N_ac, respectively. Similarly, predicted and observed Np_a values were closely correlated (Fig. 1C, n = 293, P<0.001, RRMSE = 0.21).

As carbon content in leaves was assumed to be approximately constant, we calculated a C/N ratio by dividing N_a and N_ac by the ratio between a common carbon content (fcs = 0.45 gC g⁻¹ DM; [36], [38]) and SLA. Predicted C/N matched significantly the calculated C/N, observed across environmental conditions and across species and PFTs (Fig. 1D).

Dependency of Leaf Parameters on Plant Functional Type

In the dataset (Table S1), the parameters used to calculate leaf photosynthesis and stomatal conductance were SLA, J_fac, k₃, calculated from , J_max and leaf N measurements (Eqn 12, 15). At T^r, and J_max varied between 4–141 µmol m⁻² s⁻¹ and 8–213 µmol m⁻² s⁻¹, respectively. k₃ varied from 4.6 to 350 µmol g⁻¹N s⁻¹ while J_fac values were very constrained from 1.69 to 3.71, as already observed [2]. Finally, SLA varied from 1.5 to 43.2 m² kg⁻¹ DM. All photosynthetic traits showed significant dependency to PFT (P<0.001) but with different determination coefficient (r² = 0.66, 0.64, 0.24, 0.47 and 0.40 for , J_max, k₃, J_fac and SLA, respectively). Post-ANOVA LSD tests showed that the discrimination among the PFTs was more effective for J_fac, J_max and SLA separating significantly four groups among the six PFTs (Table S7) and was much weaker for k₃ and (two groups were significantly distinguished).

k₃, J_fac and SLA can be optimized to a value which minimizes the squared differences between N_a and N_ac (Table 3A). When k₃ was optimized by PFT, N_a was accurately predicted (slope = 0.96, r² = 0.73, RRMSE = 0.23). When a single value was used for the whole dataset, N_a prediction was not satisfactory. The optimization by PFT of J_fac led to a strong prediction of N_a (slope not different from one, r² = 0.79, RRMSE = 0.23). When a single value was used for the entire dataset (J_fac = 2.11), the prediction of N_a was less accurate but the slope of the relationship between W_c and W_j remained close to one. Finally, the optimisation of SLA by PFT or to a single value for the entire dataset strongly reduced the accuracy of N_a prediction. Optimization of the k₃ and J_fac parameters showed that N_a can be acceptably predicted when their values are defined by PFT. For all traits, average values by PFT and optimized values by PFT displayed significant linear relationships (Table 3B).

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Table 3. Estimates of the optimized value (for the entire dataset and by PFT) of leaf photosynthetic traits (J_fac, k₃ and SLA).

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Dependency of Leaf Parameters to Environmental Growth Conditions

All leaf photosynthetic parameters could be predicted from environmental growth conditions (Table 4). However, SLA was poorly correlated with environmental conditions (r² = 0.15). J_max was reasonably well predicted by environment (r² = 0.64, P<0.001). It was predominantly affected by the N level experienced by plants during growth (36% of explained variance), with a high N level leading to higher J_max values. J_max was then positively affected by PPFD (7%), h_s (13%), and PPFD times T_g (5%) and was negatively affected by soil moisture level (12%), T_g (9%), and PPFD times h_s (18%). , which was significantly predicted from environmental condition during growth (r² = 0.66, P<0.001), was mainly affected by T_g (33%, negatively), N level (25%, positively) and soil moisture level (15%, negatively). Then, was positively affected by PPFD (8%) and h_s (5%) and was negatively affected by CO₂ level (5%) and PPFD times h_s (8%).

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Table 4. Effects of environmental conditions on the leaf photosynthetic traits:

J_max, J_fac, k₃ and SLA.

