A Mathematical Model of Photorespiration and Photosynthesis

A comprehensive mathematical model of C₃ leaf carbon metabolism,involving the Calvin cycle and the glycolate and glycerate pathwaysof photorespiration, is formulated in terms of a system of non-lineardifferential equations. A steady state, which is found to beeffectively stable, is derived. The model behaves realisticallywhen tested under varying external carbon dioxide and oxygenconcentrations: photosynthesis is inhibited by higher oxygenlevels, while photorespiration is inhibited by higher carbondioxide levels. Calvin cycle, differential equations, glycolate pathway, mathematical model, photorespiration, photosynthesis     

A plant for all seasons: alterations in photosynthetic carbon metabolism during cold acclimation in Arabidopsis

Low temperatures lead to the inhibition of sucrose synthesis and photosynthesis. The biochemical and physiological adaptations of plants to low temperatures include the post-translational activation and increased expression of enzymes of the sucrose synthesis pathway, the changed expression of Calvin cycle enzymes, and changes in the leaf protein content. Recent progress has been made in understanding both the signals that trigger these processes and how the regulation of photosynthetic carbon metabolism interacts with other processes during cold acclimation.     

Dissecting the molecular basis of the contribution of source strength to high fructan accumulation in wheat

Fructans represent the major component of water soluble carbohydrates (WSCs) in the maturing stem of temperate cereals and are an important temporary carbon reserve for grain filling. To investigate the importance of source carbon availability in fructan accumulation and its molecular basis, we performed comparative analyses of WSC components and the expression profiles of genes involved in major carbohydrate metabolism and photosynthesis in the flag leaves of recombinant inbred lines from wheat cultivars Seri M82 and Babax (SB lines). High sucrose levels in the mature flag leaf (source organ) were found to be positively associated with WSC and fructan concentrations in both the leaf and stem of SB lines in several field trials. Analysis of Affymetrix expression array data revealed that high leaf sucrose lines grown in abiotic-stress-prone environments had high expression levels of a number of genes in the leaf involved in the sucrose synthetic pathway and photosynthesis, such as Calvin cycle genes, antioxidant genes involved in chloroplast H₂O₂ removal and genes involved in energy dissipation. The expression of the majority of genes involved in fructan and starch synthetic pathways were positively correlated with sucrose levels in the leaves of SB lines. The high level of leaf fructans in high leaf sucrose lines is likely attributed to the elevated expression levels of fructan synthetic enzymes, as the mRNA levels of three fructosyltransferase families were consistently correlated with leaf sucrose levels among SB lines. These data suggest that high source strength is one of the important genetic factors determining high levels of WSC in wheat.     

Concentration and {sigma}13C of leaf carbohydrates in relation to gas exchange in Quercus robur under elevated CO2 and drought

The variations of leaf carbohydrate concentration, carbon isotopediscrimination () of leaf soluble carbohydrate, gas-exchangeand growth during a soil drying cycle under 350 and 700 µmolmol^-1 CO₂ concentrations ([CO₂]) inQuercus robur seedlings wereanalysed. In well-watered conditions, a doubling of [CO₂] causedan increase of CO₂ assimilation rate (A) ( +47%) and a decreaseof stomatal conductance for water vapour (g) (–25%),anddoubled the intrinsic water-use efficiency (A/g). The valuesof A were not affected by elevated [CO₂] which was consistentwith the 2-fold increase of A/g. Elevated [CO₂ also significantlyincreased sucrose and starch leaf concentrations as well asaerial growth and plant dry weight. The stimulating effect ofCO₂ enrichment on A and A/g was maintained in moderate droughtconditions, but disappeared in the most severe drought conditions.Drought induced an increase of hexose concentrations in both[CO₂], but this effect was more pronounced under elevated [CO₂],which may contribute to increase osmoregulation. From the onsetof drought, starch was depleted in both [CO₂]. Carbon isotopediscrimination decreased in response to drought, which correspondedto an increase in A/g according to the two-step model of isotopicdiscrimination. In contrast, the A/g values derived from instantaneousleaf gas-exchange measurements decreased along the drying cycle.The discrepancy observed between the two independent estimatesof water-use efficiency is discussed in terms of time-scaleintegration. The results obtained with the isotopic approachusing soluble carbohydrate suggest a predominant stomatal limitationof CO2 assimilation in response to drought. Soil drying cycle,elevated CO₂, leaf gas-exchange, leaf carbohydrate concentrations,carbon isotope discrimination, growth, Quercus robur. Key words: soil drying cycle, elevated CO₂, leaf gas-exchange, leaf carbohydrate concentrations, carbon isotope discrimination, growth, Quercus robur     

Theoretical analysis of the possibility of existence of oscillations in photosynthesis

A mathematical model for carbohydrate and carbon dioxide metabolism in a chloroplast has been constructed. If it is taken into consideration that the rate of the efflux of sugars is restricted as their concentration increases, then even with a simplified representation of the work of the Calvin cycle, it can be shown that there is a set of the parameters of the model at which stable oscillations can appear in the system.     

