Why an increase in activity of an enzyme in the Calvin–Benson cycle does not always lead to an increased photosynthetic CO₂ uptake rate?—a theoretical analysis

Abstract

Overexpressing Calvin–Benson cycle (CBC) enzyme shown to limit the flow of CO₂ through the cycle is a major approach to improve photosynthesis. Though control coefficients of CBC enzymes vary under different environmental and developmental conditions, it is usually implicitly assumed that enzymes in the CBC have a monotonic impact on the CBC fluxes. Here, with a dynamic systems model of the photosynthetic carbon metabolism, we show that, for glycerate-3-phosphate kinase (PGAK), fructose-1,6-bisphosphatase (FBPase), fructose-1,6-bisphosphate aldolase (FBA) and transketolase (TKa), individually increasing activity of these CBC enzymes theoretically leads to an initial increase then decrease in the fluxes through the CBC. Also, the inhibition constants of adenosine diphosphate (ADP) for PGAK and of fructose-6-phosphate (F6P) for FBPase influence the CBC flux in a biphasic manner. These predicted enzymes showing a biphasic manner are always located in different subcycles of the CBC, which consume the shared substrates in the early steps in the CBC and produce intermediates used as substrates for enzymes in the later reactions. We show that the excessive increase in activities of enzymes in one subcycle consuming the shared metabolite could cause low concentrations of metabolites in the other subcycles, which results in low reaction rates of the later reactions and hence lowers overall CBC flux. This study provides a model to explain the underlying reasons that overexpression of enzymes in the CBC sometimes can negatively impact photosynthesis. We find that balanced activities of enzymes in the subcycles of the CBC are required to gain a higher efficiency of the CBC.

1. INTRODUCTION

The Calvin–Benson cycle (CBC) fixes CO₂ and provides organic compounds for heterotrophic organisms on the earth and is a critical component of the global carbon cycle. The CBC is a classical autocatalytic cycle, where ribulose1,5-bisphosphate (RuBP), which is the compound reacting with CO₂, is regenerated by the CBC after CO₂ is fixed to generate 3-phosphoglycerate (PGA) (Woodrow and Berry 1988). The CBC is a complex metabolic network, which includes 13 enzymatic steps and is linked to different branching fluxes exporting intermediates for biosynthesis of compounds, such as thiamine nucleotides, shikimate, sucrose, starch and isoprenoid (Raines 2011).

In recent years, huge efforts have been investigated in identifying the enzymes that exert a high level of control over fluxes of the CBC and hence can be potentially used as the engineering targets to enhance photosynthesis. The degree of limitation of each step of the CBC efficiency is represented by flux control coefficient, which has been estimated for individual CBC enzymes through transgenic experiments (as summarized by Raines 2003, 2011; Tamoi et al. 2005) or mathematical models (Woodrow and Mott 1993; Zhu et al. 2007, 2013). Enzymes with a relative larger control coefficient are considered as primary targets for photosynthesis improvements, such as sedoheptulose-1,7-bisphosphatase (SBPase) and ribulose-1,5-bisphosphate carboxylase oxygenase (Rubisco) (Raines 2003, 2011; Long et al. 2006; Zhu et al. 2010). Overexpression of SBPase or FBPase has indeed been shown to be effective in enhancing photosynthesis when they are overexpressed in plants. For example, overexpressing SBPase increases photosynthesis and growth in tobacco at the early stage (Lefebvre et al. 2005; Tamoi et al. 2006; Simkin et al. 2015; López-Calcagno et al. 2020) and under elevated CO₂ condition (Rosenthal et al. 2011), enhances photosynthesis and the tolerance of tomato to chilling stress (Ding et al. 2016) and of rice to heat stress (Feng et al. 2007), as well as stimulates photosynthesis and grain yield in wheat under greenhouse condition (Driever et al. 2017). Additionally, in transgenic plants with increased activities of multi-enzymes, such as SBPase/fructose-1,6-bisphosphatase (FBPase) in tobacco in the greenhouse (Miyagawa et al. 2001) and in soybean in the field with feeding elevated CO₂ (Kohler et al. 2017), SBPase/FBPase/Ictb in rice (Gong et al. 2015) and tobacco (Simkin et al. 2015), and SBPase/FBPA/GDCH in Arabidopsis (Simkin et al. 2017), improved photosynthesis and growth are both achieved.