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J_fac was significantly predicted from environment (r² = 0.51, P<0.001) and the variance was shared between CO₂ level (27%, positively), h_s (19%, positively), and PPFD times h_s (24%, negatively). Note that J_fac increased with CO₂ concentration as reviewed by Ainsworth and Long [33]. The remaining variance was positively explained by PPFD (6%) and PPFD times T_g (6%) and negatively explained by N and moisture levels (10 and 8%, respectively). k₃ was significantly predicted (r² = 0.44, P<0.001) and the variance was predominantly explained by N level (65%), with higher k₃ at lower N availability level, as also reviewed by Ainsworth and Long [33]. The temperature experienced by leaves during the preceding month was also an important driver of k₃ (25%), with lower k₃ at higher temperature. The remaining variance was positively explained by PPFD (2%) and h_s (4%) and negatively explained by PPFD times h_s (3%).

Once the multiple regression models were established for each leaf photosynthetic parameter, we tested by bootstrap analysis if their prediction was robust enough to satisfy the coordination hypothesis. All random datasets generated by bootstrap (n = 220) gave significant regression models (Tables S5–S6). The parameters values of these regression models were used with the remainder of the data (n = 293–220 = 70) to predict leaf photosynthetic parameters values. Photosynthetic parameters values were then used to predict W_c, W_j and N_ac. We found that W_c matched W_j (Fig. 2A) and N_ac matched N_a (Fig. 2B, RRMSE = 0.2), whatever the random dataset to which it was applied (Tables S5–S6).

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Figure 2. Tests of the coordination hypothesis using values of leaf photosynthetic traits predicted from environmental growth conditions.

A) Relationship between the predicted rates of RuBP carboxylation/oxygenation (W_c) and RuBP regeneration (W_j) under plant growth conditions. B) Relationship between predicted (N_ac) and observed (N_a) leaf N content. The insert in Fig. 2B shows the same relationship without the very high observed N_a values for the PFT1. Symbols are as for Fig. 1.

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In an attempt to falsify the leaf photosynthesis coordination hypothesis, we have randomized environmental growth conditions among observations. This randomization resulted in a strong mismatch between W_c and W_j (RRMSE = 0.76; slope = 0.60±0.33; r² = 13%) as well as between N_a and N_ac (RRMSE = 0.72; slope = 0.80±0.40; r² = 17%).

Prediction from Our Leaf Photosynthesis Coordination Model

Under standard environmental conditions, Np_ac varied significantly with k₃ and J_fac (Fig. 3A). Np_ac decreased with increasing k₃ (Fig. 3A), which imposed a strong constraint on this physiological trait. For a given leaf Np_ac, high values of k₃ did not affect A_n (Fig. 3B), but PNUE increased linearly with k₃ (Fig. 3C). For a given k₃ value, both Np_ac (Fig. 3A) and A_n (Fig. 3B) displayed saturating responses to increasing J_fac. As a consequence, PNUE was little affected by J_fac (Fig. 3C). In our model (Eqn 1), SLA and f_ns affected N_ac, but did not affect Np_ac and consequently A_n and PNUE. Since SLA displayed a higher degree of variation, the leaf structural content per unit area and consequently the leaf N content were strongly dependent on SLA. Thus, the leaf structural N content per unit area and the leaf N content followed an inverse relationship as SLA increased.

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Figure 3. Relationships between simulated photosynthetic leaf N content (Np_ac) (A), net photosynthesis (A_n) (B) and photosynthetic N use efficiency (PNUE) (C) and the photosynthetic traits k₃ and J_fac under standard mean environmental conditions (PPFD = 666 µmol m⁻² s⁻¹, T_g = 16.9°C, h_s = 0.74).

k₃ is the ratio between and Np_a. J_fac is the ratio between J_max and . A mesh of k₃ values varying between 10 and 300 µmol g⁻¹ N s⁻¹ with 20 steps and of J_fac values varying between 1.75 and 3.5 with 0.05 steps was used. Figures D–E–F, relationships between (Np_ac) (D), net photosynthesis (A_n) (E) and photosynthetic N use efficiency (PNUE) (F) and the radiation (PPFD) and temperature (T_g) conditions during growth. Averages over the dataset of leaf photosynthetic parameters (k₃, J_fac and SLA) are used (k₃ = 59.1 µmol g⁻¹ N_pa s⁻¹, J_fac = 2.45, SLA = 17.7 m² kg⁻¹ DM). The mesh for temperature is 0.5°C between 10 and 30°C and the mesh for radiation is 50 µmol m⁻² s⁻¹ between 300 and 1200 µmol m⁻² s⁻¹. The values of h_s and T_g were fixed at 0.8 and 20°C, respectively. A_n was calculated with the coordinated leaf protein content and PNUE was calculated as the ratio between A_n and Np_ac.

