Modeling photosynthetic resource allocation connects physiology with evolutionary environments

The regulation of resource allocation in biological systems observed today is the cumulative result of natural selection in ancestral and recent environments. To what extent are observed resource allocation patterns in different photosynthetic types optimally adapted to current conditions, and to what extent do they reflect ancestral environments? Here, we explore these questions for C3, C4, and C3–C4 intermediate plants of the model genus Flaveria. We developed a detailed mathematical model of carbon fixation, which accounts for various environmental parameters and for energy and nitrogen partitioning across photosynthetic components. This allows us to assess environment-dependent plant physiology and performance as a function of resource allocation patterns. Models of C4 plants optimized for conditions experienced by evolutionary ancestors perform better than models accounting for experimental growth conditions, indicating low phenotypic plasticity. Supporting this interpretation, the model predicts that C4 species need to re-allocate more nitrogen between photosynthetic components than C3 species to adapt to new environments. We thus hypothesize that observed resource distribution patterns in C4 plants still reflect optimality in ancestral environments, allowing the quantitative inference of these environments from today’s plants. Our work allows us to quantify environmental effects on photosynthetic resource allocation and performance in the light of evolutionary history.


Scientific Reports
| (2021) 11:15979 | https://doi.org/10.1038/s41598-021-94903-0 www.nature.com/scientificreports/ around Rubisco 13 . The energy requirements of C 4 metabolism also differ from those of the C 3 pathway 14 , as further ATP is needed for the regeneration of PEP, while ATP and NADPH requirements of the photorespiratory pathway are reduced. The metabolic efficiencies of the C 3 and C 4 system depend strongly on the environment. To achieve optimal metabolic efficiency, plants have to coordinate gene expression of the Calvin-Benson cycle, photorespiration, light reactions, and, in the case of C 4 plants, the C 4 cycle; this coordination occurs in a complex response to the availability of light energy and nitrogen and of factors that influence the rate of photorespiration. The diversity of photosynthetic resource allocation patterns is emphasized by the existence of C 3 -C 4 intermediate photosynthesis in some plants, where features of the archetypical C 4 syndrome are only partially expressed. The genus Flaveria contains closely related species that employ the C 3 , C 3 -C 4 intermediate, and C 4 versions of photosynthetic metabolism, making it an ideal system to study the interaction between resource allocation and environment in photosynthesis. The selection pressures caused by environmental factors over evolutionary time scales are expected to lead to corresponding adaptations of gene regulation. In contrast, environmental variation on the time scale of individual generations may select for regulatory programs that adjust plant metabolism to the environment they currently face, a process called phenotypic plasticity. Reviewing the occurrence of phenotypic plasticity in C 3 and C 4 plants, Sage and McKown 15 argued that C 4 plants show limited regulation of Rubisco content in response to environmental factors like sunflecks and low temperatures. Although the extent of phenotypic plasticity in plants is intensively studied e.g. [15][16][17][18] , the plasticity in terms of resource allocation is not fully understood. In particular, it is not clear whether the phenotypic plasticity of different plant lineages is sufficient to acclimate optimally to the current environment; instead, many plants might still allocate at least parts of their resources in patterns that were optimal in the environments that dominated their recent evolutionary history.
The areas where C 4 dicotyledonous plants are assumed to have evolved are regions of low latitude showing combinations of heat, drought, and salinity 13 . For Flaveria, analyses that combine phylogenetic context and environmental information point toward an evolutionary origin in open habitats with high temperatures 13,19,20 . The last common C 3 ancestor of the current Flaveria species lived 2-3 million years ago 21 , when CO 2 levels were significantly lower than the current, postindustrial level 22,23 . In summary, Flaveria species likely faced high light intensities, high temperatures, and low atmospheric CO 2 levels during their recent evolutionary history.
The standard method to model the CO 2 assimilation rate of C 3 , C 4 , and C 3 -C 4 intermediate plants is based on the mechanistic biochemical models of Berry and Farquhar 24 , Farquhar et al. 25 , and von Caemmerer 9,26 . These models predict the light-and enzyme-limited CO 2 assimilation rate with great success, and take into consideration enzymatic activities and various environmental parameters, including mesophyll CO 2 level and light intensities. In many ecosystems, the most limiting resource for plant growth is nitrogen 27,28 , and a high proportion of nitrogen is used in photosynthesis 29 . The increased nitrogen-use efficiency of C 4 species compared to C 3 relatives indicates that nitrogen availability may have played a major role in C 4 evolution 30 . Models of optimal nitrogen allocation were successfully used to understand the response to environmental factors like elevated CO 2 31,32 , light 33,34 , and temperature 35 , but these approaches were limited to C 3 plants. In order to understand how optimal resource allocation patterns shifted during C 4 evolution, a new modeling framework is required.
Here, we aim for a detailed understanding of the interplay between resource allocation and current and past evolutionary environments in relation to CO 2 assimilation occurring in C 3 , C 4 , and C 3 -C 4 intermediate species.