With these studies, it becomes apparent that the flux control coefficient of an enzyme over CBC flux varies depending on the environmental conditions (Stitt and Schulze 1994; Raines 2003, 2011). In the state-of-the-art photosynthesis improvements, one implicit assumption is that overexpression of an enzyme of the CBC will have either a positive or no impact on photosynthetic efficiency. Given this assumption, it comes as a surprise when the transketolase (TK) activity was either increased or decreased, the photosynthetic rate showed a certain decrease (Henkes et al. 2001; Khozaei et al. 2015). Though export of intermediates of the CBC may be related to this phenomenon, this observation raises a possibility that the influence of some enzymes on the CBC flux might be non-monotonic.

One option to test whether there are enzymes in the CBC showing non-monotonic responses to changes in enzyme activities is to generate a series of transgenic plants with varying enzyme activities and to test their impacts on photosynthesis, as have been done in the case of TK (Henkes et al. 2001; Khozaei et al. 2015). This unfortunately has not been investigated systematically for other enzymes in the CBC. Furthermore, when one enzyme in the CBC is overexpressed in vivo, expression level and activities of many other enzymes are usually changed as well (Price et al. 1995; Haake et al. 1998, 1999; Henkes et al. 2001), which makes it difficult to precisely calculate the control coefficient of a particular enzyme on the CBC in a particular state. Here we use a dynamic systems model of the photosynthetic carbon metabolism (Zhu et al. 2013) to examine which enzyme in the CBC may cause a biphasic change in the overall CBC flux.

The CBC is highly regulated by different manners to gain its operating efficiency (Stitt 1996). These mechanisms include feedforward regulations of ribulose-5-phosphate kinase (PRK), glyceraldehydes-3-phosphate dehydrogenase (GAPDH)–oxidized nicotinamide adenine dinucleotide phosphate (NADP), SBPase and FBPase performed by the thioredoxin-mediated system (Michelet et al. 2013; López-Calcagno et al. 2014) and Rubisco activation by the Rubisco activase (Slabas and Walker 1976; Walker 1976; Stitt 1996; Raines 2003; Stitt et al. 2010) in the light. These feedforward regulations are important for the rapid activation of the CBC from low irradiance to high irradiance (Gross et al. 1991; Stitt 1996; Rascher and Nedbal 2006; Kaiser et al. 2018). The enzymes of the CBC are also feedback-inhibited by intermediates of the CBC (Walker 1976; Woodrow and Berry 1988; Stitt 1996). It is likely that the feedback mechanisms used in the CBC may also help plants in the field to gain higher response speed of CBC flux and to maintain stable metabolite concentrations in fluctuating environment (Stitt 1996). Such a negative feedback regulatory mechanism in fact also widely exists in genetic regulatory network (Rosenfeld et al. 2002). On one hand, it can accelerate the response time of the components’ concentrations in the network to external perturbations (Rosenfeld et al. 2002); on the other hand, it helps to confer the stability of the concentrations of components in the network under environmental perturbation (Becskei and Serrano 2000). So far, the significance of these regulations on the CBC efficiency under steady state has not been systematically investigated and is the topic of this study. The major advantage of using a systems modeling approach to determine the impacts on systems fluxes of the CBC is that each single kinetic parameter of the CBC enzymes can be changed by a large magnitude without changing the other parameters in the CBC cycle, so that we can individually examine the impacts of each modified parameter on the CBC fluxes.

The results from this study show that the flux through the CBC indeed interplays a biphasic response to changes in enzymatic activities for a number of enzymes. And two regulatory factors of enzymes in the CBC are identified, which also generate biphasic responses. Both these enzymes and the regulators play important roles in limiting resource distribution among the subcycle in the CBC. This study in theory demonstrates the importance of balancing the activities of the enzymes to maintain the metabolic coordination for an efficient CBC.