https://doi.org/10.1371/journal.pone.0038345.g003

When using overall dataset means of the leaf photosynthetic traits, Np_ac varied significantly with radiation and temperature (Fig. 3D). Np_ac increased linearly with PPFD and decreased with Tg according to a logistic curve (Fig. 3D, Fig. S2). For a given Np_ac, temperature affected A_n according to a quadratic curve with an optimal Tg around 20°C although PPFD affected linearly A_n (Fig. 3E). As a consequence, PNUE was affected by Tg according to a peak curve with an optimal Tg at 25°C and was positively affected by PPFD according to a logarithmic curve (Fig. 3F).

Discussion

A Successful Test of the Coordination Hypothesis of Leaf Photosynthesis

The coordination hypothesis provides a testable analytical solution to predict both photosynthetic capacity and area-based leaf N content and, hence, to couple photosynthetic C gain and leaf N investment. With the large dataset used in this study, we could not falsify this testable hypothesis. Therefore, our results strongly support the validity of the leaf photosynthetic coordination hypothesis across a wide range of C₃ plant species and of environmental conditions.

Our coordination model linking leaf photosynthesis, stomata conductance and nitrogen investment has a total of 33 parameters. Only four parameters are directly related to a coordinated investment of leaf N into carboxylation capacity (; RuBP carboxylation; Rubisco) and electron transport capacity (J_max, RuBP regeneration; light harvesting): J_fac, the ratio of J_max to determines the photosynthetic capacity; and k₃, the ratio of to leaf photosynthetic N content (Np_ac) determines the fraction of metabolic leaf N invested in photosynthesis. The ratio of f_ns to SLA determines the fraction of non-metabolic N per unit total leaf N.

Photosynthetic parameter values vary to a considerable extent across species and environmental conditions in agreement with previous studies [2], [3], [39]. For instance, Wullschleger [2] reported that, when expressed at a reference temperature of 20°C, varies in the range 5–142 (µmol m⁻² s⁻¹); J_max in the range 11–251 (µmol m⁻² s⁻¹) and J_fac in the range 0.9–3.8 (dimensionless). Despite similar large differences in our dataset in parameter values across species and environmental conditions, our photosynthetic coordination model accounts for 93% of the total variance in N_a. Moreover, the model has a low systematic RRMSE with no systematic bias. The statistical validity of this model supports the conclusion that sunlit mature leaves of C₃ plants tend to achieve photosynthetic coordination in a wide range of both optimal and sub-optimal environmental conditions.

Along the vertical profile of C₃ plant canopies, an empirical scaling law between area based leaf N content and transmitted PPFD has often been reported [15], [17], [40], [41] and has been determined as the predominant factor of N decline relative to others like leaf age or N demand [12], [40], [41]. Various hypotheses have been put forward to explain this observation [11], [22], [42], [43]. Our model of the coordination hypothesis matches this scaling law, since Np_ac scales with radiation (PPFD) along the vertical canopy profile (Eqn. 2). Air temperature (T_g), relative air humidity (h_s) and ambient CO₂ concentration (C_a) also vary with depth within the canopy. At a given PPFD, higher h_s and lower T_g at depth would reduce Np_ac, while a lower C_a would increase it. For some crop species like wheat, N limitation has been reported to accelerate the decline in N_a with PPFD [25], [40], [41], which may indicate preferential N allocation to leaves in full light, resulting in preferential photosynthetic coordination of these leaves despite N limitation.