Parameter identification of the calvin photosynthesis cycle

Summary This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.     

Computer modelling and experimental evidence for two steady states in the photosynthetic Calvin cycle.

We present observations of photosynthetic carbon dioxide assimilation, and leaf starch content from genetically modified tobacco (Nicotiana tabacum) plants in which the activity of the Calvin cycle enzyme, sedoheptulose-1,7-bisphosphatase, is reduced by an antisense construct. The measurements were made on leaves of varying ages and used to calculate the flux control coefficients of sedoheptulose-1,7-bisphosphatase over photosynthetic assimilation and starch synthesis. These calculations suggest that control coefficients for both are negative in young leaves, and positive in mature leaves. This behaviour is compared to control coefficients obtained from a detailed computer model of the Calvin cycle. The comparison demonstrates that the experimental observations are consistent with bistable behaviour exhibited by the model, and provides the first experimental evidence that such behaviour in the Calvin cycle occurs in vivo as well as in silico.     

Carbon and Nitrogen Sources for Protein Synthesis and Growth of Sugar-beet Leaves

Protein synthesis in very young leaves utilizes carbon fromphotosynthesis and from translocated sucrose, and nitrogen translocatedin both xylem and phloem. The carbon of young leaf protein isderived mainly from assimilated CO₂, while translocated sucrosecontributes proportionately more of its carbon to insolublecarbohydrate. Most protein amino-acids become labelled from¹⁴CO₂, glutamate being the notable exception. Glutamine or glutamateis synthesized from sucrose in roots, and is translocated toyoung leaves. It is suggested that a small but significant proportionof the nitrogen requirement of the young leaf is translocatedfrom roots as glutamine, in the phloem. Inorganic nitrogen istranslocated in xylem.     

Nitrate Nutrition and Temperature Effects on Wheat: Soluble Components of Leaves and Carbon Fluxes to Amino Acids and Sucrose

Amounts of some metabolites and the incorporation of ¹⁴CO₂ intophotosynthetic products were measured in the third leaf of wheat,grown with two rates of nitrate supply at two temperatures,to analyse the effects of environmental conditions on the fluxesof carbon. Ribulose bisphosphate and 3-phosphoglyceric acidcontent per unit area were greater under nitrate deficiencyand decreased with leafage, but did not differ consistentlywith temperature. Sucrose content of young leaves was largerin cool than in warm conditions and with low nitrate, and decreasedwith age to similar values in all treatments. Starch accumulatedwith leaf age, slightly more in cool than warm conditions, andwith nitrate deficiency. Glutamate (plus glutamine), aspartate(plus asparagine), glycine and serine content of leaves weregreatest with added nitrate in cool temperature; changes withleaf age and conditions are discussed. The ¹⁴C content of assimilationproducts after exposure to ¹⁴CO₂ (for up to 10 min at 20 ?C)under steady-state conditions was slightly greater in plantsgrown in the warm than in the cool temperature and with additionalnitrate. Additional nitrate increased the proportion of ¹⁴Cin, and flux of carbon to, amino acids, particularly serineand glycine, and decreased it in sugar phosphates and sucrose.Cool growth temperatures increased the proportion of ¹⁴C inamino acids (pre-dominantly glycine and serine) and decreasedthat in sucrose. Changes in the balance of carbon fluxes betweenamino acids and carbohydrates are discussed in relation to glycolatepathway metabolism and alternative routes of amino acid synthesis. Key words: Wheat, temperature, nitrate supply, carbon flux, sucrose, amino acids     

A hybrid kinetic and constraint-based model of leaf metabolism allows predictions of metabolic fluxes in different environments

While flux balance analysis (FBA) provides a framework for predicting steady-state leaf metabolic network fluxes, it does not readily capture the response to environmental variables without being coupled to other modelling formulations. To address this, we coupled an FBA model of 903 reactions of soybean (Glycine max) leaf metabolism with e-photosynthesis, a dynamic model that captures the kinetics of 126 reactions of photosynthesis and associated chloroplast carbon metabolism. Successful coupling was achieved in an iterative formulation in which fluxes from e-photosynthesis were used to constrain the FBA model and then, in turn, fluxes computed from the FBA model used to update parameters in e-photosynthesis. This process was repeated until common fluxes in the two models converged. Coupling did not hamper the ability of the kinetic module to accurately predict the carbon assimilation rate, photosystem II electron flux, and starch accumulation of field-grown soybean at two CO₂ concentrations. The coupled model also allowed accurate predictions of additional parameters such as nocturnal respiration, as well as analysis of the effect of light intensity and elevated CO₂ on leaf metabolism. Predictions included an unexpected decrease in the rate of export of sucrose from the leaf at high light, due to altered starch–sucrose partitioning, and altered daytime flux modes in the tricarboxylic acid cycle at elevated CO₂. Mitochondrial fluxes were notably different between growing and mature leaves, with greater anaplerotic, tricarboxylic acid cycle and mitochondrial ATP synthase fluxes predicted in the former, primarily to provide carbon skeletons and energy for protein synthesis.     

