Why an increase in activity of an enzyme in the Calvin Benson Cycle does not always lead to an increased photosynthetic CO 2 uptake rate? – A theoretical analysis

: Overexpressing cycle (CBC) enzyme shown to limit the flow 2 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 ADP for PGAK and of F6P for FBPase influence the CBC flux in a biphasic manner. These predicted enzymes showing a biphasic manner are always located in different sub-cycles 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 sub-cycle consuming the shared metabolite could cause low concentrations of metabolites in the other sub-cycles, 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 sub-cycles of the CBC are required to gain a higher efficiency of the CBC.

A c c e p t e d M a n u s c r i p t Abstract:Overexpressing Calvin Benson cycle (CBC) enzyme shown to limit the flow of CO 2 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-1,6bisphosphatase (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 ADP for PGAK and of F6P for FBPase influence the CBC flux in a biphasic manner. These predicted enzymes showing a biphasic manner are always located in different sub-cycles 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 sub-cycle consuming the shared metabolite could cause low concentrations of metabolites in the other sub-cycles, which results in low reaction rates of the later reactions and hence lowers overall CBC flux. This study provides a model to explain A c c e p t e d M a n u s c r i p t

Introduction
The Calvin-Benson cycle (CBC) fixes CO 2 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 RuBP, which is the compound reacting with CO 2 , is regenerated by the CBC after CO 2 is fixed to generate phosphoglyercate (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;Tamoi et al., 2005;Raines, 2011) or mathematical models (Woodrow and Mott, 1993;Zhu et al., 2007;Zhu et al., 2013). Enzymes with a relative larger control coefficient are considered as primary targets for photosynthesis improvements, such as SBPase and Rubisco (Raines, 2003;Long et al., 2006;Zhu et al., 2010;Raines, 2011). Over-expression 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 CO 2 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/FBPase in tobacco in the greenhouse (Miyagawa et al., 2001) and in soybean in the field with feeding elevated CO 2 (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 , improved photosynthesis and growth are both achieved. A c c e p t e d M a n u s c r i p t 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;Raines, 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 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 transketolase (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;Haake et al., 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 PRK, GAPDH-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 A c c e p t e d M a n u s c r i p t 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 sub-cycle in the CBC. This study in theory demonstrated the importance of balancing the activities of the enzymes to maintain the metabolic coordination for an efficient CBC.

Model description
The C 3 photosynthetic carbon metabolism module of ePhotosynthesis model constructed 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; I 2 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 C 3 photosynthesis (Fan et al., 2011); theta ( ) 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).   M a n u s c r i p t  A c c e p t e d M a n u s c r i p t

Increasing the enzyme capacity of the CBC may decrease photosynthesis
The responses of photosynthetic CO 2 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 (Figure 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, SBP aldolase, SBPase, TK b and PRK; the enzymes showing the biphasic responses in the CBC include PGAK, FBP aldolase and TKa ( Figure 1). where K c and K o represent the Michaelis-Menten constants of Rubisco for CO 2 and O 2 , respectively. 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 CO 2 releasing rate through photorespiration pathway is a half of the RuBP oxygenation rate (von Caemmerer, 2000).

Excess capacity of enzymes showing a biphasic response limits RuBP regeneration
In this study, α is fixed as a constant since the environmental conditions keep constant in all simulations. So that:

{ }
The relationship between 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 K m and the reaction rate is mainly limited by the substrate concentration (the region on the left side of the first dashed vertical line in Figure   2); in the second stage, when the substrate concentration is near its K m ,the reaction rate is limited by both the enzyme capacity and substrate concentration (the middle region bounded by dashed vertical lines in Figure 2); in the third stage, when substrate concentration is times greater than the K m , the reaction rate is limited by enzyme capacity (the region on the right side of the second dashed vertical line in Figure 2) (Fendt et al., 2010). Following equation 9, we can be informed that the reaction rate of Rubisco is approaching V max with the increase of . In other words, the greater the value of , the less the limitation by the substrate RuBP, and vice versa. A c c e p t e d M a n u s c r i p t Figure  2. The effects of the CBC enzyme capacity on the Rubisco-RuBP relationships. The RuBP/Km RuBP is the ratio of RuBP concentration to the apparent Km of Rubisco for RuBP. The V c /Vcmax is the ratio of carboxylation rate to the maximum carboxylation rate if Rubisco. The x-axis is on a log 10 scale. The color bar means the fold change of the default Vmax of each enzyme. The color of dots in each subgraph represents the fold change (corresponding to the color bar) of enzyme activity. The dark blue means the fold change close to 0.01 and yellow means fold change close to 1000. When the A c c e p t e d M a n u s c r i p t color of dots changes from blue to yellow, the maximum enzyme activity of the enzyme in each subgraph increases. The gray curve in each subgraph describes the enzyme-substrate relationship of a standard Michaelis-Menten equation for a first-order reaction. Dashed vertical lines in each subgraph separate the subgraph into three regions. The left region, middle region and right region represent substrate limiting stage (stage I), substrate and enzyme co-limiting stage (stage II) and enzymatic capacity limiting stage (stage III), respectively (Fendt et al., 2010). When colors of dots change from blue to yellow, if the corresponding positions of these dots change from left to right, then with the increase of enzyme activity, the limitation over Rubisco carboxylation shifts from RuBP concentration limitation to Rubisco activity limitation. On the other hand, if the corresponding positions of these dots change from right to left, then with the increase of enzyme activity, the limitation shifts from Rubisco capacity limitation to RuBP concentration limitation. The red dot represents a state when photosynthetic CO 2 uptake rate is maximized. For GAPDH, SBPA, SBPase, TKb and PRK, the yellow dots overlap with red dot, which means that increasing their enzymatic capcaities only slightly increases photosynthesis.
For Rubisco, however, with increase in its catalytic capacity, the gradually drops.
Additionally, the has a biphasic response curve with the increase in the activity of PGAK, FBA, FBPase and TKa. Most of the dots are located in the middle region (Figure 2), indicating that CO 2 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 ( Figure S1 to S10).