Variations in photosynthetic N protein contents (Np_ac) appear to be an overwhelming determinant of N_a. In contrast, structural leaf N (f_ns) values varied only within a narrow range [38], when they were optimized by species or by PFT (from 0.0107 to 0.0135 gN g⁻¹ DM for wheat and N-fixing trees, respectively, corresponding to 0.61 and 0.78 gN m⁻² leaf when SLA is set to 17.6 m² kg⁻¹ DM, dataset mean). Although optimized f_ns values showed little variations on a leaf dry mass basis, it accounted for 15–50% of N_a (gN m⁻²), across all species in the dataset due to the strong variation in SLA across all species. Structural N is found in cell walls (1.6–9.5% of leaf N in Polygonum cupsidatum and 40–60% for sclerophyllous tree, shrub and vine species, [34], [44]) and in nucleic acids (10–15%, [45]). In addition, other non-photosynthetic nitrogenous compounds (e.g. cytosolic proteins, amino acids, ribosomes and mitochondria) contribute to the structural leaf N pool [46]. Several experimental studies have attempted to estimate f_ns, reporting values between 0.0101 and 0.0136 gN g⁻¹ DM for a range of herbaceous C₃ species [16]. These f_ns values are in the same range as those found for dead leaves after N resorption at senescence [47]. Structural N would therefore not be redistributed by this process [48].

Determinism of Leaf N Content Variation

Genetic and environmental factors have long been recognized to interact in determining the A_max vs. leaf N relationship [5]. Our study provides a means for disentangling: i) the direct environmental effects on leaf photosynthetic N content (Np_ac); ii) the role of photosynthetic parameters for Np_ac in a given environment; and iii) the response of photosynthetic parameters i.e. the plant acclimation to plant growth environment.

First, for a given set of plant parameters, positive effects of radiation and negative effects of air temperature, air relative humidity and CO₂ concentration on Np_ac are predicted by Eqn 2 (Fig. 3D–F). These results are in accordance with the prediction by Farquhar et al’s canopy photosynthesis model [49], which links stomatal control with leaf area and leaf N content by optimizing both water and nitrogen use efficiency and predicts an increase of leaf N content and with mean radiation increase [24], [50] and mean annual rainfall [49], [51]. According to the coordination hypothesis, changes in Np_ac affect both biochemical photosynthesis capacities, and J_max. Indeed, seasonal variations in and J_max have been observed for a number of plant species [52], [53] and were related to changes in Rubisco and cytochrome-f contents in Polygonum cuspidatum [54]. Including photosynthetic capacity ( and A_max) and its relationship to leaf N content in terrestrial biosphere models resulted in substantial changes in gross primary productivity with latitude [7]. Coupled environmental variations in PPFD, T_K, h_s and C_a simultaneously affect Np_ac throughout time, which has major implications for gross primary productivity and PNUE of a given species or genotype.

Second, the coordination hypothesis implies that under a given environment, N_a tends toward a unique coordinated N_ac value (Eqn 2). As shown by the analysis of model sensitivity to parameters and input variables (Text S1, Fig. S3), k₃ and J_fac are among the most important determinants of N_ac value. Assuming a single average value of k₃ and of J_fac for all species in the dataset would increase N_a RRMSE by 50% (Table 3A). However, using a single J_fac value by PFT with species-specific k₃ and SLA values provided a strong accuracy for N_a prediction. This result is consistent with the strong linear relationship between and J_max reported by Wullschleger [2] among 109 species, which probably indicates a phylogenetic constraint for J_fac. Under given environmental conditions, our results show that there is no single combination of k₃ and J_fac that can maximize both A_n and PNUE (Fig. 3A–C). Therefore, variable combinations of these photosynthetic traits could be equally relevant. This relative independency of k₃ and J_fac suggests that these functional traits (sensu [55]) correspond to possibly overlooked axes of differentiation among C₃ plant species. k₃, which modulates the N investment at a given A_n, could be related to a plant strategy of nutrients conservation [56]. J_fac, which increases A_n for a given k₃, could be related to a plant strategy of nutrients exploitation. However, the lack of correlation between these two photosynthetic traits and SLA, which is a key morphological trait separating exploitative and conservative species strategies for nutrient use [56], suggests that these physiological traits form a secondary axis of differentiation across C₃ species.