2. MATERIALS AND METHODS

2.1 Model description

The C₃ photosynthetic carbon metabolism module of ePhotosynthesis model constructed previously (Zhu et al. 2013) was employed in this study. The module includes the metabolic pathways of the CBC, photorespiratory pathway, sucrose synthesis and starch synthesis. In this module, the adenosine triphosphate (ATP) and reduced nicotinamide adenine dinucleotide phosphate (NADPH) production through chloroplastic electron transfer chain is simplified based on equations used in Wang’s model (Wang et al. 2014). These equations assume that there is obligatory Q cycle, no-cyclic electron transfer:

adenosine diphosphate (ADP) + orthophosphate (Pi) -> ATP

NADP -> NADPH

where [ATP], [ADP], [Pi], [NADP] and [NADPH] represent the concentrations of ATP, ADP, Pi, NADP⁺ and NADPH in chloroplast, respectively; Km represents the Michaelis–Menten constant of an enzyme for its substrate; V_max16 and V_2M represent the maximum velocities of ATP synthase and ferredoxin-NADP⁺ oxidoreductase in the chloroplast, respectively. Since the maximum production rate of ATP and NADPH is also determined by the electron transport rate J, so the maximum production rate of ATP and NADPH are descripted by $min{Vmax16,DLR∗J}$ and $min{V2M,ELR∗J}$⁠, respectively (Wang et al. 2014). The D_LR and E_LR are the stoichiometric ratio of ATP/e⁻ and NADPH/e⁻, respectively. In our simulations, D_LR is assumed equal to 1 and E_LR is assumed equal to 0.5 (von Caemmerer 2000). J is calculated as follows:

where I is the photosynthetic active radiation in the simulation; I₂ is the useful radiation absorbed by photosystem II; the absorptance (abs) of leaf is usually assumed as 0.85; the correction constant for spectral quality (f) is assumed equal to 0.15; the constant 0.5 means the assumption that irradiance is equally absorbed by photosystem I and photosystem II (values of these parameters are assigned by referencing (von Caemmerer 2000)); the maximum electron transport J_max in our simulations is assumed equal to 177 μmol m⁻² s⁻¹ which is within the range of that in C₃ photosynthesis (Fan et al. 2011); theta (θ) is the convexity index, which is assumed as 0.98 according to the value estimation in the single isolated cell of a plant leaf (Terashima and Saeki 1985).

2.2 Simulation

In this study, we investigated the effects of individual kinetic parameters of enzyme in the CBC on RuBP regeneration rate by using a kinetic model of C₃ photosynthesis, which has been constructed previously (Zhu et al. 2013). The response curves of photosynthesis versus fold change of parameter values are shown in this study. Simulations were done using the MATLAB (Mathworks, ver 2012, Natick, MA, USA). All simulations were performed under a photosynthetic photon flux density (PPFD) of 1500 µmol m⁻² s⁻¹, a CO₂ concentration of 800 ppm and an ambient O₂ level of 21 %. Under these conditions, the changes of maximal photosynthetic CO₂ uptake rate are determined by the kinetic properties of enzymes in the CBC rather than the irradiance or the CO₂ concentration. In each of the simulations, only one parameter under test is perturbed while all other parameters are maintained as their default values. All simulations were conducted by varying the default values of each parameters, V_max and K_i of enzymes in the CBC, by a fold change from 10⁻² to 10³. For example, here equations (5) and (6) are used to demonstrate how we modified the V_max and K_i, respectively, where n is the fold change in the perturbation.

where v is the reaction rate; V_max is the maximum enzymatic capacity; [S] and [inhibitor] are the concentrations of the substrate and an inhibitor to the enzyme, respectively; Km is the Michaelis–Menten constant of an enzyme for its substrate; K_i is the inhibition constant of enzyme for the inhibitor.

