Plant Physiology Preview. Published on February 12, 2014, as DOI:10.1104/pp.113.230284
Running title: Elements Required for Efficient C4 Photosynthesis
Author for Correspondence:
Xin-Guang Zhu
Key Laboratory of Computational Biology, CAS-MPG Partner Institute for
Computational Biology, Shanghai Institutes for Biological Sciences, Chinese
Academy of Sciences, Shanghai 200031, China
Email: [email protected]
Fax: 86-21-54920451
Tel: 86-21-54920486
Research Area: Systems biology and synthetic biology
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Elements Required for an Efficient NADP-ME Type C4 Photosynthesis
-- Exploration using a systems model of C4 photosynthesis
Yu Wang1,2, Stephen P Long3, Xin-Guang Zhu1,2*
1. State Key Laboratory for Hybrid Rice, CAS-MPG Partner Institute for
Computational Biology, Shanghai Institutes for Biological Sciences, Chinese
Academy of Sciences, Shanghai 200031, China
2. Key Laboratory of Computational Biology, CAS-MPG Partner Institute for
Computational Biology, Shanghai Institutes for Biological Sciences, Chinese
Academy of Sciences, Shanghai 200031, China
3. Department of Plant Biology, University of Illinois at Urbana Champaign, IL,
61801
Summary
A new systems model of C4 photosynthesis is developed and used to study
systems properties of C4 photosynthesis and to quantitatively evaluate the
control of different anatomical and biochemical features to light and nitrogen use
efficiencies.
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Financial source
Funding for authors’ research is from the Bill & Melinda Gates Foundation
(Grant No. OPP1014417), National Science Foundation of China (Grant No.
30970213), Ministry of Science and Technology of China (Grant No.
2011DFA31070), the Young Talent Frontier Program of Shanghai Institutes for
Biology Sciences/Chinese Academy of Sciences (Grant No. 09Y1C11501) and
US Department of Energy (Grant No. APRA-E Petro Award 0470-1535).
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Abstract
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C4 photosynthesis has higher light, nitrogen and water use efficiencies than C3
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photosynthesis. Though the basic anatomical, cellular and biochemical features
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of C4 photosynthesis are well understood, the quantitative significance of each
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element of C4 photosynthesis to the high photosynthetic efficiency are not well
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defined. Here we addressed this question by developing and using a systems
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model of C4 photosynthesis, which includes not only the Calvin-Benson cycle,
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starch synthesis, sucrose synthesis, C4 shuttle and CO2 leakage, but also
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photorespiration and metabolite transport between the bundle sheath cells
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(BSCs) and mesophyll cells (MCs). The model effectively simulated the CO2
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uptake rates, and the changes of metabolite concentrations under varied CO2
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and light levels. Analyses show that triose phosphate transport and CO2 leakage
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can help maintain a high photosynthetic rate by balancing ATP and NADPH
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amounts in BSCs and MCs. Finally, we used the model to define the optimal
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enzyme properties and a blueprint for C4 engineering. As such, this model
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provides a theoretical framework for guiding C4 engineering and studying C4
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photosynthesis in general.
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Introduction
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C4 photosynthesis has a higher potential energy conversion efficiency
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compared to C3 photosynthesis as a result of a CO2 concentrating mechanism
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that largely eliminates photorespiration (Zhu et al., 2008); similarly, C4
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photosynthesis has higher water and nitrogen use efficiencies (Sage, 2004). The
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UN Food and Agricultural Organization predict that 70% more basic food
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stuffs will be required to feed the world in 2050 and at current rates of global
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crop yield improvement there will be a shortfall (Long, 2012). Introducing C4
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photosynthesis into C3 crops such as rice (Oryza sativa L.) is therefore viewed
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as a strategy to achieving the needed jump in genetic yield potential (Hibberd et
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al., 2008, Zhu et al., 2010, von Caemmerer et al., 2012). Most C4 plants
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compartmentalize photosynthetic reactions into two distinct cell types, i.e.,
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bundle sheath cells (BSCs) and mesophyll cells (MCs), each with a distinct
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chloroplast type. A key requirement, unique to C4 photosynthesis, is efficient
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transport of key metabolites between the two cell types and their distinct
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chloroplasts (Weber and von Caemmerer, 2010; Furbank 2011). Though the
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basic anatomical, cellular and biochemical features of C4 photosynthesis have
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long been well defined, our current understanding of the key quantitative steps
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in coordination and regulation is still rather limited (Sage and Zhu, 2011). To
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achieve informed engineering of a C4 photosynthetic system into a C3 plant, a
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primary requirement is knowledge of the qualitative and quantitative
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importance of each component of the system to the efficiency of the process.
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This will be a key to setting priorities in the practical engineering of the
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conversion of a C3 to a C4 crop.
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Historically, genetic engineering of C4 photosynthetic systems, e.g., increasing
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or decreasing the expression of individual enzymes, has been used to study the
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contribution of individual components on C4 photosynthetic efficiency. For
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example, the effects of decreasing the amount of ribulose-1,5-bisphosphate
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carboxylase/oxygenase (Rubisco), pyruvate orthophosphate dikinase (PPDK)
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and NADP malate dehydrogenase(NADP-MDH) on photosynthesis in Flaveria
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bidentis was studied systematically. This showed that in saturating light, the
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control coefficients for Rubisco was ca. 0.7, for PPDK 0.2-0.3 and for
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NADP-MDH, it was zero (Furbank et al., 1997). The control coefficient for
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phosphoenolpyruvate carboxylase (PEPC) was estimated in Amaranthus edulis
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at ca. 0.35 under saturating light and ambient CO2 levels (Bailey et al., 2000).
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Matsuoka et al. (2001) summarized the control coefficients of photosynthetic
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enzymes in different C4 plants. However, these were mainly constrained to a
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few enzymes under a few light and CO2 conditions. Given that the control
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coefficient of a particular enzyme in a metabolic system is not a property of the
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enzyme itself, rather it depends on the levels of all enzyme activities in the
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whole metabolic system (Fell, 1997) and the physico-chemical environment, a
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systematic evaluation of each enzyme to C4 photosynthetic efficiency under
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different light and CO2 conditions still needs to be conducted.
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However, with millions of potential permutations in quantities of enzymes and
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transporters, plus potential pleiotropic effects, experimental manipulation of all
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possibilities would be impractical. Besides the influence of metabolic or
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enzymatic properties on C4 photosynthetic efficiency, many anatomical and
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cellular features related to C4 photosynthesis also influence its efficiency.
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Because many anatomical or cellular features can influence more than one
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biochemical or biophysical processes simultaneously, the impact of modifying
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these properties to C4 photosynthesis is even more difficult to define than in C3
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photosynthesis. Although a high density of plasmodesmata between the MCs
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and BSCs has long been recognized as a characteristic of C4 leaves, their
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quantitative role is poorly defined. Since in most C4 species the BSCs wall is
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suberized, plasmodesmata represent the only path for metabolites diffusion
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between BSCs and MCs; however, it also provides a path for leakage of CO2
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concentrated in the BSCs. Because a decrease in plasmodesmata permeability
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would lower metabolite diffusion but limit CO2 leakage at the same time, the
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impact is not intuitive. Plasmodesmata are used here to show one of several
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features where quantitative significance is non-intuitive. Others include
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presence of different decarboxylation pathways, that operate simultaneously to
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varying degrees, and metabolite transporters in the plastid envelope and
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plasmalemma of the two cell types.
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In recent years, in silico experiments based on systems modeling have emerged
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as an effective way to understand control properties of the C3 photosynthetic
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system and focus practical engineering on key targets (Fell, 1997; Poolman et al.,
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2000; Zhu et al., 2007; Zhu et al., 2012). Steady state models of C4
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photosynthesis were first developed over 30 years ago (Berry and Farquhar,
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1978; Collatz et al 1992; von Caemmerer, 2000). And the metabolite transport
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processes of C4 photosynthesis were simply described (Hatch and Osmond,
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1976). These models have been widely used to understand the physiology and
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ecology of C4 photosynthesis due to their simplicity and robustness. They have
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also been used to understand the significance of properties such as the resistance
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to CO2 back-diffusion from the BSCs (von Caemmerer and Furbank 2003).
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However, as a result of their lack of an explicit description of the individual
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reactions of the C4 photosynthetic pathway, these steady-state models cannot be
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used directly to study the impact of manipulating a particular gene or anatomical
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feature on C4 photosynthetic efficiencies from a whole systems perspective. A
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metabolic systems model of C4 photosynthesis, which incorporated the major
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metabolic reactions involved in C4 photosynthesis, was developed by Laisk and
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Edwards (2000), and was used to estimate the metabolic control coefficients of
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different enzymes. Here we extended this model and developed a comprehensive
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dynamic systems model of NADP-malate enzyme type (NADP-ME) C4
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photosynthesis (referred to as C4 model hereafter). The NADP-ME pathway was
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chosen because major C4 food crops, Zea mays and Sorghum bicolor, and key
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C4 bioenergy crops, Miscanthus giganteus and, Saccharum officinarum, together
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with the model C4 plant, Setaria viridis, are all of this subtype; furthermore, this
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pathway has been chosen as the target C4 photosynthetic pathway to be
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engineered into rice.