Third, some environmental growth conditions such as PPFD, T_g, h_s, C_a and N availability had significant effects on k₃ and J_fac. The increase in k₃ at low N availability tends to reduce Np_ac and, hence, N demand for leaf construction thereby increasing PNUE. The increase in k₃ with PPFD tends to compensate for the direct positive effect of PPFD on Np_ac, thereby lowering N demand for leaf construction under high light environments. Similarly, the decrease of k₃ with T_g mitigates the direct negative effect of temperature on Np_ac, thereby equalizing the N demand for a range of temperature. Mostly independently from changes in k₃ (since these two traits are not correlated across plant species), J_fac increases with C_a, in agreement with the lower decline under elevated CO₂ of J_max compared to [33]. Moreover, J_fac is negatively related to PPFD, which is in good agreement with the higher allocation of leaf N to chlorophyll observed in low PPFD acclimation experiments [57]. Like the increase in k₃, the decrease in J_fac with PPFD tends to compensate for the direct positive effect of PPFD on Np_ac, especially for species with low k₃ value. Finally, the effect of temperature on J_fac is not significant which is in agreement with previous studies that reports constant J_fac with temperature (e.g. [33]).

Uncertainties in the Calculation of the Coordinated Leaf Photosynthetic N Content

Our model takes into account the two main biochemical processes controlling leaf photosynthesis as well as the biophysical process controlling stomatal conductance. Recently, leaf mesophyll conductance has also been identified as an important biophysical limitation of photosynthesis [58]–[60], particularly for species with low SLA by decreasing more than J_max [61], [62] and particularly during plant acclimation to water stress condition [58], [59]. Applying mesophyll conductance in our model would first require recalculating parameter from a non-rectangular hyperbola of the A_n-C_i curve and with a new set of Rubisco kinetic constants, for example [58]. Moreover, it would also require the incorporation in our model of the CO₂ diffusion mechanism between intercellular and chloroplast spaces according to a mesophyll conductance parameter [59], [60]. Furthermore, the coupling between A_n and g_s leading to the calculation of A_n would require solving a new system of equations and unknowns. Finally, this would require additional mesophyll conductance data, which were not available in our dataset. The inclusion of a variable mesophyll conductance [61], [62], as well as of other mechanisms implied in plant responses to water deficits [63], would allow testing the photosynthetic coordination hypothesis under severe abiotic stress conditions. With the coordination model reported here that does not include these processes, N_a values are lower than N_ac values under more severe abiotic stress conditions (data not shown).

The calculation of Np_ac relies on a number of plant parameter and environmental variables, leading to further uncertainties (see Text S1, Table S2 and Fig. S2–S3 for full details). Apart from SLA, k₃ and J_fac, all plant parameters were assumed to have a single set of values across the entire dataset (Table 2). Since the photosynthetic model was shown to be little sensitive to most of these parameters (Text S1, Fig. S3), using species-specific values would only marginally increase the accuracy of N_a prediction.

Implications

Overall, our study confirms the basic assumption of the coordination hypothesis: leaves coordinate the development of and J_max such that W_c equals W_j. This opens opportunities to couple C and N at a global scale by incorporating the coordination hypothesis into dynamic global vegetation models (DGVMs). However, the applicability of this hypothesis for improved prediction of photosynthetic capacity and leaf nitrogen content depends on the accuracy at which we can determine key parameters of the combined photosynthesis - stomatal conductance – leaf N model as well as the timescale of plant regulatory photosynthesis mechanisms. The two key parameters J_fac and k₃ seem to be predictable from a combination of environmental growth conditions - probably due to the strong dependence of the development of the photosynthetic machinery on environment variables – and information about plant growth form or PFT. However, the morphological trait SLA does not seems to be predictable with sufficient accuracy from environmental conditions which is consistent with the large functional diversity found in a given environment [64]. SLA needs to be defined at least by PFT and preferably by species. This study thus confirms the relevance of leaf morphology, represented by SLA, in photosynthesis, which has been pointed out before, (e.g. [56]). However, SLA is one of the best-studied plant traits worldwide (e.g. [36]) and it may be possible to determine SLA with sufficient accuracy for a large range of C₃ species. Finally, although the turnover of photosynthetic enzymes like Rubisco can be seen as very constrained within the C₃ plant kingdom, to our knowledge there is no study that investigates its variability across species. We therefore stress the need for further comparative research quantifying the variability of photosynthetic enzyme turnover across C₃ species. Further tests of the coordination hypothesis will require, during plant growth, coupled measurements of microclimate, of leaf gas exchanges and of photosynthetic traits, including the dynamics of Rubisco, within the canopy [65].