The simulations includes two situations for the perturbations on TK, since TK catalyses two reactions in the CBC (TKa: fructose-6-phosphate + triose phosphate <-> erythrose-4-phosphate + pentose phosphate; TKb: sedoheptulose-7-phosphate + triose phosphate <-> 2 pentose phosphate). The rate equations of TKa (equations 7 and 8) and TKb (equations 7 and 9) catalysed reactions are described as following (Zhu et al. 2013):

where PsV represents the maximum velocity of the reaction and Km represents the Michaelis–Menten constant of enzyme for a substrate. PsKE represents the equilibrium constant of a biochemical reaction. The symbols with square brackets represent the metabolite concentrations. We perturbed these two reactions by two different strategies. In the first strategy, we individually evaluate of the impact of modifying a single enzymatic reaction on the overall CBC flux. Specifically, only PsV7 in equation (8) or PsV10 in equation (9) is perturbated. Under such a scenario, the perturbations on V_max of TKa does not influence reaction catalysed by TKb; similarly, perturbations on V_max of TKb does not influence reaction catalysed by TKa. In the second strategy, the V_max of TKa always equals to that of TKb, which means PsV7 and PsV10 are perturbated simultaneously.

3. RESULTS

3.1 Increasing the enzyme capacity of the CBC may decrease photosynthesis

The responses of photosynthetic CO₂ uptake rate (A) to an increase in enzymatic activity are grouped into two classes. In the first class, A increases with the increase of enzyme activity until A is close to a plateau; while in the second class, A first increases then decreases with the increase in enzyme activity (Fig. 1). In this study, the first class of response is termed as monophasic response and the second class is termed as biphasic response. The enzymes showing a monophasic response in the CBC include Rubisco, GAPDH, sedoheptulose-1,7-bisphosphate (SBP) aldolase, SBPase, TK_b and PRK; the enzymes showing the biphasic responses in the CBC include glycerate-3-phosphate kinase (PGAK), fructose-1,6-bisphosphate (FBP) aldolase and TKa (Fig. 1).

3.2 Excess capacity of enzymes showing a biphasic response limits RuBP regeneration

Since the PPFD, CO₂ concentration and atmospheric O₂ level are not altered during simulations, changes in A should be attributed to changes in the steady-state RuBP concentration. To better differentiate the influence of enzyme activity or metabolite concentration on the CBC fluxes, we used a ratio of substrate concentration to the Michaelis–Menten constant of the substrate $(SKms)$ in a particular enzyme in the following analysis.

At a steady state of this model, without considering CO₂ released by dark respiration, the net photosynthesis can be calculated by the following equation (von Caemmerer 2000):

where V_cmax represents the maximum carboxylation rate of Rubisco; Km_RuBP represents the apparent Michaelis–Menten constant of Rubisco for RuBP; E_t represents the Rubisco active sites (2.5 mM was assigned in Zhu’s model (Zhu et al. 2013)). In this study, the value of E_t is equal to the default value (2.5 mM). And α is calculated as follows:

where K_c and K_o represent the Michaelis–Menten constants of Rubisco for CO₂ and O₂, respectively. $VomaxVcmax$ represents the ratio of maximum oxygenation rate to maximum carboxylation rate; it was assumed to be 0.24 in the previous model (Zhu et al. 2013). The constant of 0.5 represents the CO₂ releasing rate through photorespiration pathway is a half of the RuBP oxygenation rate (von Caemmerer 2000).

In this study, α is fixed as a constant since the environmental conditions keep constant in all simulations. So that:

The relationship between $vVmax$ and $SKms$⁠, which is also named as enzyme–substrate relationship, was plotted as described in Fendt et al. (2010). Following Fendt et al. (2010), we examined the reaction in three stages, i.e. in the first stage, the substrate concentration is much lower than its Km and the reaction rate is mainly limited by the substrate concentration (the region on the left side of the first dashed vertical line in Fig. 2); in the second stage, when the substrate concentration is near its Km, the reaction rate is limited by both the enzyme capacity and substrate concentration (the middle region bounded by dashed vertical lines in Fig. 2); in the third stage, when substrate concentration is times greater than the Km, the reaction rate is limited by enzyme capacity (the region on the right side of the second dashed vertical line in Fig. 2) (Fendt et al. 2010). Following equation (9), we found that the reaction rate of Rubisco is approaching V_max with the increase of $RuBPKmRuBP$⁠. In other words, the greater the value of $RuBPKmRuBP$⁠. the less the limitation by the substrate RuBP, and vice versa.