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Since roles of individual steps in the process, as shown above, can be
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non-intuitive, it was considered necessary to expand on previous models by
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including all discrete steps in C4 NADP-ME carbon metabolism from CO2
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assimilation in the MCs cytoplasm to carbohydrate end-product synthesis in the
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BSCs. Therefore, this new C4 model includes all reactions of the Calvin-Benson
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cycle, photorespiration, starch synthesis, and sucrose synthesis, as well as the C4
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shuttle, CO2 leakage and metabolite transport processes between BSCs and MCs.
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The model was validated against measured CO2 assimilation rate (A) and
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metabolite levels under different light and CO2 levels. In this study, we
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systematically quantified through modeling the impacts of modifying different
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biochemical and anatomical features of C4 photosynthesis to the efficiency of
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CO2 uptake. These were used to predict the critical changes required to engineer
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an artificial C4 system into a C3 leaf.
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Results
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Model validation
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The model realistically predicted the response of CO2 uptake rate (A) to
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intercellular CO2 concentration (Ci) and the response of A to the photosynthetic
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photon flux density (PPFD) (Fig. 2). The predicted photorespiration rate of
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0.75 μmol m-2 s-1 under ambient [CO2] and [O2] conditions, which is
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comparable to the measured value of about 1.6% of A in maize (Deveau and
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Burris, 1989). The predicted CO2 compensation point around 7 μbar, which is a
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unique feature of C4 plants (Meidner, 1962; Moss, 1962). The simulated
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maximum quantum yield of 0.057 mol/mol (mol CO2 per mol photon) is also
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comparable to previously reported quantum yields of NADP-ME subtype
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plants (Ehleringer and Bjorkman, 1977; Monson et al., 1982; Ehleringer and
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Pearcy, 1983; Dai et al., 1993).
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We further examined the responses of metabolite concentrations to changes in
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intercellular CO2 concentration (Ci) (Fig. 3). Most of the predicted trends are
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broadly similar to experimental data (Leegood and von Caemmerer, 1989),
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except in the case of fructose bisphosphate (FBP). The predicted FBP trend is
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contrary to experimental measurement. The predicted responses of C4 related
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photosynthetic intermediates to changes in PPFD are similar to experimental
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data (Fig. S1). The predicted pool sizes of 3-phosphoglycerate (PGA), triose
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phosphate (T3P) are about half of the measured values.
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Significance of different enzymes to C4 photosynthetic efficiency
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Five enzymes, i.e. PEPC, NADP-ME, PPDK, Rubisco and MDH, have been
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usually regarded as exerting the greatest metabolic control over the rate of C4
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photosynthesis (Furbank et al., 1997; Bailey et al., 2000; Matsuoka et al., 2001).
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We used the C4 model to predict the influence of manipulation of these five
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enzymes activities on the A-Ci curve (Fig. 4). Out of these five enzymes, only
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PEPC activity influenced the initial slope of the A-Ci curve; NADP-ME and
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Rubisco activities influenced both the convexity and maximal CO2 uptake rate
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of the A-Ci curve, while NADP-MDH and PPDK activities affected the
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maximal CO2 uptake rate of the A-Ci curve. Under a high PPFD of 2500 μmol
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m-2 s-1, the maximum rate of photosynthetic electron transport (Jmax_T) was a
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limiting factor for the CO2 assimilation. Jmax_T is defined as the total electron
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transport capacity which includes the maximum rate of linear electron transport
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in MCs (Jmax_m) and the maximum rate of cyclic electron transport in BSCs
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(Jmax_b) (Method).
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The model was then used to calculate the flux control coefficient (CC) of each
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enzyme with respect to CO2 uptake rate (Table I, Table SI). The results
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suggested that, under a high PPFD of 2000 μmol m-2 s-1, Jmax_T and
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Calvin-Benson Cycle enzymes, e.g. Rubisco and SBPase, had the greatest CC
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under an ambient Ci of 150 μbar. PEPC and mesophyll conductance (gm)
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showed the greatest CC under a low Ci of 50 μbar (Table I). Under a PPFD of
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200 μmol m-2 s-1, PPFD and Jmax_T had the greatest CC (Table I).
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An optimization algorithm was applied to identify the optimal amounts of
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active enzymes required to achieve maximal A under a fixed total amount of
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protein-nitrogen. Compared to the optimal enzyme activities under an ambient
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pre-industrial [CO2] of 275 μbar, less CA and PEPC were required to gain an
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optimal CO2 uptake under the current ambient [CO2] of 394 μbar, while the
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optimal amounts of most other enzymes required were higher (Fig. 5A).
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Given that Rubisco is a critical enzyme for CO2 fixation in the Calvin-Benson
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cycle and a major goal of C4 engineering is to repress Rubisco’s RuBP
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oxygenation activity, we optimized the ratios of activities of different enzymes
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to that of Rubisco for current atmospheric CO2 condition (Fig. 5B). Compared
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to Rubisco activity, the optimal activities of CA and the major enzymes
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involved in the C4 shuttle, i.e. PEPC, MDH, NADP-ME, were higher for
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higher A (Fig. 5B). In addition, more triose phosphate transporter, which
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transports PGA and triose phosphate across chloroplast envelope, would be
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needed (Fig. 5B).
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Many enzymes, functioning in C4 photosynthesis, which play important
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metabolic roles in C3 plants (Aubry et al., 2011) have undergone specific
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changes in their amino acid sequence and correspondingly their catalytic
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properties during their cooption into C4 photosynthesis, i.e. the homologs used
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in C4 photosynthesis differ from their C3 homologs (Engelmann et al., 2003;
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Maier et al., 2011; Chastain et al., 2011; Aubry et al., 2011). So far, it is unclear
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how much difference introducing the C4 homologs versus using the
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endogenous C3 homologs might have on photosynthetic CO2 uptake rate and
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nitrogen use efficiency during C4 engineering. We evaluated the effect of C4 or
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C3 homologs of C4 photosynthetic enzymes on both photosynthetic CO2
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uptake rate and nitrogen cost. The nitrogen cost ratio was defined as the ratio of
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nitrogen required for synthesis of a C3 homolog of enzyme to that needed for
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synthesis of a C4 homolog. The nitrogen cost was calculated based on catalytic
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constant (kcat) and molecular weight (Table II, Table SII) of both C3 and C4
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homologs. Compared to the C3 homolog, the C4 homolog of PEPC has a
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higher affinity to HCO3-, whereas the C4 homolog of NADP-MDH, PPDK,
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NADP-ME and Rubisco all have lower affinities to their substrate and higher
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turnover numbers (Table II, Table SII). Simulation results indicated that a
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lower substrate binding affinity did not decrease reaction rates (Table II),
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possibly because the lower affinity was compensated by increased substrate
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concentrations. On the other hand, higher kcat of these enzymes are indeed
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beneficial through decreasing the nitrogen demand for a given Vmax.
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2.2 Predicted changes of carbon isotope (13CO2) discrimination signals
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We compared the predicted carbon isotope composition (δ13C) and
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discrimination (Δ) to reported values. C3 and C4 plants have distinct Δ and
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δ C values, thus both are commonly used to distinguish these two
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photosynthetic types. Typical δ13C for C3 species are between -30 and -22‰
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(Troughton et al., 1974), but ca. -12‰ for C4 plants (Cousins et al., 2006).
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Typically a C3 plant has a Δ value around -20‰, and a C4 plant has Δ value
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around 4‰ (Farquhar et al., 1989).The current model predicted a C4 δ13C value
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of 12.4‰ and a Δ value of 4.1 ‰ under a PPFD of 1500 μmol m-2 s-1 (Fig. 6).
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Interestingly, the model predicted decreased Δ, increased δ13C together with
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concurrent decrease in CO2 with increasing light intensity (Fig. 6).
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2.4 The influence of intra- and inter-cellular metabolite transport
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processes on C4 photosynthetic efficiency
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Compared to C3 photosynthesis, C4 photosynthesis requires extensive
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metabolite transport between different cell types and organelles. Properties of
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the metabolite transport processes and CO2 diffusion can influence A. Our
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model assumes that metabolite transport through chloroplast envelopes in both
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MCs or BSCs follow typical Michaelis-Menten kinetics. Metabolite
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movements between BSCs and MCs are assumed to be a simple diffusion
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process through plasmodesmata, as has been suggested earlier (Stitt and Heldt,
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1985b). In the current model CO2 transport between the two cell types and
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across the chloroplast envelope were both modeled as simple first-order
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diffusion processes.
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The effect of variation in the activity of the triose phosphate transporter (TPT),
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which transports PGA and T3P across the chloroplast envelope, on A was
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shown in Fig. 7. The simulated results indicated that a high TPT rate is required
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to obtain a high CO2 assimilation rate and to decrease CO2 leakage (Fig. 7).