To achieve this goal, we developed a mathematical model for these photosynthetic types that integrates knowledge of resource costs and relevant environmental factors. Using this model, we seek to understand (1) to what extent resource allocation is phenotypically plastic and to what extent it appears adapted to an environment the plants were facing during their evolutionary history; and (2) if resource allocation patterns can be used to identify unique environments to which allocation is optimally adapted.

Methods
Model overview. Here, we present a nitrogen-dependent light-and enzyme-limited model for the steadystate CO 2 assimilation rate, which-depending on its parameterization-can describe C 3 , C 3 -C 4 intermediate, and C 4 photosynthetic types. Figure 1 shows a schematic overview, highlighting the relationships between the major pools of photosynthetic nitrogen (Rubisco, C 4 cycle, and thylakoids). The definitions of the corresponding model parameters are listed in Table 1. Not all parameters are represented explicitly in Fig. 1, e.g., the schematic figure does not distinguish linear and cyclic electron transport, or the two enzymes PEPC and PPDK that represent the C 4 cycle. In this study, we parameterize the model to describe species from the genus Flaveria; parameter values are listed in Supplementary Table S1. Before describing the model components in detail, we provide an overview of the model in the following paragraphs.
We extended the light-and enzyme-limited C 3 -C 4 models originally developed by von Caemmerer 9 and modified by Heckmann, et al. 2 . We added a fixed budget of nitrogen constraining the total abundance of photosynthetic proteins using previous knowledge about the major nitrogen requirements of photosynthetic components, e.g., Rubisco 36 . Furthermore, we extended the existing models by explicitly modeling the ATP and NADPH production of the linear and cyclic electron transport (LET and CET, respectively). Thus, an environmentdependent photosynthetic nitrogen budget is distributed across the enzymes of the Calvin-Benson cycle in the mesophyll and bundle sheath cell, the C 4 cycle, and the proteins of the LET and CET in the thylakoid membranes. Combining this model with the temperature dependency of the photosynthetic apparatus 37 results in a detailed model of photosynthesis that incorporates leaf nitrogen level, light intensity, mesophyll CO 2 and O 2 levels, and the effects of temperature.
In order to understand physiological data in the context of environmental adaptation, we aim to find optimal resource allocation in a given environment. To this end, we assume that resource allocation has been optimized by natural selection to maximize the CO 2 assimilation rate (A, [µmol m −2 s −1 ]) 23 www.nature.com/scientificreports/ optimization pipeline that reliably finds optimal resource allocation dependent on environments and photosynthetic types. In previous work, optimality assumptions were successfully used in a variety of photosynthetic systems; examples are the explanation of the coordination of ribulose-1,5-bisphosphate carboxylation and regeneration during C 3 photosynthesis 40,41 , optimal nitrogen allocation in C 3 plants in different environments [31][32][33][34][35]42 , the exploration of evolutionary trajectories from C 3 to C 4 photosynthesis 2 , the exploration of alternative inter-cellular transport pathways in C 2 plants 43 , and the prediction of proteome allocation in cyanobacteria 44 . We use optimality of the modeled CO 2 fixation rate to determine (1) the optimal relative investment of nitrogen into Rubisco, the C 4 cycle enzymes, and the proteins of the light-dependent reactions, (2) the optimal partitioning of NADPH between the Calvin-Benson cycle and the photorespiratory pathway, (3) the optimal partitioning of ATP across the Calvin-Benson cycle, photorespiratory pathway, and C 4 cycle (if relevant), and (4) the optimal proportion of LET and CET.
Environmental factors and evolutionary parameters. We specify the environment in terms of the following factors: light intensity, leaf nitrogen level, temperature, and CO 2 and O 2 mesophyll partial pressures. The photosynthetic type is defined by six parameters: the Rubisco distribution between mesophyll and bundle sheath cells (β); the Rubisco kinetics, (specified through a single parameter, k ccat [s −1 ], due to the known tradeoff relationships between the kinetic parameters 45 ); the maximal C 4 cycle activity (V pmax , [µmol m −2 s −1 ]); the fraction of glycine decarboxylated by the glycine decarboxylase complex in the bundle sheath cell that is derived from oxygenation by Rubisco in the mesophyll cell (ξ); the Michaelis constant of PEPC for bicarbonate (K p , [µbar]), and the bundle sheath cell conductance for CO 2 (g s , [µmol m −2 s −1 ]) (see Heckmann, et al. 2 for details). The values for the parameters are taken from the literature (see Supplementary Table S1 for details).

Nitrogen allocation.