Discovery of the canonical Calvin–Benson cycle

It has been 65 years since the Calvin–Benson cycle was first formulated. In this paper, the development of the concepts that are critical to the cycle is traced and the contributions of Calvin, Benson, and Bassham are discussed. Some simplified views often found in text books such as ascending paper chromatography and the use of the “lollipop” for short labeling are discussed and further details given. Key discoveries that underpinned elucidation of the cycle such as the importance of sedoheptulose phosphate and ribulose 1,5-bisphosphate are described. The interchange of ideas between other researchers working on what is now called the pentose phosphate pathway and the development of the ideas of Calvin and Benson are explored while the gluconeogenic aspects of the cycle are emphasized. Concerns raised about anomalies of label distribution in glucose are considered. Other carbon metabolism pathways associated with the Calvin–Benson cycle are also described. Finally, there is a section describing the rift between Calvin and Benson.

     

Photosynthetic carbon metabolism in wild, primitive and cultivated forms of wheat at three levels of ploidy: Role of the glycolate pathway

¹⁴CO₂ assimilation was studied with diploid, tetraploid, hexaploidspecies of the genera Triticum and their wild relatives Aegilops.Attached mature leaves of 3–4 weekold plants were allowedto undergo photosynthesis under air at ambient temperature.The pattern of distribution of ¹⁴C was notably similar in Triticumand Aegilops species whatever the level of ploidy. Sucrose wasthe sink for photosynthetic carbon. ¹⁴C for sucrose synthesis was supplied either through the glycolatepathway by glycolate, the product of the photorespiration orby the Calvin cycle intermediates exported into the cytoplasm.Depending on the species, the glycolate pathway provided 40to 75%of the sucrose ¹⁴C. The higher labeling of sucrose was associated with the greaterparticipation of the glycolate pathway in the wild diploid (DD)A. squarrosa and in the cultivated hexaploid (AABBDD) T. aestivum.The results suggest that the expression of the male D genomeis dominant over the female AB genome in T. aestivum. In T. aestivum under ambient conditions lowering (low temperature)or hindering (1% O₂ ) photorespiration, sucrose labeling decreased,but serine and glycine labeling was favoured. We propose thatin wheat leaves, the role of photorespiration is to drain artof the carbon exported from the chloroplast as glycolate, towardssucrose synthesis. (Received March 16, 1979; )     

Photosynthetic Carbon Fixation Characteristics of Fruiting Structures of Brassica campestris L

Activities of key enzymes of the Calvin cycle and C₄ metabolism, rates of CO₂ fixation, and the initial products of photosynthetic ¹⁴CO₂ fixation were determined in the podwall, seed coat (fruiting structures), and the subtending leaf (leaf below a receme) of Brassica campestris L. cv `Toria.' Compared to activities of ribulose-1,5-bisphosphate carboxylase and other Calvin cycle enzymes, e.g. NADP-glyceraldehyde-3-phosphate-dehydrogenase and ribulose-5-phosphate kinase, the activities of phosphoenol pyruvate carboxylase and other enzymes of C₄ metabolism, viz. NADP-malate dehydrogenase, NADP-malic enzyme, glutamate pyruvate transaminase, and glutamate oxaloacetate transaminase, were generally much higher in seed than in podwall and leaf. Podwall and leaf were comparable to each other. Pulse-chase experiments showed that in seed the major product of ¹⁴CO₂ assimilation was malate (in short time), whereas in podwall and leaf, the label initially appeared in 3-PGA. With time, the label moved to sucrose. In contrast to legumes, Brassica pods were able to fix net CO₂ during light. However, respiratory losses were very high during the dark period.     