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In maize, there is a large concentration difference of many metabolites, such as
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PGA, T3P and malate, between BSCs and MCs (Leegood, 1985; Stitt and Heldt,
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1985ab), which indicates that metabolites transport through plasmodesmata is
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likely a limiting factor of CO2 assimilation. Here we used the C4 model to
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systematically examine how different factors related to metabolite transport
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influence A. First, the permeability to each metabolite was varied to determine
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its influence on A. As expected, increasing the permeabilities to malate and
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pyruvate increased A (Fig. S2). In the simulation, the same permeability was
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assumed for both T3P and PGA (C3P), since they have the same diffusion
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properties (Sowinski et al., 2008). At a given permeability to C3P transport,
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increasing the permeability of plasmodesmata to CO2 first increases and then
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decreases A (Fig. 8A). For any given C3P permeability, there is an optimal
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permeability to CO2 that achieves the maximum A (Fig. 8A, C). Increased C3P
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permeability resulted in a higher light-saturated A (Amax) (Fig. 8B). Furthermore,
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a higher optimal CO2 permeability is predicted for Amax under a lower C3P
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permeability (Fig. 8C).
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Diffusion of metabolites across the cell walls at the BSC-MC interface depends
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on the length and quantity of plasmodesmata and the metabolite diffusion
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coefficient. Based on these principles impacts of varying the properties of the
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plasmodesmata on A were explored. The simulated impact of changing the
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surface fraction of plasmodesmata (Φ) and BSC-MC interface cell wall
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thickness (Lpd) on A is shown in Fig. 9A. At any given Φ, increasing Lpd first
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increases and then decreases A (Fig 9A). The optimal Lpd for maximal A is as Φ
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is increased (Fig. 9A). At Φ equal to 0.03, increased Lpd lowered the rate of
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photorespiration (Fig. 9B) as a result of increased [CO2] in the BSCs (Fig. 9C),
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which subsequently increased A (Fig. 9B). The increased CO2 concentration
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also led to an enhanced CO2 leakage (Fig 9C). A was maximal at an Lpd
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between 500 nm and 800 nm (Fig. 9B). CO2 leakiness reached a minimum at an
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Lpd value of ca.150 nm (Fig. 9C).
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Discussion
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In this section, the novelty of this model compared to earlier models is
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summarized. Then, the significance of different biochemical and anatomical
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features on C4 photosynthetic efficiency, as revealed by the model are
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discussed. Finally, the application of the model in guiding selection of
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components process for engineering C4 photosynthesis into C3 crops is
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examined.
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Novelty and Capacity of this new C4 photosynthesis model
The large increase in, and wider availability of, computational power over the
past decade provides support for more complex kinetic models than available
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when the previous model of C4 photosynthesis by Laisk and Edwards (2000)
was completed. As a result, the present model of C4 photosynthesis
incorporates many new features and reactions to provide a more complete
description of the C4 photosynthetic process combined with Kranz leaf
anatomy. This model not only includes more detailed and updated description
of the BSC and MC metabolism, i.e. incorporation of the Calvin-Benson cycle,
starch, sucrose, mitochondria respiratory and photorespiration in a cell specific
manner, but also incorporates detailed diffusion of metabolites between these
two cell types. For example, sucrose synthesis is assumed to occur in the
cytosol of MCs according to experimental data (Furbank et al., 1985; Lunn and
Furbank 1997). The metabolite transport between BSCs and MCs was
described as a diffusional process through plasmodesmata, and the metabolite
transport across chloroplast envelope was assumed to follow Michaelis-Menten
kinetics according to Stitt and Heldt (1985b) and Weber and von Caemmerer
(2010). Incorporation of the effects of different plasmodesmata properties on
diffusion coefficients enables the model to evaluate the implications of
changing these anatomical features on photosynthetic efficiency. We also
assumed that starch synthesis and breakdown occur at the same time (Stitt and
Heldt, 1981). Finally, equations to calculate the electron transfer rate, directly
linked to ATP and NADPH synthesis were included. This is in contrast to Laisk
and Edward (2000), where the ATP production rate was determined by the
NADPH production rate via NADP-ME in BSCs.
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This C4 model accurately predicted the experimentally measured A under
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different [CO2] and PPFD (Fig. 1, 2). The model predicted photorespiratory
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rate, CO2 compensation point and a maximum quantum yield that are all
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comparable to previously measured values in C4 plants (Deveau and Burris,
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1989; Meidner, 1962; Moss, 1962; Ehleringer and Bjorkman, 1977; Monson et
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al., 1982; Ehleringer and Pearcy, 1983; Dai et al., 1993).
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Most of the predicted trends of metabolite concentrations to variation in [CO2]
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and PPFD were similar to experimental observations (Leegood and von
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Caemmerer 1989) (Fig. 3; Fig. S1), excepting [FBP]. The discrepancy between
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modeled and experimentally observed responses of [FBP] to variations in [CO2]
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may have two causes. Firstly, FBP plays a role not only in the Calvin-Benson
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Cycle and sucrose synthesis, but also in glycolysis and the pentose phosphate
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pathway, which are currently not included in the model. Slowly labeled FBP in
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pool is not directly involved in Calvin-Benson Cycle (Szecowka et al., 2013).
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Secondly, the regulatory mechanisms controlling the activity of the enzymes of
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photosynthetic carbon metabolism were not described in the model. Additional
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features incorporated into this model may be able to further improve the
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model’s predictive ability. A low rate of starch breakdown can replenish F6P in
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BSCs, and this has enabled the model to correctly predict the increasing
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response of the RuBP pool with decreasing [CO2] (Fig. 3) as observed in
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experiments (Usuda et al. 1987; Leegood and Caemmerer 1989), in contrast to
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previous models where low ambient [CO2], RuBP concentration decreased with
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further decrease in ambient [CO2] (Laisk and Edwards 2000). The predicted
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pool sizes of PGA and T3P were lower than experimental date, but they can be
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improved by increasing total phosphate concentration in bundle sheath plastid
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and increasing Michaelis-Menten constants (Km) for PGA and T3P in related
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enzymes is another way to specifically modify PGA and triose phosphates
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contents (Fig S6-8). Similarly the pool size of FBP also can be increased by
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increasing the Km for FBP in cytolsolic FBPase (Fig S9). More research is
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needed to determine whether which one or combinations of these possibilities
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or others might be contributed to the predicted lower than measured metabolite
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levels.
CO2 labeling experiment in Arabidopsis indicated that a large part of FBP
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The model predicted a δ13C and Δ value is within the range of values for a
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typical C4 plant (Fig. 6) (Farquhar et al., 1989). The model further predicted
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that carbon isotope discrimination and CO2 leakiness were reduced with
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increasing PPFD (Fig. 6), which is consistent with experimental observations
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(Henderson et al., 1992; Kromdijk et al., 2008; Tazoe et al., 2008; Cousins et
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al., 2006, Farquhar et al., 1989). These results demonstrate that the C4 model
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can realistically simulate the experimentally observed carbon isotope
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discrimination of C4 species.
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Even with all the above-mentioned features and capacity, this new C4 model
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should be regarded as a living model, i.e. one designed to support continual
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improvement. First, the current model assumes that two thirds of the light
352
energy is absorbed by MCs and one third is absorbed by BSCs. However,
353
reliable estimates of this partitioning are not yet available. Secondly, though we
354
have conducted a comprehensive literature search, kinetic parameters for a
355
number of the enzymes of the C4 system had to be taken from the literatures
356
for C3 plants. A number of parameters that are currently unavailable for C4
357
plants include: kinetic parameters describing transporters, concentrations of
358
components of the electron transfer chain in both BSCs and MCs, the diffusion
359
properties of the membranes, cell walls and plasmodesmata for different
360
metabolites. Even the exact diffusion properties of the cytosol are not well
361
characterized to date. Possibly as a reflection of all these uncertainties, our
362
predicted pool sizes and BSC/MC concentration gradients of T3P and PGA
363
(Fig. 3, S1are lower than those reported in literature (Leegood and von
364
Caemmerer, 1989; Stitt and Heldt 1985ab). More accurate measurements of
365
kinetic
366
concentrations in different compartments of both BSCs and MCs, and
367
metabolite fluxes under varied [CO2] and PPFD will undoubtedly help improve
368
the C4 systems model. Fortunately, various techniques in metabolomics (Fiehn,
369
2002; Sumner et al., 2003; Weckwerth, 2003; Kopka et al., 2005;
370
Oksman-Caldentey and Saito, 2005) and fluxomics (Fernie et al., 2005;
parameters,
metabolite
concentrations,
especially
metabolites
16
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
371
Wiechert et al., 2007; Szecowka et al., 2013) are rapidly emerging, which can
372
help fill in this data demand.
373
374
Despite these caveats, the model is shown to predict A-PPFD, A-Ci, with
375
quantitative and qualitative reality, as well as responses of metabolite
376
concentrations to varying PPFD and Ci levels. Thus, it is already well-suited to
377
serve as a platform to study the properties of C4 photosynthesis and identify
378
key elements required for efficient NADP-ME C4 photosynthesis.