As to other enzymes of the CBC, increasing their enzymatic capacities influence [RuBP] and further influence the enzyme–substrate relationship of Rubisco (Fig. 2). With the increase of capacity of enzymes showing monophasic responses, both A (Fig. 1) and $RuBPKmRuBP$ (Fig. 2) increase. On the contrary, with the increases of activities for enzymes showing biphasic responses, $RuBPKmRuBP$ initially increases with the increase of A (red dots in the Fig. 2 represent the maximum steady-state photosynthesis); then, further increase of the enzyme activity leads to decreased $RuBPKmRuBP$ and enhanced the substrate limitation to photosynthesis (Fig. 2).

The $RuBPKmRuBP$ and A show the same responses to changes in catalytic capacity for enzymes in the CBC (Figs 1 and 2), except Rubisco. With a larger catalytic capacity of GAPDH, sedoheptulose-1,7-bisphosphate aldolase (SBPA), SBPase, TKb and PRK, the $RuBPKmRuBP$ increases and reaches a plateau.

For Rubisco, however, with increase in its catalytic capacity, the $RuBPKmRuBP$ gradually drops. Additionally, the $RuBPKmRuBP$ has a biphasic response curve with the increase in the activity of PGAK, fructose-1,6-bisphosphate aldolase (FBA), FBPase and TKa. Most of the dots are located in the middle region (Fig. 2), indicating that CO₂ fixation is limited by both the Rubisco catalytic capacity and RuBP concentration in most perturbations. During the perturbations of enzymatic capacity of each enzyme in the CBC, the relationship of enzyme–substrate of every enzymatic reaction is also simulated [see  Supporting Information—Figs S1–S10].

3.3 The enzymes showing biphasic responses control distribution of substrates in different subcycles of the CBC

In CBC, there are a few metabolites which are consumed by multiple reactions, e.g. ATP is used as a shared substrate by both PGAK- and PRK-catalysed reactions, and T3P is used as a shared substrate by four steps in the CBC. They are the enzymatic steps catalysed by FBA, TKa, SBPA and TKb (Fig. 3). Existence of substrates used by multiple reactions creates different subcycles for the CBC. After careful examination of the location of enzymes generating biphasic responses, we found that these enzymes always catalyse reactions in a subcycle consuming one of the shared substrates (Figs 1 and 3), meanwhile producing the product which is used as a substrate for a reaction of the next subcycle. As a result, with changed capacity of these enzymes, the imbalance of the coordination between different subcycles will lead to the shared substrate being predominantly used in one subcycle and thus becoming a limiting substrate for reactions in another subcycle. For example, with increase in the capacity of PGAK, the substrate limitation to RuBP regeneration by PRK moves from the short of ribulose-5-phosphate (Ru5P) to the insufficient ATP [see  Supporting Information—Fig. S2]; similarly, with the increase of capacity for FBA or FBPase or TKa, the substrate limitation over TKa moves from limiting availability of sedoheptulose-7-phosphate (S7P) to a limitation in the level of T3P [see  Supporting Information—Figs S4, S5  and  S6].

3.4 Two negative feedback loops play dominant roles in coordination of the CBC

The above analyses clearly show that, levels of activity of enzymes in one subcycle consuming shared substrate and producing intermediates required for another subcycle play a critical role in determining flux through the CBC (Fig. 3). The reaction rate is determined by both enzyme capacity and effectors. Here we used the regulatory constants to describe the regulations in model construction, such as activation constants and inhibition constants for the involved regulators. To test whether there are regulators critical for coordinating the consumption of shared metabolites between subcycles, we further tested whether modifying these regulatory constants may also generate biphasic responses in the fluxes through the CBC. In the carbon metabolism module of Zhu’s model, 13 regulators are included (Table 1; Zhu et al. 2013), which are by chance all inhibitors for enzymes. Similar to what we have done for the enzymatic capacity, here we systematically perturbated the inhibition constant by manipulating the default value by 10⁻² to 10³ folds. We found that out of these 13 regulatory constants, only two inhibitors resulted in biphasic response of photosynthesis. They are the inhibition of ADP to PGAK and inhibition of fructose-6-phosphate (F6P) to FBPase (Fig. 4). The enzymes related to these two inhibitions, as expected, locate on the pathways consuming shared metabolites in different subcycles.