Conclusion

This study bridges a gap concerning the coupling of C and N fluxes in C₃ plant species. It confirms the basic assumption of the leaf photosynthesis coordination hypothesis and demonstrates that this hypothesis can be successfully applied across species and PFTs and under a wide range of climates. Moreover, we have shown that k₃ and J_fac in combination with SLA are major plant functional traits, which reflect plant adaptation to light, temperature and N availability during growth. Surprisingly, few studies provide both leaf photosynthetic parameters and environmental conditions during plant growth. Improved datasets combining the k₃ and J_fac photosynthetic traits with the SLA morphological trait are needed to further increase our understanding of leaf economics (C–N stœchiometry) and plant strategies. The leaf photosynthesis coordination model reported here has been successfully used in a patch scale grassland vegetation model [66], [67]. Further applications include modeling at regional and global scales the role of plant diversity for the carbon and nitrogen cycles.

Supporting Information

Figure S1.

Details on the leaf photosynthesis coordination hypothesis. Variation of leaf carboxylation rates with leaf nitrogen content for three levels of radiations (A–C). According to the leaf photosynthesis coordination theory, a leaf photosynthetic N content is determined as colimiting the carboxylation/oxygenation of ribulose-1,5-bisphosphate (RuBP) by the enzyme ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco; W_c), and the regeneration of RuBP by the electron transport chain (W_j). Below N_pac, the photosynthesis will be limited by the Rubisco activity and therefore by the amount of leaf proteins. Beyond N_pac, the marginal gain of photosynthesis per unit of leaf proteins is weak. Along the vertical canopy profile, N_pac declines with transmitted radiation when all other variables are equal.

https://doi.org/10.1371/journal.pone.0038345.s001

(TIF)

Figure S2.

Mean temperature functions of the maximum rates of carboxylation () and electron transport (J_max) and their ratio (/). Functions were calculated using the parameters related to temperature sensitivity (activation and deactivation enthalpies and entropy) as calibrated by Kattge & Knorr (2007) for many species (48 species for , 32 for J_max and 29 for their ratio). The error bars correspond to the standard errors among species representing the inter-specific variability.

https://doi.org/10.1371/journal.pone.0038345.s002

(TIF)

Figure S3.

Sensitivity analysis of the photosynthesis-stomatal conductance model. Following Félix & Xanthoulis (2005), a sensitivity analysis of the models calibrated for Dactylis glomerata with common one-to-one variation of parameters (±15%). Output variables are shown as lines, parameters as columns. The sensitivity index (IOS) was calculated as the maximal ratio of output variation to parameter variation during a climatic scenario (air temperature, PPFD, h_s and C_a) recorded from an upland site in central France (Theix, 45°43′N, 03°01′E, 870 m) for years 2003–2004. Color tones indicate sensitivity index (positive, red; negative, blue).

https://doi.org/10.1371/journal.pone.0038345.s003

(TIF)

Table S1.

Dataset used for the validation of leaf photosynthesis coordination. The excel file includes the leaf photosynthetic parameters and the environmental growth conditions used to calculate W_c, W_j and N_ac.

https://doi.org/10.1371/journal.pone.0038345.s004

(XLS)

Table S2.

Range of the observed values among literature of the parameters used in the leaf photosynthesis – stomatal conductance model. The categories were the minimum, the maximum, the median and the percentage of variation of parameters range. The sources of observations were also reported. The sources, where the minimum and maximum values were observed, were annotated with – and +. A reference temperature of 20°C was used.

https://doi.org/10.1371/journal.pone.0038345.s005

(DOC)

Table S3.