379
380
Control properties of key enzymes for C4 photosynthetic efficiency
381
The biochemical models of C4 photosynthesis described by Collatz et al. (1992)
382
and von Caemmerer (2000) predict the C4 photosynthetic rate assuming that the
383
A is limited by three enzymes, at steady-state i.e. Rubisco, PEPC and PPDK. The
384
wide use of these models in predicting C4 photosynthetic rates warrants a
385
systematic test of these assumptions. Here we tested these assumptions by
386
predicting the impacts of varying activities of these enzymes on A-Ci curves (Fig.
387
4). Our analysis confirmed that PEPC and Rubisco are two major enzymes
388
influencing the A-Ci response curves. Consistent with the steady-state models,
389
our simulations suggested that PEPC controls the initial slope of the A-Ci
390
response curve and Rubisco controls the plateau of the A-Ci response curve
391
(Collatz et al., 1992; von Caemmerer, 2000).
392
393
In addition to the effect of PEPC and Rubisco, our results suggested that PPDK,
394
NADP-ME and NADP-MDH also affect the A-Ci response (Fig. 4). NADP-ME
395
influenced both the convexity and maximal CO2 uptake rate of the A-Ci curve,
396
which is consistent with previous experimental observations (Pengelly et al.,
397
2012).
398
399
Besides enzymes directly involved in the C4 shuttle, some Calvin-Benson Cycle
400
enzymes, e.g. SBPase and PRK, showed certain control coefficients over A under
17
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
401
certain conditions, e.g. under high light (Table I), suggesting that these enzymes
402
may be targets to engineer for improving C4 photosynthesis. Interestingly, many
403
of these identified enzymes were experimentally shown to influence C3
404
photosynthetic efficiency, e.g. SBPase (Lefebvre et al., 2005; Tamoi et al., 2006),
405
PRK (Paul et al., 2000), and GAPDH (Price et al., 1995), therefore, these
406
predicted impacts on C4 photosynthetic efficiency warrant future transgenic
407
testing. Of particular significant here is the observation that in C3 crops, plants
408
transgenically over-expressing SBPase showed a greater increase in A at elevated
409
[CO2] than in ambient [CO2] (Rosenthal et al., 2011). This suggests that
410
increased SBPase may be of particular value in the elevated [CO2] environment
411
of the BSCs of C4 crops.
412
413
One caveat here is that the predicted flux control coefficients (CC) of an enzyme
414
depend on the default Vmax of all enzymes in the model and also the percentage of
415
decrease of the enzyme under study. For example, in this paper, we presented CC
416
calculated by the difference in the A when Vmax was decreased and increased by
417
1% only. In this case, our predicted CC for PPDK was zero, suggesting that in
418
the current system with default Vmax values for all enzymes, PPDK confers no
419
control over the photosynthetic rate. However, when we decreased the Vmax of
420
PPDK by 50%, we predicted a decrease of A of about 13% (Fig. 4), which is
421
consistent with the reported decrease of A about 10%-20% (Furbank et al., 1997).
422
To address the issue of uncertainties in the Vmax involved in the model, we conducted a
423
systematic sensitivity analysis. Specifically, Vmax of each enzyme was decreased by 20%
424
to calculate control coefficient individually (Table S2). To gain a precise estimate of
425
the CC for an enzyme in a species grown under a particular environment,
426
accurate measurements of the Vmax of the involved enzymes in the system are
427
essential. Another potential reason that underlies the difference in the predicted
428
CC and the measured CC is the pleotropic effect of manipulation a particular
429
gene on other metabolic processes. The CC predicted from the current model
18
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430
therefore only represents the control coefficient of the particular enzyme
431
assuming properties of all other enzymes are maintained as constant.
432
433
An evolutionary algorithm was applied to the system to determine the optimal
434
investment of nitrogen between the proteins of the pathways and transporters, as
435
depicted in Fig. 1, to maximize the light saturated rate of CO2 uptake at
436
pre-industrial and current atmospheric [CO2]. This optimization predicted that to
437
maximize A under elevated [CO2], nitrogen needs to be re-allocated from PEPC
438
and CA to enzymes in the Calvin-Benson Cycle, starch and sucrose synthesis
439
(Fig. 5A). Previous optimization on a C3 photosynthetic metabolism model
440
suggested that Rubisco activity should be reduced under elevated [CO2], but our
441
simulated results show that the optimized Rubisco activity increased under
442
elevated [CO2] in C4 photosynthesis (Fig. 5A). Rubisco is the first enzyme fixing
443
CO2 in C3 photosynthesis; in contrast, in C4 photosynthesis, CO2 is first fixed by
444
PEPC with the help of CA. If environmental [CO2] increases, the control
445
coefficient of the enzyme which first fixes CO2 will decrease. This explains why
446
in the optimization process, nitrogen moved away from Rubisco in C3
447
photosynthesis, and nitrogen moved away from PEPC and CA to other enzymes
448
including Rubisco in C4 photosynthesis.
449
450
Fig. 5B showed optimal ratios of different enzyme activities to Rubisco activity
451
under ambient CO2 condition, which provided a blueprint to guide C4 metabolic
452
engineering. Though the predicted optimal combinations of enzymes can result
453
in an efficient C4 photosynthetic system, the optimization results provided here
454
might not necessarily represent the unique optimal combination of enzymes for
455
the highest C4 photosynthesis efficiency, i.e. a local maximum might be
456
identified by our optimization algorithm.
457
458
19
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459
The role of triose phosphate transporter (TPT) in C4 photosynthetic
460
efficiency
461
The assimilation of one CO2 in the Calvin-Benson cycle needs two NADPH for
462
PGA reduction while only one NADPH is produced when one CO2 is released by
463
NADP-ME catalyzed malate decarboxylation in BSCs (Fig. 1). Because in many
464
NADP-ME type C4 plants, e.g. maize, photosystem II activity in BSC
465
chloroplasts is negligible (Majeran et al., 2008), the MCs has to provide
466
additional NADPH required for PGA reduction. C4 plants achieve this by
467
transporting a portion of PGA from the BSC chloroplasts to the MC chloroplasts,
468
where it is reduced to T3P. Then most of T3P is transported back to the BSC
469
chloroplasts to complete the Calvin-Benson cycle (Hatch, 1987, Weber and von
470
Caemmerer, 2010). The transport of PGA and T3P across MC and BSC
471
chloroplast envelopes is facilitated by TPT (Weber and von Caemmerer, 2010).
472
Therefore, TPT is critical to balance NADPH production and utilization between
473
BSCs and MCs. The model suggests that a high TPT capacity is required to
474
obtain a high A and to decrease the CO2 leakage (Fig. 7). Indeed proteomic
475
studies indicate that TPTs were highly abundant in C4 plants (Brautigam, 2008,
476
Majeran et al., 2010), which supports the prediction here that TPTs in both BSCs
477
and MCs are critical for effective C4 photosynthesis. It follows that where the
478
goal of converting a C3 plant to a C4 is to achieve increased A then these high
479
levels of TPT in both plastid types will also be key.
480
481
The role of CO2 leakage to C4 photosynthetic rate
482
CO2 leakage, or back-diffusion of CO2 from the BSCs to MSs, is usually
483
considered detrimental to C4 photosynthetic rate. Since the C4 dicarboxylate
484
cycle needs ATP for phosphoenolpyruvate (PEP) regeneration, more leakage of
485
CO2 out of the BSC increases the ATP requirement for fixing one CO2. The rate
486
of CO2 leakage from the BSCs depends on the permeability of the BSC-MC
487
interface to CO2 and the gradient of [CO2] between these two cell types, which in
488
turn is determined by the relative biochemical capacities of the C4 and C3 cycles
20
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
489
(von Caemmerer and Furbank 1999; von Caemmerer, 2000). Across a range of
490
C4 species, leakiness has been estimated to vary between 0.08 and 0.29 (Hatch,
491
et al., 1995; von Caemmerer and Furbank, 2003). A low CO2 permeability across
492
the BSC-MC interface is usually regarded as an essential feature in gaining a
493
high C4 A (von Caemmerer and Furbank, 2003). Simulations in this study
494
suggested that under high PPFD when the capacity of C3P transport is limited,
495
leakage can, counter-intuitively, be beneficial for C4 photosynthetic rate (Fig. 8A,
496
C). This is because under high light, when ATP supply is high, NADP-ME
497
catalyzes generation of CO2 and NADPH from malate in BSC. The leakage of
498
CO2 from BSC will increases the NADPH/CO2 ratio of BSCs, which can
499
alleviate the lack of NADPH in BSCs and thus helps decrease demand of PGA
500
and T3P transporters between BSCs and MCs. However, in some C4 plants, i.e.
501
maize, aspartate is also used as a C4 acid, which transferred from MCs to BSC
502
(Saccardy et al 1996; Furbank, 2011). The usage of aspartate will also change the
503
NADPH/CO2 ratio in BSC, because aspartate doesn’t bring NADPH from MC to
504
BSC.