To calculate the CO 2 assimilation rate, we focus on the photosynthetic nitrogen pool (N ps , [µmol m −2 ]). In our model, N ps can be allocated across the following major pools of leaf photosynthetic nitrogen: the main enzyme of the Calvin-Benson cycle (n Etot ), Rubisco; the main enzymes of the C 4 cycle (n C4 ), PEPC and PPDK (we decided to focus on PEPC and PPDK as the major nitrogen pools of the C 4 cycle based on the enzyme molecular weights and turnover numbers 46 ); and the thylakoids (n Jmax ), which include the photosynthetic electron transport chains. The CO 2 assimilation rate and other model parameters can be predicted for a freely chosen nitrogen allocation. Note that we are interested in determining the optimal nitrogen allocation (see Section "Optimization procedure" for details). The environment-specific N ps is calculated as a fraction of total leaf nitrogen (N t , [µmol m −2 ]) based on phenomenological observations (see Supplementary Methods S1 for details).
Nitrogen allocated to Rubisco. We only consider the nitrogen requirements of Rubisco in the Calvin-Benson cycle, as it accounts for the major nitrogen costs of this cycle 47 . The amount of catalytic sites of Rubisco (E tot , [µmol m −2 ]) is calculated from the invested nitrogen by Eq. (1), where n Etot represents the fraction of N ps invested into Rubisco: The number of catalytic sites per nitrogen is 1.27 × 10 -3 [ c E , µmol catalytic sites (µmol nitrogen) −1 ] and was derived from Harrison et al. 36 .
(1) E tot = n Etot · N ps · c E ,  The optimal fraction of photosynthetic nitrogen pool invested into the main enzymes of the C 4 cycle under the evolutionary scenario fraction n growth C4 The optimal fraction of photosynthetic nitrogen pool invested into the main enzymes of the C 4 cycle under the growth scenario fraction The optimal fraction of photosynthetic nitrogen pool invested into the Calvin-Benson cycle under the growth scenario fraction n fit The proportion of nitrogen invested into the thylakoids as a function of the leaf nitrogen level (a fit to empirical data) fraction n Jmax The fraction of photosynthetic nitrogen pool invested into the thylakoids, which include the electron transport chains fraction n evo

Jmax
The optimal fraction of photosynthetic nitrogen pool invested into the thylakoids under the evolutionary scenario fraction n growth Jmax The optimal fraction of photosynthetic nitrogen pool invested into the thylakoids under the growth scenario fraction We use previous knowledge about the relationship of thylakoid nitrogen costs and cyt as well as data from Ghannoum et al. 49 for abundances of PSI and PSII to include phenomenological stoichiometry rules between The convexity of the transition between the initial slope and the plateau of the hyperbola 0.7 9 unitless ξ The fraction of glycine decarboxylated in the bundle sheath cell that is derived from oxygenation by Rubisco in the mesophyll cell fraction  (7)]; pII Chl , pI Chl , and l Chl represent mol Chl (mol complex) −1 for PSII, PSI, and LHC, respectively). While we parameterize our model for Flaveria, the data of Ghannoum et al. 49 is for C 4 grasses and for C 3 dicots; however, as the data was very similar between the diverse species examined, it is likely that values in Flaveria are very similar. We assume that the chlorophyll content is shared between PSI, PSII, and LHC [Eqs. (6), (7)]. We extended the previous work by splitting these complexes according to the proportion of LET (p) and CET (1-p). For the LET, J max is related to N thy as described in Eqs. (8)- (11). N thy LET represents the available amount of nitrogen for the thylakoids with n Jmax representing the fraction of photosynthetic nitrogen pool invested into the thylakoids [Eq. (8)], accounting for LHC, PSII, PSI, and cyt [Eqs. (9), (10)]. The amount of cyt can be calculated according to Eq. (10) and related to J max via the empirical cyt Jmax ; cyt Jmax describes the relation of cyt to J max and was measured by Niinemets and Tenhunen 50 , who determined 156 mmol e -(mmol cyt s) −1 across various C 3 species. We are not aware of a comparable data set for C 4 plants. Assuming 95% of LET in C 3 plants, this leads to a capacity of 172 mmol e -(mmol cyt s) −1 for cyt Jmax .
Chlorophyll content (Chl, [µmol m −2 ]) is calculated based on an empirical factor 39 that relates the amount of nitrogen invested into thylakoids to the amount of chlorophyll in C 3 plants (see Supplementary Methods S2 for details). We again use work from Ghannoum et al. 49 to relate N thy to the amount of cyt [Eqs. (8)-(10)]; c N represents mol nitrogen per mmol cyt, and pII N , pI N , and l N represent mol nitrogen per mol Chl for PSII, PSI, and LHC, respectively).
The derivation for the CET is analogous to the case of the LET: in the last equation, we additionally required the factor Jmax CL , which describes the scaling of J max with cyt for the CET. This factor is assumed to be 3, as PSII is more expensive in terms of nitrogen compared to PSI 47,49 .
In summary, the free optimization parameters related to nitrogen allocation to the light reactions, p and n Jmax , affect J max in LET and CET via the cytochrome f content.