Multiple regression analyses of Vc_max and J_max from environmental growth conditions for the bootstrap analysis. Independent variables: X₁: air CO₂ concentration (C_g); X₂: N level; X₃: soil H₂O level; X₄: radiation (PPFD); X₅: air growth temperature (T_g); X₆: air relative humidity (h_s). The number of observations was 236.

https://doi.org/10.1371/journal.pone.0038345.s006

(DOC)

Table S4.

Multiple regression analyses of k₃ and J_fac from environmental growth conditions for a bootstrap analysis. Independent variables were the same as Table S3. The number of observations was 236.

https://doi.org/10.1371/journal.pone.0038345.s007

(DOC)

Table S5.

Prediction of W_c and W_j (µmol m⁻² s⁻¹) in using the parameters Vc_max and J_max calculated from regression analyses on the independent part of the dataset in a bootstrap analysis (Table S3). Characteristics of the W_c/W_j relationship. The intercepts of regression for each PFT were set to zero (since there were not significantly different from zero) to estimate the slopes. RRMSE: relative root mean square error.

https://doi.org/10.1371/journal.pone.0038345.s008

(DOC)

Table S6.

Prediction of N_ac in using the parameters k₃ and J_fac calculated from the regression analyses on the independent part of the dataset in a bootstrap analysis (Table S4). Characteristics of the relationship between predicted and observed leaf N content (N_ac/N_a, gN m⁻²). The intercepts of regression for each PFT were set to zero (since there were not significantly different from zero) to estimate the slopes. Abbreviation: RRMSES and RRMSEU are systematic and unsystematic relative root mean square error, respectively.

https://doi.org/10.1371/journal.pone.0038345.s009

(DOC)

Table S7.

Dependence of leaf photosynthetic parameters on plant functional type (PFT). ANOVA model and mean comparison test by LSD method of the PFT effect on leaf photosynthetic traits used in the test of coordination hypothesis (, J_max, k₃, J_fac and SLA). The values of k₃ and J_fac were log-transformed and all residuals followed a normal distribution. For a given variable, PFTs with the same letter belong to the same group.

https://doi.org/10.1371/journal.pone.0038345.s010

(DOC)

Text S1.

Sensitivity analysis of the photosynthesis – stomatal conductance model.

https://doi.org/10.1371/journal.pone.0038345.s011

(DOC)

Text S2.

Demonstration of the formalism of the coordinated leaf photosynthetic N content.

https://doi.org/10.1371/journal.pone.0038345.s012

(DOC)

Acknowledgments

Authors thank V. Allard, N. Gross, J. Schymanski, N. Viovy and P. Ciais for constructive comments on a previous version of the manuscript.

Author Contributions

Conceived and designed the experiments: JFS VM. Analyzed the data: VM PM JK JFS. Wrote the paper: VM PM JK JFS. Assembled the data: JK VM PM FG GE. Provided model development and statistical methods: VM. Commented on the manuscript: GE SF FG.

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Figures

Abstract

Introduction

Methods

A Model Coupling Leaf N with CO2 and H2O Fluxes

Coordinated N Content of Sunlit Leaves

Dataset

Data Analysis

Coordinated Wc and Wj.

Prediction of the coordinated leaf N content.

Dependence of leaf photosynthetic parameters on plant functional type (PFT).

Dependence of leaf photosynthetic parameters on environmental growth conditions.

Prediction from our leaf photosynthesis coordination model.

Results

Leaf Photosynthesis Shows Co-limitation Under Mean Growth Conditions

Predicted Coordinated Leaf N Content (Nac) Matches Observed Leaf N Content (Na)

Dependency of Leaf Parameters on Plant Functional Type

Dependency of Leaf Parameters to Environmental Growth Conditions

Prediction from Our Leaf Photosynthesis Coordination Model

Discussion

A Successful Test of the Coordination Hypothesis of Leaf Photosynthesis

Determinism of Leaf N Content Variation

Uncertainties in the Calculation of the Coordinated Leaf Photosynthetic N Content

Implications

Conclusion

Supporting Information

Acknowledgments

Author Contributions

References

A Model Coupling Leaf N with CO₂ and H₂O Fluxes

Coordinated W_c and W_j.

Predicted Coordinated Leaf N Content (N_ac) Matches Observed Leaf N Content (N_a)