505
506
The impacts of varying plasmodesmata length on C4 photosynthetic
507
efficiency
508
According to Eqn. (12), the rate of metabolite movement through the
509
plasmodesmata is determined by the length of the pathway, the BSC-MC
510
interface per unit leaf area, the surface fraction of plasmodesmata and the
511
diffusion coefficient for the given metabolite. The diffusion coefficient is
512
determined not only by the physical properties of the molecule, but also by those
513
of the medium that the metabolite diffuses through. Our simulation results
514
suggested complex impacts of altering the properties of plasmodesmata on A. Fig.
515
9A showed that both the surface fraction of plasmodesmata (Φ) and
516
plasmodesmata length (Lpd, assuming it is equal to cell wall thickness) can affect
517
A. Lpd also influences leakiness and photorespiratory flux (Fig. 9B, C). Taking
518
Lpd as an example to illustrate this complex relationship, a longer diffusion path
21
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
519
through the plasmodesmata helps maintain a high [CO2] in BSCs and decrease
520
photorespiration (Fig. 9B). The high CO2 gradient between BSCs and MCs
521
however can increase CO2 leakage (Fig. 9C). A thickened cell wall will also
522
inevitably decrease the rate of metabolite transport between the two cell types
523
which will correspondingly decrease A (Fig. S4). Therefore, it is not intuitive to
524
predict the responses of A to changes in the density or length of these
525
plasmodesmata. Simulations suggested that an optimal cell wall thickness to
526
minimize leakiness is around 150 nm (Fig. 9C); to reduce photorespiratory flux,
527
a thicker cell wall is always better (Fig. 9B); but to maximize A, an optimal cell
528
wall thickness is around 500 nm, at Φ was 0.03 (Fig. 9B). When BSC/MC
529
interface have little resistance (Fig. 9C), CO2 concentration in BSC cytosol is
530
close to Ci. While, the BSC chloroplast membrane is still an important barrier for
531
CO2 leakage, which helps to keep a higher CO2 concentration around Rubisco
532
and maintain a part of C4 photosynthesis rate (Fig. 9B).
533
534
All these above predictions were made assuming that metabolites diffuse through
535
plasmadestma
536
biophysical properties of these plasmodesmata are still far from being well
537
understood at present. For example, a high density of plasmodesmata at the
538
MC-BSC interface has been found in C4 species (Evert et al., 1977; Botha et al.,
539
1992) and large concentration gradients between two cell types has been
540
observed (Leegood, 1985; Stitt and Heldt 1985ab). This indicates that a rapid
541
diffusion between BSCs and MCs can potentially be supported. However, a
542
recent theoretical analysis based on plasmodesmatal structure and its diffusional
543
properties showed that the required metabolite gradient between BSCs and MCs
544
to support observed rate of C4 photosynthetic CO2 uptake should be at least three
545
orders of magnitude higher than experimentally measured (Sowinski et al., 2008).
546
Recent and historical measurement indicated that unidirectional transport of
547
fluorescent protein through plasmodesmata is exist in unique surfaces
548
(Christensen et al., 2009; Arisz, 1969), which suggested that active transport or
with
defined
permeability constants.
However,
detailed
22
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
549
accelerated diffusion of small molecule of certain size may occur through
550
plasmodesmata. However, the underlying mechanism is still unclear and no
551
kinetic studies on this phenomenon are available. Understanding the movement
552
of metabolites through plasmadesmata will be key to developing the engineering
553
framework for conversion of C3 to C4 crops.
554
555
Choice of enzymes with kinetic properties suitable for C4 engineering
556
C4 photosynthesis differs from C3 photosynthesis not only in the required leaf
557
anatomical structure, cellular biology and metabolism (Hatch, 1987), but also
558
in the kinetic properties of specific enzymes. Though it is usually considered
559
that C4 engineering requires expression of the C4 homologs of the involved
560
enzymes into C3 systems, this has not been examined quantitatively. The C4
561
homolog of PEPC in the mesophyll cytoplasm has a higher affinity for HCO3-
562
than its C3 and heterotrophic counterpart, while C4 homolog of NADP-MDH,
563
PPDK, NADP-ME and Rubisco all have lower affinities to their substrates but
564
higher kcat (Table SII). Are all of these changes needed to “build” an effective
565
C4 leaf? The model developed here was used to systematically evaluate the
566
impacts on A of using these alternative homologs of these enzymes. Simulation
567
results showed that for NADP-ME, PPDK, NADP-MDH, and Rubisco, the
568
lower substrate binding affinities do not decrease A under both current and even
569
low CO2 concentrations (Table II). This is because the substrate concentrations
570
are sufficiently high to eliminate the potential negative effects of low enzyme
571
affinity on their reaction rates. It is worth noting that the predicted results
572
depend on the Vmax values of used enzymes. When Vmax is too high, further
573
modifying their kinetic parameters will not affect CO2 uptake rates and hence a
574
near-zero flux control coefficients (Table I).
575
576
However, the lower kcat of the C3 homologs of these enzymes increase the
577
required nitrogen input for achieving a given Vmax (Table II). For example, to
578
achieve the same Vmax, only 20% of the protein nitrogen is required when the
23
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579
C4 homolog of NADP-MDH is used (Table II). Similarly, there is a substantial
580
nitrogen saving if the C4 homolog of Rubisco is used for C4 engineering.
581
Therefore, the analysis suggested that though all enzymes required to establish
582
the C4 photosynthetic pathway exist in C3 plants (Aubry et al., 2011), kinetic
583
properties of the C4 homologs would provide major benefits in resource use
584
efficiency replacing the C3 Rubisco in BSCs . However, this would only apply
585
if [CO2] can be elevated in the BSCs to the level of C4 crops, such as maize. If
586
the CO2 concentration around Rubisco in C4 rice is not as high as typical C4
587
plant, the C4 homolog of Rubisco may not be appropriate because of the lower
588
specificity compared to that of C3 plants.
589
590
Elements and steps needed to engineer C4 rice with high photosynthetic
591
efficiency
592
A number of earlier studies have explored the major features (Hatch, 1987;
593
Leegood, 2002; Kajala et al., 2011) required for an NADP-ME type C4
594
photosynthesis. In this study, through quantitative studies, we showed a number
595
of features that are critical for gaining efficient NADP-ME type C4
596
photosynthesis. These mainly include a proper combination of cell wall thickness
597
and plastodesmata density to balance CO2 leakage and metabolite transport and
598
the choose of C4 homologs of the key enzymes, which are needed to improve
599
nitrogen use efficiency when aiming to gain the sustainability benefits of C4
600
photosynthesis in converting a C3 crop.
601
602
Conclusions
603
This paper presents a new systems model of C4 photosynthesis, which can
604
effectively simulate the responses of CO2 uptake rates, metabolite concentrations,
605
and isotope discrimination signals. The control properties of different enzymes
606
on C4 photosynthetic efficiency were systematically characterized using this
607
model. We further used this model to demonstrate that a) triose phosphate
608
transporters are critical elements for an efficient NADP-ME type C4
24
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
609
photosynthesis; b) CO2 leakage can also help balancing ATP and NADPH
610
amounts in BSCs and MCs; c) the plasmodesmata density and cell wall thickness
611
need to be considered simultaneously to improve the CO2 uptake rate, and finally
612
d) C4 versions of the enzymes used in C4 engineering can dramatically increase
613
the nitrogen use efficiency. Based on these results, we proposed required
614
elements and procedures to engineer a NADP-ME type C4 photosynthetic
615
pathway into a C3 plant. In summary, this C4 model cannot only be used as a
616
platform to study systems properties and controls over C4 photosynthesis, but
617
also be used as a tool to guide engineering C4 photosynthesis for improved light
618
and nitrogen use efficiency in either C4 plants or into a plant with C3
619
photosynthetic machinery.
620
621
Materials and Methods
622
1. Development of the C4 kinetic model
623
The overall C4 model developed here is depicted diagrammatically in Fig. 1. The
624
carbon metabolism part of photosynthetic C3 carbon assimilation and
625
photorespiratory C2 metabolism (Zhu et al., 2007) was used as a basis of the
626
kinetic model of C4 metabolism, upon which MS-BSC metabolite transfer
627
reactions were added.
628
C4 model are described below:
629
630
The four major components required for developing this
(1) Rate equations. In the C4 model, the reactions were divided into six
categories:
631
a) Enzymatic reactions
632
Rate equations describing each discrete step of carbon metabolism
633
were either taken from the literature or developed based from standard
634
Michaelis-Menten rate equations. The complete set of rate equations is
635
presented in Supplementary data (Section 2). Reactions were
636
categorized as either equilibrium or non-equilibrium reactions based on
25
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
637
their equilibrium constants. The inter-conversion between the
638
following compounds were assumed to be in equilibrium: (1)
639
glyceraldehyde-3-phosphate (GAP) and dihydroxyacetone phosphate
640
(DHAP) independent
641
xylulose-5-phosphate
642
ribulose-5-phosphate (Ru5P) in the chloroplast stroma of the BSCs ;
643
and (3) fructose-6-phosphate (F6P), glucose-6-phosphate (G6P), and
644
glucose-1-phosphate (G1P) independent of the location of the reactions
645
(Fig. 1).