The enzymes showing biphasic responses control distribution of substrates in different sub-cycles of the Calvin Benson cycle
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-catalyzed reactions, and T3P is used as a shared substrate by 4 steps in the CBC. They are the enzymatic steps catalyzed by FBA, TKa, SBPA and TKb (Figure 3). Existence of substrates used by multiple reactions creates different sub-cycles for the CBC. After careful examination of the location of enzymes generating biphasic responses, we found that these enzymes always catalyze reactions in a sub-cycle consuming one of the shared substrates (Figure 1, Figure 3), meanwhile producing the product which is used as a substrate for a reaction of the next sub-cycle. As a result, with changed capacity of these enzymes, the imbalance of the coordination between A c c e p t e d M a n u s c r i p t M a n u s c r i p t

Two Negative feedback loops play dominant roles in coordination of the CBC
The above analyses clearly show that, level of activity of enzymes in one sub-cycle consuming shared substrate and producing intermediates required for another sub-cycle play a critical role in determining flux through the CBC (Figure 3) 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 F6P to FBPase (Figure 4). The enzymes related to these two inhibitions, as expected, locate on the pathways consuming shared metabolites in different sub-cycles.

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 sub-cycles, we developed an analytical model representing a simplified metabolic network with sub-cycles competing for shared resources (Figure 5a). The The concentration of C corresponding to the maximum flux rate of Product formation at the steady state is: A c c e p t e d M a n u s c r i p t , v of the Y-axis has been normalized to the maximum v under the corresponding conditions, and it represents the relative flux of the auto-catalytic cycle. In the simulation: K 1 = 1, when K 1 >K 2 , K 2 = 0.05 (red curve); when K 1 = K 2 , K 2 = 1 (green curve); when K 1 <K 2 , K 2 = 20 (purple curve). The dotted line indicates the x corresponding to the maximum v. The gradient bars show that, with the increase of x from 0 to 1, the concentration (light green gradient bar) of C increases and concentration (dark green gradient bar) of B decreases.

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 analyzed by employing the systems kinetic This work will promote our better understanding on the CBC operation and its regulations.
In this theoretical study, we didn't 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 catalyzed by PGAK, FBA, FBPase or TKa is beyond its optimal level, it decreases rather than increases the flux of the CBC (Figure 1).  usually causes the changes in many other enzymes (Haake et al., 1998;Haake et al., 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 CO 2 conditions. However, transgenic plants with larger enhancement of FBA relative activity show slightly lower stimulation of photosynthesis and of growth under elevated CO 2 (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 . Transgenic plants with reduction of FBPase activity show a decrease in A compared with those in WT (Koßmann et al., 1994;Haake et al., 1998;Haake et al., 1999), while over-expressing 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 catalyzed by the transketolase 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 ( Figure S12). Interestingly, over-optimal capacity of TK leads to the accumulation of R5P and decreased T3P contents ( Figure 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).
A c c e p t e d M a n u s c r i p t 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). It 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 CO 2 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 sub-cycles. They are the auto-negative regulations of PGAK by ADP and of FBPase by F6P (Figure 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 A c c e p t e d M a n u s c r i p t 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 sub-cycles 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) (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 (Figure 1 and 5). Interestingly, all the identified reactions or regulators which are responsible for the shared metabolites coordination are located in the sub-cycles of earlier steps in the CBC (Figure 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 sub-cycles, including both their enzyme activities and their regulatory properties, need to be well coordinated to achieve an efficient CBC at steady state. A c c e p t e d M a n u s c r i p t   A c c e p t e d M a n u s c r i p t   of the Y-axis has been normalized to the maximum v under the corresponding conditions, and it represents the relative flux of the auto-catalytic cycle. In the simulation: K 1 = 1, when K 1 >K 2 , K 2 = 0.05 (red curve); when K 1 = K 2 , K 2 = 1 (green curve); when K 1 <K 2 , K 2 = 20 (purple curve). The dotted line indicates the x corresponding to the maximum v. The gradient bars show that, with the increase of x from 0 to 1, the concentration (light green gradient bar) of C increases and concentration (dark green gradient bar) of B decreases. A c c e p t e d M a n u s c r i p t