3.5 A simplified mathematical interpretation of the non-linear responses systems flux to changes in enzyme activities

To gain quantitative insights into what may influence the optimal distribution of shared substrates between subcycles, we developed an analytical model representing a simplified metabolic network with subcycles competing for shared resources (Fig. 5A). The simplified conceptual model only includes two subcycles. Substrate element M (we assume M content is saturated in the analysis) is assimilated by the metabolic cycle to produce Product. Here the intermediate C is a shared metabolite; B is a product with the consumption of C by one subcycle (catalysed by the enzyme E₁); the intermediate B together with C are the substrates for another subcycle which is catalysed by the enzyme E₂. Assuming that there is a limiting element in C and B with a total of the limiting element being 1, then, if we assume that the steady-state concentration of C is x (0 < x < 1), then the steady-state concentration of B is 1 − x. Then, on the basis of Michaelis–Menten kinetics equation, the steady-state rate of this cycle, represented here as the flux of production formation, can be described as follows:

where V_max is the maximum velocity of the reaction catalysed by enzyme E₂, K₁ and K₂ represent the Michaelis–Menten constant of E₂ for C and B, respectively. The relationships between reaction rate with the concentration of C (or B) (Fig. 5B) show that, there is a biphasic response curve of reaction rates to the increasing concentration of C. The maximum flux rate of this cycle (v_max) can be obtained.

where $P=Vmax2×K1×(K1+1)×K2×(K2+1)(K1+K2+1)4$⁠.

The concentration of C corresponding to the maximum flux rate of Product formation at the steady state is:

when K₁ = K₂,

when K₁ < K₂,

when K₁ > K₂,

With the increase in the concentration of C, $xK1+x$ increases, while $(1−x)$ and $1−xK2+(1−x)$ decrease. Such that there is a switch of the limitation between B and C over the systems flux. The concentration of C at the maximal systems flux rate, which is represented as $xvmax$ above, depends on Michaelis–Menten constants K₁ and K₂, but does not depend on catalytic capacity of enzymes (equations 14, 15 and 16).

4. DISCUSSION

It has been proposed that both the enzyme capacity and its regulation are important to determine the efficient operation of the CBC (Stitt 1996). In this study, in silico parameter perturbation experiments were performed and analysed by employing the systems kinetic model of C₃ photosynthetic carbon metabolism (Zhu et al. 2013). The quantitative simulations theoretically demonstrate that balanced investment in subcycles of the CBC, which consume a shared intermediate and produce a substrate used by another subcycle, is required to gain a high flux through the CBC. The enzymatic steps (Fig. 1) and regulators (Fig. 4) contributing to coordinating the metabolic fluxes within the CBC are predicted. This work will promote our better understanding on the CBC operation and its regulations.

In this theoretical study, we did not consider the limitation of total enzyme amounts in the CBC but investigated the potential impacts of each enzymatic step or regulator on the CBC efficiency. Our results show that in the CBC, when the enzymatic capacity of the step catalysed by PGAK, FBA, FBPase or TKa is beyond its optimal level, it decreases rather than increases the flux of the CBC (Fig. 1). Since there are a number of limiting resources in the CBC, e.g. the adenylate residue and total phosphate concentration, the level of either total metabolites or single intermediate in the CBC is constrained by the limiting resources. The uncoordinated consumptions of shared metabolites through enzymes of subcycles in the CBC may result in the imbalanced distribution of limiting resources (Figs 3 and 4), and ultimately limit the whole CBC efficiency. In theory, PGAK can coordinate ATP consumptions by the subcycle with PGAK and by the subcycle with PRK, while FBA, FBPase and TK can coordinate the consumption of T3P by different subcycles (Fig. 3).