Optimization procedure. Theoretically, model predictions can be made using a freely chosen resource allocation. To understand the raised questions about environmental adaptation, we will analyze the fittest plants, i.e., plants with the resource allocation that results in the maximal CO 2 assimilation rate. To find the maximal CO 2 assimilation rate under the given environmental, physiological, and biochemical constraints, we optimize the allocation of photosynthetic nitrogen (assumed to depend only on total leaf nitrogen) into Rubisco (n Etot ), C 4 cycle (n C4 ), LET, and CET (the latter two represented by p and n Jmax ) through an augmented Lagrangian approach using the auglag-function of the package 'nloptr' 51 . The optimization is constrained to make sure that the results are biologically realistic with respect to the modeled photosynthetic type, e.g., C 3 species were not able to invest nitrogen into the C 4 cycle (see Supplementary Table S2 for details). The model and its optimization were implemented in the R environment 52 (18). I is related to J t by a widely accepted empirical hyperbolic function [Eq. (16)], 9,53 that includes the following parameters: (1) J max , the maximum electron transport rate; (2) Θ, the convexity of the transition between the initial slope and the plateau of the hyperbola; (3) α, the leaf absorptance; (4) f, a correction factor accounting for the spectral quality of the light; and (5) p, the fraction of absorbed quanta that reaches PSI and PSII of LET (with (1 − p) reaching the CET). I abso is set to either I LET or I CET depending on the considered path of electron transport. The fraction of irradiance www.nature.com/scientificreports/ that is absorbed by the LET is shared equally between PSI and PSII [resulting in the factor 0.5 in Eq. (17)], while the fraction of irradiance that is absorbed by the CET is assumed to reach PSI in full.
In our model it is assumed that the electron transport chain is the only source of ATP and NADPH and that both are used exclusively for CO 2 fixation 9 . As NADPH production results from LET, the amount of electrons is calculated using Eqs. (16) and (18). The amount of electrons utilized for ATP production depends on both LET and CET. There are multiple pathways of CET 55 ; the model considers those pathways with an active Q-cycle and a ratio of two protons per electron. Note that Rubisco is assumed to be fully activated, independent of the irradiance 9 .
The available energy needs to be partitioned between five pools: (1) the Calvin-Benson cycle in the mesophyll; (2) the Calvin-Benson cycle in the bundle sheath; (3) the photorespiratory pathway in the mesophyll; (4) the photorespiratory pathway in the bundle sheath cell; and (5) the C 4 pathway. This means that the available energy is calculated in total and then partitioned 54 into J mp , J mc , and J s , the fractions of J max invested into the C 4 cycle, the Calvin-Benson cycle and the photorespiratory pathway in the mesophyll, and the Calvin-Benson cycle and the photorespiratory pathway in the bundle sheath cell, respectively. During optimization, the activity of each process is constrained by its allocated energy pool, i.e., the energy allocation equals the relative energy allocation of the processes (see Supplementary Methods S3 for details). In summary, the optimal energy allocation is a function of the nitrogen pools. The model for the CO 2 assimilation rate when the electron transport rate is not limiting (A c ) is taken from Heckmann et al. 2 and extended by a parameter representing the fraction of PSII activity in the bundle sheath cells, which affects O 2 generation. This parameter is set to p. In the whole model, each limitation is considered independently; the plant's CO 2 assimilation rate is determined by the lower of the two limitations: Temperature-dependence. Temperature affects the CO 2 assimilation rate by changing the maximal activity of the C 4 cycle, the carboxylation rate of Rubisco, and the electron transport rate. Temperature also affects the specificity of Rubisco and the Michaelis constants of Rubisco and PEPC. We model the temperature response by an extended Arrhenius function that describes two counteracting effects: rate increases with increasing temperature and enzyme inactivation through thermal instability 37 . We use parameters taken from literature or fitted to available data.
The extended Arrhenius function is given by Massad et al. 37 : The parameters of the extended Arrhenius function are: (1) Table S3 for the parameters).
Data used in the analyses. As the raw data of Vogan and Sage 39 were not available, we extracted it from the corresponding figures using the Graph Grabber software provided by Quintessa Limited (Version 1.5.5). The measured data include curves of the CO 2 assimilation rate as a function of intercellular CO 2 concentration (C i ) and the ratio of atmospheric CO 2 concentration (C a ) and C i . We derive the CO 2 concentration in the mesophyll cell (C m ) for a given C a by considering this C a /C i -ratio and assuming that the ratio of C m to C i is 0.85 (as CO 2 enters the mesophyll through diffusion, the C m / C i ratio has to be below 1). As can be seen from our sensitivity analysis (see below and Supplementary Fig. S1), the exact value for the C m / C i ratio does not affect our conclusions.
To transform the in vitro PEPC activity given by Dwyer et al. 56 to an in vivo activity, the in vitro value is divided by 3 57-59 .