646
With the exception of reactions catalyzed by Rubisco, ADP-glucose
647
pyrophosphorylase, and glycine decarboxylase, all non-equilibrium
648
reactions were assumed to obey Michaelis-Menten kinetics, modified
649
as necessary for the presence of inhibitor(s) or activator(s). Equations
650
for the three exceptions were as given by Zhu et al. (2007).
651
Otherwise, a general reversible reaction of the form A + B < --> C + D
652
was assumed, following the standard kinetic equation of a reversible
653
reaction with two substrates and two products (Cleland, 1963), as in
654
(Zhu et al., 2007).
of the location
(Xu5P),
of the reactions; (2)
ribose-5-phosphate
(Ri5P),
and
655
656
b) Light reactions
657
A biochemical model (Ögren and Evans, 1993; von Caemmerer, 2000)
658
was used to calculate the electron transport rate (J):
659
J=
I 2 + J max − ( I 2 + J max ) 2 − 4θ I 2 J max
2θ
(1)
660
Where I2 is the photosynthetic active radiation absorbed by
661
photosystem II (PSII), Jmax is the maximal electron transport rate and Θ
662
is an empirical curvature factor (default value is 0.7) (Evans, 1989; von
663
Caemmerer, 2000).
664
The present model assumes that linear electron transport process
665
operate in MCs, while in BSCs only the cyclic electron transport
26
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
666
through PSI operates. The electron transport rates in MCs and BSCs
667
were calculated as following:
668
669
670
Jm =
Jb =
I m + J max_ m -
(I
+ J max_ m ) - 4θ I m J max_ m
2
m
2θ
I b + J max_ b −
(I
+ J max_ b ) − 4θ I b J max_ b
(2)
2
b
2θ
1
I m = X m ⋅ I ⋅ abs ⋅ (1 − f ) ⋅
2
(3)
(4)
671
Jmax_ m = Ym ⋅ Jmax_ T
(5)
672
I b = X b ⋅ I ⋅ abs ⋅ (1 − f )
(6)
673
J max_ b = Yb ⋅ J max_ T
(7)
674
675
Where, abs represents the leaf absorbance (the default value is 0.85)
676
and f accounts for the spectral distribution of light, i.e. a proportion of
677
the absorbed light cannot be effectively used by photosystems (0.15;
678
Evans, 1987). Xm and Xb are light partition coefficients for MCs and
679
BSCs. The sum of Xm and Xb is 1. Ym and Yb also sum to 1, and
680
partition the maximum rate of photosynthetic electron transport (Jmax_T)
681
between MCs and BSCs, respectively. Here we assume MCs receives
682
two thirds of the absorbed light, i.e. Xm =2/3, and the Jmax_T partition
683
coefficient for MCs is 0.6, i.e. Ym=0.6.
684
J, either Jm or Jb, is the electron transport rate which is used to directly
685
calculate the rates of ATP (or NADPH) synthesis in the model. The
686
maximum rate of ATP and NADPH synthesis reactions were described
687
as:
688
Vmax = min(Vmax E , Vmax J )
689
Where, VmaxE is the maximum rate of ATP and NADPH synthesis
690
determined by the kinetic properties of ATP synthase and NADP+
(8)
27
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
691
reductase. VmaxJ is the maximum rate of ATP (or NADPH) synthesis as
692
limited by the electron transport rate:
693
Vmax J = ε ⋅ J
694
Where ε is the ATP/e- ratio or NADPH/e- ratio.
(9)
695
696
c) Metabolite transport across the chloroplast envelope
697
Metabolite transport across membranes was described as for
698
enzyme-catalyzed reactions in the following generalized equation:
[ A]b
)
Ke
K mA + [ A]a
Vmax ([ A]a −
699
vt =
(10)
700
Where vt is the flux of metabolite A, [A]a is the concentration of
701
metabolite A in compartment a; [A]b is the concentration of metabolite
702
A in compartment b. The direction of transport is from compartment a
703
to compartment b and; Km is the Michaelis-Menten constant for A,
704
reflecting the affinity of the transporter for the metabolite.
705
706
d) Metabolite transport between MCs and BSCs.
707
Metabolite fluxes via the plasmodesmata (vA_PD) spanning the
708
BC-MSC interface were calculated as:
709
v A _ PD = PA _ PD ⋅ ([ A]a − [ A]b )
710
vA _ PD =
DA _ PD S w ⋅ φ
⋅
⋅ ([ A]a − [ A]b )
lPD
Sl
(11)
(12 )
711
These two equations assume that metabolite transport process is
712
entirely driven by diffusion, i.e. the rate is determined by both the
713
permeability (PA_PD) and the concentration gradient of the metabolite
714
between these two compartments ([A]a-[A]b). Eqn. 12 assumes that the
715
permeability between BSCs and MCs is determined by the length of
716
plasmodesmata (lPD), the cell wall area at the BSC-MC interface per
28
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
717
unit leaf area (Sw/Sl), the fraction of the BSC-MC interface
718
cross-sectional area that is permeated by plasmodesmata (Φ) and the
719
diffusion coefficient of a metabolite (DA_PD for metabolite A) in the
720
cytosol. It further assumes that the cytosol of the BSCs and MCs is
721
continuous through the cytoplasmic sleeves of the plasmodesmata (Eqn.
722
12).
723
Different metabolites have different diffusion coefficients in the
724
cytosol (Dcyt), according to molecular sizes. In this model, the Dcyt of
725
C3P is assumed to be 5.25×10-10 m2 s-1 (Sowinski et al,. 2008). CO2
726
leakage is described also as a diffusion process with a diffusion
727
coefficient in the cytosol of 1.7×10-9 m2 s-1 (Evans et al., 2009).
728
Apoplastic diffusion of CO2 is not considered because the outer cell
729
wall of the BSCs of NADP-ME plants usually includes a suberin band,
730
which effectively eliminates apoplastic leakage of CO2 (Dengler and
731
Nelson, 1999). CO2 flux across the BSCs chloroplast envelopes is
732
simulated as a simple diffusion process with a permeability coefficient
733
of 2×10-5 m s-1 (Uehlein et al., 2008, Evans et al., 2009). We used an
734
assumed value of BS chloroplast surface area per unit leaf area which
735
is 10 m2/m2 to convert the unit. Rate equations and parameters are
736
listed in the Supplementary data (Section 2and 3).
737
738
e) Sucrose and starch synthesis, and photorespiration
739
Sucrose is limited to the cytosol of the MCs and starch synthesis is in
740
the chloroplasts of the BSCs (Fig. 1), as indicated by observed
741
localization of relevant substrates, products, and enzymes (Furbank et
742
al., 1985, Lunn and Furbank, 1997). Although immunohistological
743
(Cheng et al., 1996), activity (Ohsugi and Huber, 1987) and proteomic
744
analyses have indicated that sucrose phosphate synthase (SPS), a key
745
enzyme in sucrose synthesis, was also found in the BSCs cytosol
746
(Majeran et al., 2010), the SPS is assumed to be involved in sucrose
29
Downloaded from on June 14, 2017 - Published by www.plantphysiol.org
Copyright © 2014 American Society of Plant Biologists. All rights reserved.
747
synthesis during starch degradation at night rather than participating in
748
photosynthesis during the day. Following Stitt and Heldt (1981), starch
749
synthesis and degradation are assumed to occur simultaneously. For
750
simplicity, starch degradation was simplified to one reaction, i.e. a
751
‘hypothetical’ reaction which directly converts starch to G6P.
752
For photorespiration, although glycerate kinase has been identified in
753
MC chloroplasts (Usuda and Edwards, 1980), we simplified the model
754
by assuming that reactions related to photorespiration only occur in
755
BSCs, because most of the enzymes of the photorespiratory pathway
756
have been shown to be localized to the BSCs of C4 plants (Majeran et
757
al., 2005).
758
(2) Equations for conserved quantities
759
The total concentration of the adenylate nucleotides ([CA]) chloroplast
760
was assumed constant(Pettersson and Ryde-Pettersson, 1988; Poolman
761
et al., 2000; Zhu et al., 2007, Zhu et al., 2012). Similarly, the sum of
762
[NADPH] and [NADP] in chloroplast stroma ([CN]) was assumed
763
constant in both the MCs and BSCs.
764
and sugar-bound, phosphate in chloroplast stroma ([CP]) was also
765
assumed constant in both BSCs and MCs (Fliege et al., 1978; Zhu et al.,
766
2007). These conserved quantities were expressed as algebraic
767
equations following Zhu et al. (2007).
768
The sum of inorganic phosphate
(3) Ordinary differential equations
769
The rate of metabolite concentration change was calculated as the
770
difference between the rate(s) of the reaction(s) generating the
771
metabolite (v1) and the rate(s) of the reaction(s) consuming the
772
metabolite (v2). A parameter, Vol (the volume per unit leaf area for a
773
compartment, unit: L m-2) was used to convert the unit of V1 and V2
774
from mmol m-2 s-1 to mmol L-1.