So far, conclusive experimental data directly showing such biphasic responses of fluxes in the CBC to the CBC enzyme activities are still absent. On one hand, it is difficult to estimate the impacts of perturbing a single enzyme on the fluxes within the CBC. This is because, in the transgenic experiments, when the activity of one enzyme is altered, it usually causes the changes in many other enzymes (Haake et al. 1998, 1999; Henkes et al. 2001). However, there are some signs of biphasic responses indeed shown in literatures. For example, in transgenic tobacco overexpressing FBA, increasing FBA activity generally stimulates photosynthesis and growth under either ambient or elevated CO₂ conditions. However, transgenic plants with larger enhancement of FBA relative activity show slightly lower stimulation of photosynthesis and of growth under elevated CO₂ (Uematsu et al. 2012). Consistently, in transgenic Arabidopsis with overexpressing FBA, stimulations of plant growth are also slightly weaker in plants with greater increase in FBA activity (Simkin et al. 2017). Transgenic plants with reduction of FBPase activity show a decrease in A compared with those in wild type (WT) (Koßmann et al. 1994; Haake et al. 1998, 1999), while overexpressing FBPase increases A and growth in tobacco (Tamoi et al. 2006). In contrast with these observations in plants, under most testing conditions, increasing chloroplastic FBPase activity by overexpressing FBPase in Chlamydomonas reinhardtii dramatically inhibited both the cell growth and biomass accumulations of transgenic strains compared with that of WT (Dejtisakdi and Miller 2016). For TK, either an increase or a decrease of TK activity in tobacco results in decreased growth, and leaf photosynthesis is decreased in TK antisense lines and in two of three reported TK overexpression lines (Henkes et al. 2001; Khozaei et al. 2015). Here one caveat is that we have simulated the two reactions in the CBC catalysed by the TK independently. Therefore, the conclusions drawn based on TKa and TKb represent conceptual and network topological structural scenarios. When we simulated the TKa and TKb synchronously, the biphasic response of photosynthesis disappears [see  Supporting Information—Fig. S11]. Interestingly, over-optimal capacity of TK leads to the accumulation of R5P and decreased T3P contents [see  Supporting Information—Fig. S12, S13], which promotes the use of R5P to synthesize hydroxymethylpyrimidine pyrophosphate (HMPP), but constrains the synthesis of hydroxyethylthiazole phosphate (HETP), through consuming T3P, ultimately inhibiting thiamine pyrophosphate (TPP) synthesis since both HETP and HMPP are the substrates for TPP production (Henkes et al. 2001; Khozaei et al. 2015).

In this simulation study, PGAK also shows biphasic impacts on A. Besides the potential impacts of altering one enzyme on activities of other enzymes, a few other reasons might also contribute to this discrepancy between the experimental observation and the theoretical predictions. First, we discussed the function of enzymes to the CBC metabolism coordination only, while the metabolites are highly connected to other metabolic pathways (Raines 2011). These connections may need to be fully considered to accurately predict the impact on systems flux, when activities of these enzymes are modified. Furthermore, the model used for the analysis might still need to be better parameterized, e.g. the activities of enzymes in the CBC model might be far from the real values in one plant species; as a result, it is hard to judge at this point where the enzyme activities from the WT or transgenic plants might resides on the response curve of A to changes in enzyme activities. In addition to these possibilities, experimental results indicate that the impacts of modifying enzyme activity on photosynthesis are also dependent on the environmental conditions (Feng et al. 2007; Uematsu et al. 2012; Ding et al. 2016; López-Calcagno et al. 2020) or developmental stages (Lefebvre et al. 2005; López-Calcagno et al. 2020). Therefore, more studies using plants with greatly enhanced PGAK activity are still needed to test whether their activity might have a biphasic impact on photosynthetic CO₂ uptake rate. In previous studies, less than twice activity of that in WT were usually reported in transgenic plants with overexpressing the CBC enzymatic genes (Miyagawa et al. 2001; Lefebvre et al. 2005; Tamoi et al. 2006; Feng et al. 2007; Rosenthal et al. 2011; Uematsu et al. 2012; Gong et al. 2015; Khozaei et al. 2015; Simkin et al. 2015; Driever et al. 2017; Kohler et al. 2017; Simkin et al. 2017; López-Calcagno et al. 2020). Now it is possible to create lines with much higher increase or lower decrease in enzyme activity using synthetic promoters (Cai et al. 2020).