(16) J t = I abso + J max − (I abso + J max ) 2 − 4θ I abso J max 2θ (17) www.nature.com/scientificreports/ Required nitrogen re-allocation (δ n ). Required nitrogen re-allocation (δ n , [fraction]) is defined as the total fraction of nitrogen that needs to be re-allocated between photosynthetic pools to optimally adjust photosynthesis from the evolutionary scenario ( n evo Etot , n evo C4 , n evo Jmax ) to a given experimental growth environment ( n growth Etot , n growth C4 , n growth Jmax ): Statistical information. The differences between adaptation scenarios are tested with Wilcoxon rank sum tests. For details about the calculation of the resource allocation for the data set of Vogan and Sage 30 (Fig. 3) see Supplementary Methods S8. All statistical analyses were conducted in R 52 . The difference of δ n for various photosynthetic types was tested by sign tests.

Results
Optimal resource allocation in the evolutionarily relevant environment explains physiological data and outperforms models based on the experimental growth environment in C 4 Flaveria plants. Do photosynthetic types exhibit differences in phenotypic plasticity, i.e., do they differ in their ability to adjust their photosynthetic resource allocation to optimally fit the environment in which they were grown? Or is resource investment static and reflects past environments in which the plants' ancestors evolved?
To compare these competing hypotheses in the genus Flaveria, we predict physiological data of plants that are either optimally adapted to the experimental growth conditions (EGC) used in the respective studies ('growth scenario') or to the environments in which they likely evolved ('evolutionary scenario'); with respect to our model, these environments differ in terms of atmospheric CO 2 concentration, temperature, and light intensity (Supplementary Tables S4-S7). This in silico experiment also serves as validation for our modeling framework; if the parameterization for Flaveria and our optimality assumptions are correct, we would expect the model to explain physiological responses in one of the two or in an intermediate scenario.
To predict the physiological data of plants that are optimally adapted to the evolutionary scenario, we use our model to identify the optimal resource allocation for C 3 , C 3 -C 4 intermediate, and C 4 Flaveria species in the evolutionary environment. This environment is based on the suggested environment of C 4 evolution in Flaveria 13,19,20 , with high light intensities, high temperature, and 280 µbar atmospheric CO 2 concentration (see Supplementary  Table S4 for Table S5). In an independent experiment, Vogan and Sage 30 measured the dependence of CO 2 assimilation rate on leaf nitrogen levels in C 3 , C 3 -C 4 intermediate, C 4 -like, and C 4 Flaveria species. The plants were grown at 554 µmol quanta m −2 s −1 light intensity, 30 °C at daytime, at 380 µbar atmospheric CO 2 and current atmospheric O 2 concentrations (Supplementary Table S6). Dwyer et al. 56 performed detailed experiments on the photosynthetic resource allocation and performance of the C 4 species F. bidentis. The Dwyer et al. 56 data set allows us to compare the predicted nitrogen investment into the three major photosynthetic components-Rubisco, C 4 cycle, and electron transport chain-, and the corresponding CO 2 assimilation rate, to experimentally observed resource allocation patterns. The plants were grown under 25 °C or 35 °C at daytime, 550 µmol quanta m −2 s −1 , 380 µbar CO 2 , and current atmospheric O 2 concentrations (Supplementary Table S7).
In the three studies, the experimental measurement conditions (EMC) differ from both the EGC and the evolutionary condition. Typically, the EMC shows higher light intensities than the EGC. In contrast, the major difference between the evolutionary environment and the EMC is the atmospheric CO 2 concentration. There are additional differences between the conditions that are study-specific, e.g., differences in temperature; detailed comparisons of conditions are listed in Supplementary Tables S4-S7. For C 3 Flaveria species (F. pringlei or F. robusta), the model results assuming an optimal allocation under the evolutionary scenario agree qualitatively with the measured data of Vogan and Sage 30,39 , and visually, they appear to fit the data better than results assuming optimality under the EGC 30 (Figs. 2, 3; Supplementary Figs. S2-S5). To allow a statistical comparison between the quality of the two predictions, for each of the two scenarios, we calculated the squared residuals across all C 3 Flaveria data points in Figs. 2, 3 and Supplementary Figs S2-S5 (see Supplementary Table S9); these two distributions were then compared through a Wilcoxon rank sum test. This test was not statistically significant at the 5% level (P = 0.31). Thus, it is possible that the somewhat better fit for the evolutionary scenario is caused by random fluctuations or experimental errors rather than by a superiority of one scenario over the other.
The result was very similar for the C 3 -C 4 intermediates, F. ramosissima and F. floridana. Again, the predictions assuming an optimal allocation under the evolutionary scenario agree qualitatively with the measured data of Vogan and Sage 30,39 , and seem to fit the data better than predictions under the EGC (Figs. 2, 3; Supplementary Figs. S2-S5); however, the prediction errors are again not statistically significantly different between the two scenarios (P = 0.86, Wilcoxon rank sum tests, Supplementary Table S9).