775
d[C ]
1
= (v1 − v2 ).
dt
Vol
(13)
30
Downloaded from on June 14, 2017 - Published by www.plantphysiol.org
Copyright © 2014 American Society of Plant Biologists. All rights reserved.
776
The complete system of ODEs for the C4 model is listed in
777
Supplementary data (Section 2). The proportion of MC and BSC volume
778
were based on maize leaf cross sections and subcellular volumes was
779
based on barley leaf (Winter et al., 1993).
780
parameters are listed in Supplementary data (Section 3). There were 56
781
differential equations to calculate 56 metabolite concentration variables
782
in the model.
783
All the volume related
(4) Numerical Integration
784
The ode15s procedure of MATLAB (version 2008a; MathWorks) was
785
chosen to solve the system. The solution of the ODEs provided by
786
ode15s is the time evolution of the concentration of each metabolite in
787
each compartment, which in turn allows calculation of leaf CO2 and O2
788
fluxes.
789
790
791
2. CO2 assimilation rate calculation
792
when simulated metabolite concentrations do not change with time any more.
793
The steady state metabolite concentrations and flux rates were extracted from the
794
model for CO2 assimilation rate calculation and further analysis. The CO2
795
assimilation rate (A) was calculated as (Farquhar et al., 1980):
796
A = vc − 0.5vo − Rd
797
where vc and vo are the rates of RuBP carboxylation and oxygenation
798
respectively. Rd is the rate of mitochondrial respiration. The default value for Rd
799
is 1 µmol m-2 s-1 with the rate of respiration in both BSCs (Rb) and MCs (Rm)
800
being equal as 0.5 µmol m-2 s-1.
During the simulation, we assumed that the model has reached a steady state
(14)
801
802
In von Caemmerer’s C4 model (von Caemmerer, 2000), CO2 assimilation was
803
calculated by two equations. Besides Eqn. 14, the following equation was also
804
used:
31
Downloaded from on June 14, 2017 - Published by www.plantphysiol.org
Copyright © 2014 American Society of Plant Biologists. All rights reserved.
805
A = v p − vLeak − Rm
806
The minimum of Eqn. 14 and 15 determines the actual A. While in our model,
807
both calculation methods always reach the same result at the steady state (See
808
Supplemental data section 6 for detailed derivations).
(15)
809
8103. Parameterization
811
Kinetic constants for the enzymes of Calvin-Benson cycle, photorespiratory C2
812
metabolism, starch and sucrose synthesis, were as provided in detail by Zhu et al.
813
(2007). For Rubisco, the kinetic properties reported for Zea mays (Cousins et al.,
814
2010) were used to replace those used in the earlier C3 model (Zhu et al., 2007).
815
Kinetic properties and their sources for the unique C4 enzymes are given in
816
Supplemental Data.
817
818
4. Model validation
819
The model was validated by comparing the predicted and measured patterns of
820
response photosynthetic CO2 uptake rate (A) and metabolite concentrations to
821
variation in intercellular CO2 concentrations (Ci) and photosynthetic photon flux
822
densities (PPFD) (Leegood and von Caemmerer, 1989; Kanai and Edwards,
823
1999).
824
825
5. Model applications
826
5.1 Identification of key enzymes controlling different phases of the steady
827
state A-Ci response curve
828
The model was first used to simulate A under high light and increasing Ci to
829
develop an A-Ci curve. Subsequently, the Vmax values of specific enzymes were
830
decreased individually to evaluate the impact of these enzymes on the initial
831
slope of the A-Ci response and the maximal A at saturating Ci.
832
833
5.2 Calculation of the control coefficients for specific features of C4
32
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
834
photosynthesis
835
The Vmax of each enzyme was increased and decreased by 1% individually in the
836
model to calculate new A (A+ and A-) for two different conditions of light and Ci.
837
The flux control coefficient (CC) of each enzyme was calculated as:
838
CC =
A+ − A −
A0 ⋅ 0.02
(16)
839
840
5.3 Identification of optimal distribution of enzymes related to C4
841
photosynthesis to maximize photosynthetic efficiency
842
Following Zhu et al. (2007), a genetic algorithm was used to identify, assuming a
843
constant leaf nitrogen level, the optimal investment in the proteins of the
844
photosynthetic apparatus to maximize photosynthetic rate. A MATLAB® GA
845
Toolbox, GATBX (The Genetic Algorithm Toolbox, developed by the
846
University of Sheffield), was used. Briefly, this genetic algorithm mimics the
847
process
848
recombination, natural selection, and survival of the fittest. Candidate sets of the
849
enzyme concentrations play the role of individuals in a population and the CO2
850
assimilation rate is used as the selection pressure in the algorithm. “Mutation”
851
here was limited to altering the amount of an enzyme, but the enzyme properties
852
were otherwise unchanged.
of
natural
biological
evolution,
i.e.
reproduction,
mutation,
853
854
5.4 Prediction of changes of carbon isotope (13C) discrimination signals
855
To estimate 13C discrimination, 13CO2 and H13CO3- were included as metabolites
856
in the model together with the dominant 12CO2 and H12CO3-. The model includes
857
the difference between the binary diffusivities of
858
differences between the kinetic constants for
859
catalyzed reactions, and for H13CO3- and H12CO3- at PEP carboxylase. Taking
860
Rubisco as an example:
861
vc _ h = vc ⋅
12
13
CO2 and
CO2 and
12
CO2, and
13
CO2 in Rubisco
1 [13 CO2 ]Bchl
⋅
α 5 [ 12CO2 ]Bchl
(17 )
33
Downloaded from on June 14, 2017 - Published by www.plantphysiol.org
Copyright © 2014 American Society of Plant Biologists. All rights reserved.
862
where vc_h is the 13CO2 fixation rate of Rubisco and vc is the 12CO2 fixation rate
863
of Rubisco. α5 is the isotope effect of Rubisco with the value taken from
864
Farquhar et al., (1989), [13CO2]Bchl and [12CO2]Bchl are
865
concentrations in BSCs chloroplast respectively. The complete set of rate
866
equations and parameters are presented in Supplementary data (Section 2 and 3).
13
CO2 and
12
CO2
867
868
δ13C is the established value for expressing the ratio of
869
calculated as:
870
δ 13C =
871
where Rs and Rp are the molar abundance ratios of l3C/12C of the standard and
872
photosynthetic product. The Rs was calculated based on carbon in carbon dioxide
873
generated from a fossil belemnite from the Pee Dee Formation, denoted PDB (Rs
874
= 0.0112372, Craig, 1957). Farquhar and Richards (1984) proposed the use of Δ
875
as an alternative measure of the carbon isotope discrimination by plants:
876
Δ=
877
where Ra is the isotopic abundance in the air. In this model, we assumed a Ra of
878
free atmosphere as 0.0111473 (Farquhar et al., 1989). In contrast to δ, Δ is
879
independent of Ra (Farquhar et al., 1984).
880
In the model, the steady state 13CO2 and 12CO2 fixation flux of Rubisco were used
881
to calculate Rp :
882
Rp =
Rp
Rs
13
C to
12
C and was
−1
Ra
−1
Rp
vc _ h
vc _ h + vc
(18)
(19)
(20)
883
884
Acknowledgement: The authors gratefully acknowledge Dr. Danny Tholen for
885
critical discussions and comments on earlier draft of this paper. We thank the
886
Chinese Academy of Sciences and the Max Planck Society for support.
887
888
Author Contributions
34
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
889
X.G.Z. and Y.W. designed the research. Y.W. developed the model, performed
890
analysis. Y.W., S.P.L., X.G.Z wrote the paper.
891
892
35
Downloaded from on June 14, 2017 - Published by www.plantphysiol.org
Copyright © 2014 American Society of Plant Biologists. All rights reserved.
893
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Synthase
Activity
between
Mesophyll-Cells
and
Bundle
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reduction of chloroplast glyceraldehyde-3-phosphate dehydrogenase activity by
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1161
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1163
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1164
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1165
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1166
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1167
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1168
45
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
1169
Figure Legends
1170
Figure 1 The structure of the systems model of NADP-ME type C4
1171
photosynthesis.
1172
The rectangles indicate enzymes or transporters; colors differentiate these by
1173
function. Green: Calvin Benson cycle; Pale yellow: transporters; Grey:
1174
photorespiratory pathway; Cyan: C4 dicarboxylate cycle; Red: starch and
1175
sucrose synthesis; Yellow: light reactions. Enzymes are denoted by their EC
1176
numbers (Tables I and SI). Rm and Rb represent mitochondria respiration in
1177
MCs and BSCs
1178
1179
Figure 2 Model predicted photosynthetic CO2 uptake rate.