The CBC enzymes are highly regulated by multiple mechanisms in vivo. This study additionally shows that, besides enzymatic capacity, there are two feedback inhibitions playing important roles in gaining a high efficiency of the CBC at steady state, through maintaining the shared metabolite concentration and hence to balance the fluxes through different subcycles. They are the auto-negative regulations of PGAK by ADP and of FBPase by F6P (Figs 4A and B). The function of these two inhibitions predicted in the CBC needs to be tested in transgenic experiments. Negative autoregulation is a mechanism to decrease its own production. Interestingly, at physiological levels, only F6P (near 20 metabolites in chloroplast have been tested) performs an effective and allosteric inhibition for FBPase, which produces a shift from hyperbolic to sigmoidal substrate saturation kinetics for plastic FBPase (Gardemann et al. 1986). This kind of regulation is theoretically demonstrated to be responsible for the homeostasis of metabolites (Hofmeyr and Cornish-Bowden 2000). This may indirectly reflect the critical role of FBPase activity and its inhibition by F6P in coordinating fluxes among different subcycles within the CBC. As to coordinating ATP consumption by PRK and PGAK, the inhibitions of ADP and RuBP to PRK are important, because the affinity of PRK to ATP is greater than that of PGAK (Stitt 1996). However, considering the greater affinity of PRK for ATP (in current model, the default value of Km of PRK and PGAK for ATP are 0.059 mM and 0.39 mM, respectively (2013)). Simulations show that it is the enzymatic activity of PGAK or ADP inhibition to PGAK more important than that of PRK to coordinate ATP consumption in the CBC (Figs 1 and 5). Interestingly, all the identified reactions or regulators which are responsible for the shared metabolites coordination are located in the subcycles of earlier steps in the CBC (Figs 1 and 5). This may be because, the later reaction rates are dependent on not only the shared metabolites concentration, but also the rates of the former steps to supply reactants. In other words, the structural location in the CBC rather than the enzymatic affinity might play a more important role in coordinating the consumption of shared metabolites in this cycle.

In summary, this study shows a new dimension of using a systems model to gain more insights into the operation of the CBC. The stability of the steady state in a metabolic autocatalytic cycle can be influenced by the kinetic properties, i.e. the Michaelis–Menten constant and catalytic number, of involved enzymes (Woodrow et al. 1985; Antonovsky et al. 2016; Barenholz et al. 2017). In this study, analysis for a simplified network shows that the kinetic properties of the enzymes in the subcycles, including both their enzyme activities and their regulatory properties, need to be well coordinated to achieve an efficient CBC at steady state.

SUPPORTING INFORMATION

The following additional information is available in the online version of this article—

Figure S1. The effects of the Rubisco activity on the enzyme–substrate relationships of reactions in the CBC. The red cycle represents the steady state of the maximum net photosynthesis, and it is the same in Supporting Information—Figs S2–S10.

Figure S2. The effects of the PGAK activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S3. The effects of the GAPDH activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S4. The effects of the FBA activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S5. The effects of the FBPase activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S6. The effects of the TKa activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S7. The effects of the SBPA activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S8. The effects of the SBPase activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S9. The effects of the TKb activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S10. The effects of the PGAK activity on the enzyme–substrate relationships of reactions in the CBC.

Figure S11. The responding curves of net photosynthetic CO₂ uptake rates versus the maximal activities of TK (V_max) in the CBC.

Figure S12. The responding curves of pentose phosphate concentration versus the maximal activities of TK (V_max) in the CBC.

Figure S13. The responding curves of T3P phosphate concentration versus the maximal activities of TK (V_max) in the CBC.

ACKNOWLEDGEMENTS

We thank Dr Mingnan Qu and Xinyu Liu for valuable suggestions on this manuscript.

SOURCE OF FUNDING

We acknowledge support from the general program of the National Science Foundation of China (31870214), the Ministry of Science and Technology of China (2018YFA0900600, 2019YFA09004600), the Chinese Academy of Sciences (XDB27020105) and Bill and Melinda Gates Foundation (OPP1129902).

CONTRIBUTIONS BY THE AUTHORS

H.-L.Z., X.-G.Z. designed this project; H.-L.Z. and Y.X. conducted the simulation; H.-L.Z., Q.-M.T. and T.-G.C. performed the analyses. H.-L.Z. and X.-G.Z. wrote the paper.

CONFLICT OF INTEREST

None declared.

LITERATURE CITED