The C 4 -like species F. palmeri is only considered in the data set of Vogan and Sage 30 (Fig. 3). The model results for F. palmeri assuming optimal resource allocation in the evolutionary scenario are consistent with the measured    39 , we find that the squared residuals for the evolutionary scenario is statistically significantly smaller than that for the growth scenario (P = 8.3 × 10 -5 , Wilcoxon rank sum tests, Supplementary Table S9).
Dwyer et al. 56 performed detailed experiments on the photosynthetic resource allocation and performance of the C 4 species F. bidentis. First, we analyze the discrepancy of each model prediction with the empirical measurement. Model predictions of chlorophyll content and the amount of photosystem II agree within a factor of 1.10 to 1.22 (this corresponds to a factor 0.13 to 0.28 assuming a log2-scale as presented in Fig. 4) with values measured by Dwyer et al. 56 (see Supplementary Table S10 for absolute values). For plants grown at 25 °C, the resource allocation determined under the evolutionary scenario agrees with the measured data within a factor of 0.29 to 1.19 (this corresponds to a factor of − 1.8 to 0.25 assuming a log2-scale; Fig. 4A); at 35 °C, agreement is within a factor of 0.29 to 1.09 (this corresponds to a factor − 1.8 to 0.12 assuming a log2-scale; Fig. 4B). In both cases, agreement is much lower for predictions in the growth scenario (which are 0.10 to 1.42 or − 3.26 to 0.50 on a log2-scale for 25 °C (Fig. 4A) and 0.11 to 1.34 or − 3.12 to 0.42 on a log2-scale for 35 °C (Fig. 4B)). Then, we analyze the overall discrepancy of model prediction and empirical measurement presented in Fig. 4. We determine the deviation ('error') between all model predictions and measurements as the squared residuals (normalized to fractions of the experimental means).We assessed the statistical significance of the superior performance of the evolutionary scenario (compared to the growth scenario) by comparing the errors. The resource allocation calculated for the evolutionary scenario outperforms the growth scenario for the data represented in Fig. 4 (P = 1.0 × 10 -4 , Wilcoxon rank sum test). In Fig. 4, there is a discrepancy between measured in vitro PEPC activity and predicted in vivo activity, a disparity that has been noted before [57][58][59] . When in vitro PEPC activity is corrected using independent data on in vitro-in vivo differences (Supplementary Fig. S8; for derivation see Methods), the model successfully predicts all measurements; the agreement is within a factor of 0.86 to 1.19 at 25 °C and 0.77 to 1.09 at 35 °C (this corresponds to a factor of − 0.21 to 0.25 at 25 °C and − 0.37 to 0.12 at 35 °C assuming a log2-scale).
Although we could obtain the majority of our model parameters from the literature, the relationship of cytochrome f and the maximal electron transport rate of the CET had to be estimated (see Methods). We performed a sensitivity analysis to examine the robustness of the results to changes in the estimated parameters and to uncertainties in values obtained from the literature, focusing on parameters with high uncertainty or major expected effect on model predictions (Supplementary Methods S7 and Table S11). The predictions based on the evolutionary scenario outperform those based on the growth environment consistently across all parameter sets ( Supplementary Fig. S1).
Adjustments in the nitrogen allocation require substantial changes to protein abundances, which can only be achieved through massive protein breakdown and de-novo synthesis (see Moejes, et al. 60 for a general discussion www.nature.com/scientificreports/ and Schmollinger, et al. 61 for an example in Chlamydomonas). Thus, we assume that plants require multiple hours to days in order to adjust their protein levels to a new environmental condition. Accordingly, we assume that plants cannot adapt their resource allocation patterns on the timescale of a measurement, which lasts on the order of minutes to hours. This is our rationale for simulating plants optimally adapted to the EGC, even when analyzing data collected at rather different EMCs. However, it is conceivable that at least the energy allocation, including the proportion of LET, can adjust to the EMC on the timescale of the experiment. We thus performed simulations under an alternative model, where nitrogen allocation is optimized for the EGC, but energy allocation is subsequently optimized for the EMC. The results are qualitatively similar to the above results from simulations where both nitrogen and energy allocation are optimized for the EGC (Supplementary Figs. S9-S16).
The model suggests a unique evolutionary environment for C 4 photosynthesis in Flaveria. Compared to a parameterization optimized for the growth scenario, the model optimally adapted to the evolutionary scenario leads to superior predictions of plant performance and resource allocation in C 4 plants across diverse physiological data sets. The inferior performance of the growth scenario model indicates a lack of phenotypic plasticity of resource allocation in C 4 plants, a result that is in agreement with previous reports based on experimental observations 15 . The lack of phenotypic plasticity points to the possibility that the environment most relevant for recent evolutionary adaptation of a given C 4 plant could be inferred quantitatively from observations on plant physiology and resource allocation. Thus, to infer a typical evolutionary environment for C 4 Flaveria bidentis, we calculated optimal resource allocation under conditions covering plausible ranges of mesophyll CO 2 partial pressure, temperature, and light intensities, and we then identified the conditions that best explain the empirical data (Fig. 5). As atmospheric O 2 concentration remained almost constant for at least the last few million years 23 , this environmental parameter is set to a constant value. We compare the simulations to the empirical data of Dwyer et al. 56 , as this data set comprises detailed measurements for each nitrogen pool and the resulting CO 2 assimilation rate, allowing us to quantify the discrepancy between modeled and measured values as the mean squared residuals (normalized to fractions of experimental means). The model environment that shows the smallest prediction error defines a unique environment (Fig. 5), characterized by 1343.75 µmol quanta m −2 s −1 light intensity, 30 °C, a mesophyll CO 2 level of 100 µbar, and an O 2 level of 200 mbar. This environment corresponds to an atmospheric CO 2 concentration of about 280 µbar (Supplementary Table S8). Some similar environments lead to only slightly worse fits to the empirical data; the areas in which the model successfully describes the empirical values generally show high light intensities, intermediate to high temperatures, and a trend towards low CO 2 partial pressures (Fig. 5).