1180
(A) The predicted photosynthetic CO2 uptake rate (A) vs intercellular CO2
1181
concentration curve (Ci) (black line) at a PPFD of 1600 μmol m-2 s-1. The
1182
dotted line is the predicted photorespiratory rate. Circles are experimental data
1183
from Kanai and Edwards (1999); (B) The predicted A vs PPFD curve. The
1184
black dots are experimental data from Leegood and von Caemmerer (1989).
1185
1186
Figure 3 Predicted changes in steady-state contents of key metabolites of
1187
photosynthetic carbon metabolism with increase in (Ci).
1188
Black lines represent model predictions using and black dots are experimental
1189
data from Leegood and von Caemmerer (1989). The PPFD used in the
1190
simulation was 1600 μmol m-2 s-1.
1191
1192
1193
Figure 4 Model predicted A vs Ci curves under different maximal enzyme
1194
activities (Vmax) and maximum electron transport rates (Jmax_T).
1195
The PPFD was 2500 μmol m- 2 s- 1.
1196
1197
Figure 5 The optimized distribution of nitrogen resources between
1198
photosynthetic enzymes for maximize light saturated A.
46
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
1199
(A) The ratio of optimal enzyme concentrations identified by the evolutionary
1200
algorithm required to re-optimize the system for a pre-industrial atmospheric
1201
CO2 concentration (Ca) of 275 μbar, relative to today’s Ca of 394.5 μbar. In this
1202
simulation, Ci = 0.4 Ca was assumed (Leakey et al., 2004). (B) Shows the
1203
enzyme and transporter activities relative to that of Rubisco that this
1204
optimization predicts for the current atmospheric CO2 concentration
1205
1206
Figure 6 Predicted carbon isotope discrimination (Δ), composition (δ13C)
1207
and CO2 leakiness vs PPFD.
1208
(A) Δ, (B) δ13C, (C) CO2 leakiness, Ci was 150 μbar.
1209
1210
1211
Figure 7 Effect of triose phosphate transporter (TPT) rate on A and CO2
1212
leakiness.
1213
This simulation assumes TPTs in MCs and in BSCs have the same maximal
1214
rate at a PPFD of 2000 μmol m- 2 s- 1and a Ci of 150 μbar.
1215
1216
Figure 8 The predicted influence of the permeability to C3P (PGA and
1217
T3P) and CO2 between BSCs and MCs on A.
1218
(A) The permeability of CO2 and C3P across the BSC-MC interface affects the
1219
CO2 uptake rate. Black arrows indicate the maximum CO2 uptake rate (Amax).
1220
(B) The permeability of CO2 needs to be coordinated with the permeability of
1221
C3P to obtain Amax. (C) The Amax increases with an increase in the permeability
1222
of C3P between bundle sheath and mesophyll cell. PPFD used in the
1223
simulation was 2000 μmol m- 2 s- 1 and Ci was 150 μbar.
1224
1225
Figure 9 Plasmodesmata properties effect on A.
1226
(A) Predicted effect of plasmodesmata length (Lpd) on photosynthetic CO2
1227
uptake rates at different surface fractions of plasmodesmata in the interface (Φ).
1228
(B) Plasmodesmata length influences the CO2 uptake rate and photorespiration
47
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
1229
rate (Φ=0.03). (C) Plasmodesmata length influences CO2 concentration in BSC
1230
cytosol and CO2 leakiness from BSC to MC (Φ=0.03). PPFD used in the
1231
simulation was 2000 μmol m- 2 s- 1 and Ci was 150 μbar.
1232
1233
1234
List of supplemental data file, figure and tables
1235
1236
Supplemental file S1. List of abbreviations and their definitions.
1237
Supplemental file S2. Equations used in the model.
1238
Supplemental file S3. Parameters used in the model.
1239
1240
These above files are needed for users to use the C4 photosynthesis systems
1241
model. The following figures and tables are helpful, but not required, to support
1242
the conclusions of the paper.
1243
1244
Supplemental figure S1 Predicted changes in contents of key metabolites with
1245
changes in PPFD. As for Figure 3, but the response of metabolites to light. The
1246
intercellular CO2 concentration (Ci) used in the simulation was 150 μbar.
1247
Supplemental figure S2. Effects of metabolite permeability between BSC and
1248
MC on A and CO2 leakiness.
1249
Supplemental Figure S3 The proportion of Jmax_T partitioned into BSC (Yb)
1250
influences CO2 leakiness, A and proportion of PGA transport to MC.
1251
Supplemental Figure S4 Effect of plasmodesmata length on A and metabolite
1252
fluxes between MCs and BSCs.
1253
Supplemental Figure S5 The effect of the chloroplast envelope permeability
1254
to CO2 on photosynthesis, photorespiration and leakiness.
1255
Supplemental Figure S6 The effects of modifying phosphate concentration in
1256
bundle sheath plastid on steady-state contents of key metabolites of
1257
photosynthetic carbon metabolism.
48
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
1258
Supplemental Figure S7 The effects of modifying PGA and T3P related
1259
enzyme kinetic parameters effects on key metabolites contents.
1260
Supplemental Figure S8 The effects of modifying phosphate concentration
1261
and enzyme kinetic parameters on key metabolites contents.
1262
Supplemental Figure S9 The effects of modifying cytolsolic FBPase enzyme
1263
kinetic parameters on key metabolites contents.
1264
Supplemental Table SI. Photosynthetic flux control coefficients of enzymes
1265
and diffusion related parameters.
1266
Supplemental Table SII. Comparison of the impacts of using C3 and C4
1267
homologs of enzymes related to C4 photosynthesis on A and nitrogen demand.
1268
1269
The following files are used to interpret the choices of equations and default
1270
parameters used in the model.
1271
Supplemental file S6.1. Rationale underlying the choice of the rate equation
1272
used to calculate CO2 uptake rates.
1273
Supplemental file S6.2. Rationale underlying the choice of the default CO2
1274
permeability coefficient.
1275
49
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
1276
Tables
1277
Table I Flux control coefficients determined from their effect on A of enzymes
1278
and diffusion related parameters. We simulated the following scenarios: High
1279
light: PPFD=2000 μmol m-2 s-1, Ci=150 μbar; Low light: PPFD=200 μmol m-2
1280
s-1, Ci=150 μbar; Low CO2: PPFD=2000 μmol m-2 s-1, Ci=50 μbar. Bold
1281
numbers denote Flux Control Coefficients above 0.02. The definitions of
1282
abbreviations were listed in supplemental data section1.
Enzyme
Abbreviation
Vmax
EC Number
(μmol m-2 s-1)
CA
PEPC
Rubisco_CO2
SBPase
PRK
Flux Control Coefficient
High
Low
Low
light
CO2
light
4.2.1.1
4.1.1.31
4.1.1.39
3.1.3.37
2.7.1.19
2.7.2.3M
PGAK_M
&1.2.1.13
&GAPDH_M
M
4.1.1.39
Rubisco_O2
PGAsink
PGA Sink
Jmax_T
I
200000
170
65
29.18
1170
0.001
0.004
0.185
0.364
0.000
0.000
0.254
0.030
0.026
0.099
0.000
0.000
0.073
0.010
300
0.002
-0.123
0.009
7.15
2
500
2000 or 200
-0.017
0.029
-0.063
0.005
0.600
-0.008
-0.018
0.037
0.074
0.134
-0.008
0.969
Diffusion parameter
Value
Flux Control Coefficient
Low
High
Low
light
light
CO2
gm
0.7mol m-2
s-1bar-1
0.002
0.495
0.000
0.000
0.041
0.000
-0.045
-0.047
-0.042
-0.023
-0.004
-0.020
-0.045
-0.028
-0.040
0.044
0.028
0.040
0.028
1283
Dmal_PD
Dco2_PD
Pco2_Bchl
Φ
Lpd
6.77×10-10 m2 s-1
1.7×10-9 m2 s-1
20 μm s
0.03
400 nm
-1
1284
1285
50
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Copyright © 2014 American Society of Plant Biologists. All rights reserved.
1286
Table II Comparison of the impacts of using different homologs of C4 related
1287
enzymes on A and nitrogen cost.
1288
Kinetic parameters for C3 and C4 homologs of the enzymes involved in C4
1289
photosynthesis were used as inputs to the model to predict CO2 uptake rates
1290
under low and high CO2 conditions. The CO2 uptake ratio is ratio of CO2
1291
uptake rates predicted using kinetic parameters from a C3 homolog to that
1292
using a C4 homolog. Nitrogen cost for the synthesis of an enzyme was
1293
calculated based on the kcat, molecular weight and Vmax of the enzyme. The
1294
nitrogen cost ratio was defined as the ratio of nitrogen required for synthesis of
1295
a C3 homolog to that for a C4 homolog.
1296
Enzymes
Comparison
(C3/C4)
Ci=50
CO2
μbar
uptake
Ci=150
ratio
μbar
Nitrogen cost ratio
PEPC
NADPMDH
PPDK
NADPME
Rubisco
0.35
1.00
1.00
1.00
1.03
0.51
1.00
1.00
1.00
1.03
1.10
5.14
1.20
1.39
1.24
1297
1298
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