Current views on the regulation of autotrophic carbon dioxide fixation via the Calvin cycle in bacteria

The Calvin cycle of carbon dioxide fixation constitutes a biosynthetic pathway for the generation of (multi-carbon) intermediates of central metabolism from the one-carbon compound carbon dioxide. The product of this cycle can be used as a precursor for the synthesis of all components of cell material. Autotrophic carbon dioxide fixation is energetically expensive and it is therefore not surprising that in the various groups of autotrophic bacteria the operation of the cycle is under strict metabolic control. Synthesis of phosphoribulokinase and ribulose-1,5-bisphosphate carboxylase, the two enzymes specifically involved in the Calvin cycle, is regulated via end-product repression. In this control phosphoenolpyruvate most likely has an alarmone function. Studies of the enzymes isolated from various sources have indicated that phosphoribulokinase is the target enzyme for the control of the rate of carbon dioxide fixation via the Calvin cycle through modulation of existing enzyme activity. In general, this enzyme is strongly activated by NADH, whereas AMP and phosphoenol-pyruvate are effective inhibitors. Recent studies of phosphoribulokinase inAlcaligenes eutrophus suggest that this enzyme may also be regulated via covalent modification.     

Effects of Manipulations of Source and Sink on the Carbon Exchange Rate and Some Enzymes of Sucrose Metabolism in Leaves of Soybean [Glycine max (L.) Merr.]

Soybean plants [Glycine max (L.) Merr. cv. AGS129], two andthree weeks after depodding and defoliation, respectively, wereused to examine the possibility of end-product regulation onthe carbon exchange rate and activities of enzymes involvedin sucrose metabolism in leaves. Removal of one and two lateralleaflets per trifoliate leaf reduced the total leaf area by20% and 47%, respectively. Removal of one pod per node reducedthe total pod number by 23% per plant. Dry weights of roots,stems and petioles decreased with reductions in leaf area. Bycontrast, removal of pods resulted in an increase in these parameters.The carbon exchange rate and transpiration rate of leaves increasedwith defoliation and decreased with depodding. The intercellularconcentration of CO₂ in leaves was reduced by defoliation andincreased by depodding. Furthermore, defoliation increased thelevel of leaf chlorophyll in leaves while depodding decreasedit. Removal of pods decreased the activities of sucrose-phosphatesynthase and -amylase but increased that of sucrose synthase.A significant positive correlation was found between the activityof leaf sucrose-phosphate synthase and both the carbon exchangerate and the sucrose content of leaves. Thus, manipulation ofthe sink and source in soybean plants influenced the relationshipbetween sucrose metabolism and the carbon exchange rate in intactleaves. ³Faculty of Agriculture, Okayama University, Tsusimanaka Okayama,700 Japan ⁴Faculty of Agriculture, Saga University, Honjo-machi, Saga,840 Japan ¹Present address: Faculty of Agriculture, Sriwijaya University,J1 Raya Indralaya, OK1 30662, Indonesia ²Present address: Faculty of Agriculture, Saga University, Honjo-machi,Saga, 840 Japan     

Effects of Certain Inhibitors on Photorespiration by Wheat Leaf Segments

The effect on the carbon metabolism of wheat leaf segments ofcertain inhibitors of photorespiration was studied. Sodium 2-hydroxy-3-butynoatesupplied for 40 min resulted in accumulation of ¹⁴C in glycolicacid with only a 7% inhibition of photosynthesis; when suppliedfor 90 min, photosynthesis was inhibited by 47%. When ¹⁴CO₂was replaced by 1000 vpm ¹²CO₂, radioactivity in glycine decreasedbut increased more rapidly in sucrose with less release of ¹⁴CO₂.Isonicotinyl hydrazide (INH) inhibited photosynthesis from ¹⁴CO₂by 50% and glycine replaced sucrose as the main product. When,after 15 min, ¹⁴CO₂ was replaced by 150 vpm ¹²CO₂, in the presenceof INH less ¹⁴CO₂ was released, ¹⁴CO in glycine decreased moreslowly, and less [¹⁴CO]sucrose accumulated. Glycidate (potassium2,3-epoxypropionate) at 2 mM had no effect on photosyntheticrate and little effect on carbon metabolism; 20 mM glycidateinhibited photosynthesis by 64% and resulted in less radioactivityin glycine, more in phosphate esters, and less ¹⁴CO₂ released.When photosynthesis was measured in 1000 vpm CO₂ the inhibitorsgave smaller effects on metabolism than during photosynthesisfrom 150 vpm ¹⁴CO₂ but 20 mM glycidate still resulted in a 42%inhibition of photosynthesis. When U- [¹⁴CO]glycerate was appliedto leaf segments in air with 320 vpm ¹⁴CO₂ the total uptakeof glycerate was not changed by the inhibitors. INH and glycidateboth decreased the amount of glycerate metabolised. More ¹⁴COaccumulated in glycine in the presence of INH and in phosphateesters and serine in the presence of glycidate. Hydroxybutynoateincreased the production of glycolate from glycerate but didnot affect the total amount of glycerate metabolised. Although all three inhibitors affected photorespiratory metabolismnone stimulated photosynthesis. The results are consistent withthe main release of CO₂ in photorespiration arising from theconversion of glycine to serine.