In contrast to our findings for C 4 and C 4 -like plants, the performance of the evolutionary and the growth scenario models is similar for C 3 and C 3 -C 4 intermediate Flaveria species (Figs. 2, 3; Supplementary Figs. S2-S5 and Table S9). It is conceivable that the lack of superior performance for the evolutionary scenario in C 3 Flaveria species is due to an inappropriate parameterization of the evolutionary scenario. The environment most relevant for the recent evolution of C 3 Flaveria may be different from the environment used in the simulations, which was chosen based on its relevance for the C 4 lineages. To explore this possibility, we simulated a wide range of alternative environments, testing if resource allocation optimized for any of these leads to significantly improved model predictions for the data from Vogan and Sage 39 for C 3 plants. However, none of the environments tested led to a significant improvement (Supplementary Figs. S6-S7).
Optimal resource allocation patterns are determined by an interplay between the different environmental factors. For C 4 species, high light intensities (as in the evolutionary scenario) tend to favor an increased nitrogen investment into the dark reactions, which goes along with a reduced investment into the electron transport www.nature.com/scientificreports/ chain. The effect of temperature is of special importance for plants using the C 4 cycle, as temperature increases PEPC activity drastically 37 and therefore reduces the necessary nitrogen investment into the C 4 cycle. This allows an increased investment into Rubisco and the electron transport chain, both of which show reduced activity at elevated temperatures due to thermal instabilities. Lower mesophyll CO 2 levels tend to increase the investment into the C 4 cycle while decreasing the investment into the electron transport chain and (albeit by a small factor) into Rubisco.
Limited phenotypic plasticity is linked to a high requirement of nitrogen re-allocation. Our results indicate that C 4 Flaveria species show a lower degree of photosynthetic phenotypic plasticity than closely related C 3 species (indicated by the inferior performance of the growth model compared to the evolutionary scenario for C 4 Flaveria species, there is no significant difference observed in C 3 Flaveria species; Figs. 2, 3 and Supplementary Figs S2-S5). On a molecular level, phenotypic plasticity predominantly requires the re-allocation of nitrogen between the major photosynthetic protein pools, in addition to post-translational control. After finding the optimal nitrogen allocation patterns in the evolutionary and growth scenarios, we calculated the absolute difference in the fraction of photosynthetic nitrogen allocated to each major pool of photosynthetic nitrogen (Calvin-Benson cycle; C 4 cycle; electron transport). We then summed these fractions to quantify the total fraction of nitrogen that needs to be re-allocated between photosynthetic pools to adjust photosynthesis between the two optimal nitrogen allocation patterns (δ n , see Methods). Table 2 shows this amount of nitrogen re-allocation for C 3 , C 3 -C 4 intermediate, C 4 -like, and C 4 Flaveria species at four different leaf nitrogen levels. We find that photosynthetic types that utilize C 4 photosynthesis require a consistently higher amount of re-allocation compared to C 3 plants (P = 1.5 × 10 -5 , sign test). Our results thus indicate a link between required nitrogen re-allocation and limited photosynthetic phenotypic plasticity, suggesting a possible causal relationship.

