A mathematical model of the Calvin photosynthesis cycle

1. A mathematical model is presented for photosynthetic carbohydrate formation in C3 plants under conditions of light and carbon dioxide saturation. The model considers reactions of the Calvin cycle with triose phosphate export and starch production as main output processes, and treats concentrations of NADPH, NAD+, CO2, and H+ as fixed parameters of the system. Using equilibrium approximations for all reaction steps close to equilibrium steady-state and transient-state relationships are derived which may be used for calculation of reaction fluxes and concentrations of the 13 carbohydrate cycle intermediates, glucose 6-phosphate, glucose 1-phosphate, ATP, ADP, and inorganic (ortho)phosphate. 2. Predictions of the model were examined with the assumption that photosynthate export from the chloroplast occurs to a medium containing orthophosphate as the only exchangeable metabolite. The results indicate that the Calvin cycle may operate in a single dynamically stable steady state when the external concentration of orthophosphate does not exceed 1.9 mM. At higher concentrations of the external metabolite, the reaction system exhibits overload breakdown; the excessive rate of photosynthate export deprives the system of cycle intermediates such that the cycle activity progressively approaches zero. 3. Reactant concentrations calculated for the stable steady state that may obtain are in satisfactory agreement with those observed experimentally, and the model accounts with surprising accuracy for experimentally observed effects of external orthophosphate on the steady-state cycle activity and rate of starch production. 4. Control analyses are reported which show that most of the non-equilibrium enzymes in the system have a strong regulatory influence on the steady-state level of all of the cycle intermediates. Substrate concentration control coefficients for cycle enzymes may be positive, such that an increase in activity of an enzyme may raise the steady-state concentration of the substrate is consumes. 5. Under optimal external conditions (0.15-0.5 mM orthophosphate), reaction flux in the Calvin cycle is controlled mainly by ATP synthetase and sedoheptulose bisphosphatase; the cycle activity approaches the maximum velocity that can be supported by the latter enzyme. At lower concentrations of external orthophosphate the cycle activity is controlled almost exclusively by the phosphate translocator.(ABSTRACT TRUNCATED AT 400 WORDS)     

Analysis of the role of the phosphate translocator and external metabolites in steady-state chloroplast photosynthesis

The role of the phosphate translocator and the importance of the extrachloroplastic concentrations of phosphate, 3-phosphoglycerate, and dihydroxyacetone phosphate in steady-state photosynthesis is examined with a kinetic model. The steady-state stromal concentrations of these compounds are calculated as a function of the rate of the various partial reactions of photosynthesis, at various external concentrations which span those likely to occur in vivo. It is shown how the net transport requirements of the various reactions necessitate different adjustments in the stromal concentrations of these compounds, away from the equilibrium values expected in the absence of metabolism. Under most circumstances, the high exchange capacity of the phosphate translocator relative to the transport requirements of CO₂ fixation limits the extent of these displacements, but conditions when the phosphate translocator is limiting photosynthesis are observed and discussed. The model provides a basis for a more quantitative understanding of the role of the phosphate translocator and the external concentrations of phosphate, 3-phosphoglycerate, and dihydroxyacetone phosphate in photosynthesis.     

A Mathematical Model of the Calvin Cycle: Analysis of the Steady State

A complete steady-state solution of a recently published mathematicalmodel of the Calvin photosynthesis cycle is obtained in termsof the rate constants of the cycle and certain conservationrules. By means of analytical and numerical tests, the steadystate is shown to be effectively stable over a wide range ofinitial conditions and parameter values. Other properties ofthe steady state, such as its variation with the rate of carbondioxide fixation, are also discussed. Mathematical model, Calvin cycle, photosynthesis, steady state, stability analysis     

小麦磷酸丙糖转运器的特性及其对同化物分配的调节

磷酸丙糖转运器(tnose phosphate/phosphatetranslocator,TPT)是源、库间光合产物分配的第一调控部位,研究TPT的特性及其对同化物分配的调节,对于提高光合作用同化物利用效率有着重要意义.我们首先采用Percoll密度梯度离心从小麦(Triticum aestivum L.)叶片中分离制备了完整性达91%以上、具有较高纯度的完整叶绿体.利用TPT不可逆抑制剂[H3]2-DIDS标记和SDS-PAGE,以及小麦TPT抗体进行Western blotting分析,证明TPT蛋白仅存在于叶绿体被膜中,约占被膜总蛋白的15%,其分子量为35 kD,而在液泡膜和线粒体膜上不存在.采用硅油离心法研究TPT对磷酸二羟丙酮(dihydroxyacetone phosphate,DHAP)、磷酸烯醇式丙酮酸(phosphoenolpyruvate,PEP)、葡萄糖-6-磷酸(glucose-6-phosphate,G6P)与Pi的反向运输动力学的结果表明,DHAP/Pi的最大运输活性最高,PEP/Pi次之,G6P/Pi最低.TPT与这些运输底物的Km值由小至大,分别为DHAP、Pi、PEP和G6P,证明TPT的最适运输底物为DHAP.用DIDS处理时,TPT对DHAP运输活性的抑制达95%.TPT运输活性受到抑制时,可导致叶绿体内大量积累淀粉.TPT在调控小麦叶绿体同化产物的分配中起着重要作用,在保证卡尔文循环正常运转的前提下,通过TPT外运到胞质中参与蔗糖合成和其他代谢活动的磷酸丙糖(triose phosphate,TP)约占93.6%,而用于叶绿体内合成淀粉的TP仅占6.4%.生理条件下其功能是高效率地把大部分光合同化产物TP及时运出叶绿体到胞质中,用于合成蔗糖并运输到其他库器官的需要.     