Discussion
Our novel modeling framework allows us to study the interplay between photosynthetic performance, the environment, and resource investment on the molecular level. Comparisons of model predictions with phenotypic and molecular data from the genus Flaveria (Figs. 2,3,4) show that models of C 4 plants adapted to an evolutionary environment outperform models that consider the experimental growth conditions. These results suggest a low phenotypic plasticity in terms of resource allocation in C 4 plants of the model genus Flaveria, supporting earlier hypotheses on a low photosynthetic plasticity of C 4 plants 15 . In a recent study, Pignon and Long 62 found that C 4 plants do not appear to have adapted their photosynthetic gene expression to modern levels of atmospheric CO 2 , a result that confirms a low phenotypic plasticity in these plants. This limited phenotypic plasticity may potentially be explained by the large amount of nitrogen that needs to be re-allocated by C 4 plants to optimally adapt to a given growth environment ( Table 2): adaptation of C 4 photosynthesis requires more drastic changes in gene expression than C 3 photosynthesis. The relatively young age of many C 4 species compared to their C 3 ancestors 63 might further enhance this effect, because the required gene-regulatory networks had less time to evolve than those of their C 3 ancestors. Plants with low photosynthetic phenotypic plasticity might contain information about their adaptive environment in their relatively static gene expression patterns. Based on this reasoning, we make quantitative predictions for the environments that dominated the recent evolution of C 4 Flaveria (Fig. 5). Previously, environments relevant for C 4 photosynthesis evolution have been inferred-mostly qualitatively-based on C 3 -C 4 habitat comparisons 13,19,20 and geophysiological considerations 21 . Our results are consistent with and refine these earlier estimates. When C 4 species grow under low CO 2 levels, the model assuming optimality in the growth scenario explains the measured data better than the evolutionary model (Supplementary Figs. S3-S4 and Table S9). To some extent this is consistent with the results presented in Fig. 5, where lower mesophyll CO 2 concentrations and light intensity than assumed in the evolutionary scenario lead to a better fit of simulated and measured data, thus refining our prior assumptions about the evolutionary environment.
Although the predictions for total nitrogen investment into the thylakoids based on the evolutionary scenario are highly consistent with the measurements performed by Dwyer et al. 56 Supplementary Table S10). However, the experimental error of the measurements is uncertain, as no replicate measurements were performed for this parameter 56 . Discrepancies between model predictions and observations may also be in part due to error propagation from Table 2. Required nitrogen re-allocation (δ n , [fraction]) for different leaf nitrogen levels for various Flaveria species. The required nitrogen re-allocation represents the total fraction of nitrogen that needs to be re-allocated between photosynthetic pools to optimally adjust photosynthesis from the evolutionary scenario to a given experimental growth environment. www.nature.com/scientificreports/ modeled amounts of chlorophyll and the photosystems. In each simulation, we optimized resource allocation for an environment that represents a static approximation to the dynamic environment a plant is facing. As diurnal and annual variations (which are no focus of this work) potentially show short-term trade-offs 44,64 , these might lead to a discrepancy between modeled and real evolutionary scenarios. In particular, the natural ancestral habitat must have exhibited periodically as well as randomly fluctuating conditions, compared to the stable EGCs in audited growth chambers and the statically modeled evolutionary scenario. Given the complexity of our physiological model, we needed to make a number of assumptions. We addressed uncertainties in model parameters through sensitivity analyses, showing that our conclusions are robust against variation in these parameters (Supplementary Fig. S1). Furthermore, our predictions assume that nitrogen availability in the evolutionary scenario was identical to current nitrogen availability. As the role of nitrogen availability in C 4 evolution remains unclear, further research is needed to assess the effect of nitrogen availability on plants under the ancestral, current, and transitional environments. Furthermore, while our approach of maximizing the assimilation rate per available CO 2 concentration will account for water-use efficiency implicitly, a promising avenue for future evolutionary studies will be the explicit inclusion of stomatal responses (see, e.g., Bellasio and Farquhar 65 ).
There are only a limited number of data sets available that include the information for each considered environmental factor. In the three available data sets that included all necessary information, plants were not grown under the same conditions under which experiments were performed (i.e., EGC and EMC differed). The EGC and EMC show their biggest difference in the light intensities, but other factors differ also, e.g., temperature (Supplementary Tables S4-S7). While the disparity between EGC and EMC complicated the analysis and interpretation, we argue that the analysis of different photosynthetic types (C 3 , C 3 -C 4 intermediates, and C 4 ) across a wide range of environmental conditions provides a solid basis for the presented results. The complexity of the analysis is reduced by considering the model genus Flaveria that allows us to focus on the effect of different photosynthetic types rather than differences across genera.
In contrast to the findings in C 4 and C 4 -like plants, the predictive performance of the evolutionary and the growth scenario models is similar for C 3 and C 3 -C 4 intermediate Flaveria species (Supplementary Table S9). This similarity could be caused by the similar assimilation rates found for the evolutionary and growth scenario models in C 3 and C 3 -C 4 plants, which make it difficult to quantify model performance on noisy data (Figs. 2, 3 and Supplementary Figs. S2-S5). Overall, our results point to a higher phenotypic plasticity of C 3 and C 3 -C 4 intermediate plants compared to C 4 and C 4 -like plants. Thus, in contrast to the latter photosynthetic types, it may not be possible to estimate ancestral evolutionary environments for C 3 plants based on our approach.
Our model provides a powerful tool to analyze the resource allocation of photosynthetic organisms and its dependence on environmental factors, allowing estimates for the maximal electron transport rate for LET and CET, the proportion of LET and CET as well as the nitrogen and energy allocation for which measurements are currently infeasible or impractical. This may prove to be of particular utility for systematically assessing the likely performance of crops in environments distinct from their natural habitats and for suggesting engineering targets in cases of limited phenotypic plasticity.