小麦磷酸丙糖转运器的特性及其对同化物分配的调节(英文)

磷酸丙糖转运器(triosephosphate/phosphatetranslocator,TPT)是源、库间光合产物分配的第一调控部位,研究TPT的特性及其对同化物分配的调节,对于提高光合作用同化物利用效率有着重要意义。我们首先采用Percoll密度梯度离心从小麦(TriticumaestivumL.)叶片中分离制备了完整性达91%以上、具有较高纯度的完整叶绿体。利用TPT不可逆抑制剂[H3]2-DIDS标记和SDS-PAGE,以及小麦TPT抗体进行Westernblotting分析,证明TPT蛋白仅存在于叶绿体被膜中,约占被膜总蛋白的15%,其分子量为35kD,而在液泡膜和线粒体膜上不存在。采用硅油离心法研究TPT对磷酸二羟丙酮(dihydroxyacetonephosphate,DHAP)、磷酸烯醇式丙酮酸(phosphoenolpyruvate,PEP)、葡萄糖-6-磷酸(glucose-6-phosphate,G6P)与Pi的反向运输动力学的结果表明,DHAP/Pi的最大运输活性最高,PEP/Pi次之,G6P/Pi最低。TPT与这些运输底物的Km值由小至大,分别为DHAP、Pi、PEP和G6P,证明TPT的最适运输底物为DHAP。用DIDS处理时,TPT对DHAP运输活性的抑制达95%。TPT运输活性受到抑制时,可导致叶绿体内大量积累淀粉。TPT在调控小麦叶绿体同化产物的分配中起着重要作用,在保证卡尔文循环正常运转的前提下,通过TPT外运到胞质中参与蔗糖合成和其他代谢活动的磷酸丙糖(triosep     

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     

Expression of the triose phosphate translocator gene from potato is light dependent and restricted to green tissues

The export of primary photosynthesis products from chloroplasts into the cytoplasm is mediated by the triose phosphate translocator. The transporter is an integral membrane protein localized at the inner envelope of chloroplasts. In order to study the expression of the major chloroplast envelope protein gene E29, which is assumed to function as the translocator, we have isolated corresponding cDNA clones from potato. A full-length clone was sequenced and shown to be highly homologous to the E29 gene from spinach. Expression on the RNA level is restricted to green tissues, is light dependent and cannot be induced by sucrose in darkness. The presence of a single-copy gene argues for the existence of different translocator systems responsible for import and export of carbohydrates in chloroplasts and amyloplasts.     

The redox state of the NADP system in illuminated chloroplasts

Pyridine nucleotide levels were measured in intact spinach chloroplasts. The NADPH/NADP ratio was close to unity in darkened chloroplasts. On illumination, chloroplast NADP levels decreased rapidly. The decrease was more prominent at low than at high light intensities. In the presence of bicarbonate, NADP subsequently increased to reach a steady-state level. The kinetics of the increase were related in general, but not in detail, to the lag phase of photosynthesis. In the steady state, chloroplast NADP was sometimes, particularly during photosynthesis at high light intensities, less reduced in the light than in the dark. In the dark-light transition, phosphoglycerate reduction is driven by increases in the ratios NADPH/NADP and ATP/ADP. When photosynthesis accelerates after the initial lag phase, the NADPH/NADP ratio decreases and a high ratio of phosphoglycerate to triose phosphate becomes an important factor in driving carbon reduction. Under photosynthetic flux conditions, the redox state of the chloroplast NADP system appeared to be governed largely by the chloroplast ratio of phosphoglycerate to dihydroxyacetone phosphate and by the phosphorylation potential [ATP]/[ADP] [P_i]. The inhibitor of cyclic electron transport, antimycin A, increased reduction of the chloroplast NADP system. Even when reduction was almost complete in the presence of 5 μM antimycin A, photosynthesis was still significant at low light intensities. Electrons appeared to be effectively distributed between the cyclic electron-transport pathway and the noncyclic route to NADP at NADPH/NADP ratios as low as about 1. When bicarbonate was absent, the NADP system remained largely reduced in the light. The energy-transfer inhibitor, Dio-9, and uncouplers and agents which interfered with pH regulation of the Calvin cycle increased reduction of the NADP system while decreasing photosynthesis.     

Adenine nucleotide translocase-dependent anion transport in pea chloroplasts

Pea chloroplasts were found to take up actively ATP and ADP and exchange the external nucleotides for internal ones. Using carrier-free [14C]ATP, the rate of nucleotide transport in chloroplasts prepared from 12-14-day-old plants was calculated to be 330 mumol ATP/g chlorophyll/min, and the transport was not affected by light or temperature between 4 and 22 degrees C. Adenine nucleotide uptake was inhibited only slightly by carboxyatractylate, whereas bongkrekic acid was nearly as effective an inhibitor of the translocator in pea chloroplasts as it was in mammalian mitochondria. There was no counter-transport of adenine nucleotides with substrates carried on the phosphate translocator including inorganic phosphate, 3-phosphoglycerate and dihydroxyacetone phosphate. However, internal or external phosphoenolpyruvate, normally considered to be transported on the phosphate carrier in chloroplasts, was able to exchange readily with adenine nucleotides. Furthermore, inorganic pyrophosphate which is not transported by the phosphate carrier initiated efflux of phosphoenolpyruvate as well as ATP from the chloroplast. These findings illustrate some interesting similarities as well as differences between the various plant phosphate and nucleotide transport systems which may relate to their role in photosynthesis.     

Adenine nucleotide translocase-dependent anion transport in pea chloroplasts

Pea chloroplasts were found to take up actively ATP and ADP and exchange the external nucleotides for internal ones. Using carrier-free [¹⁴C]ATP, the rate of nucleotide transport in chloroplasts prepared from 12–14-day-old plants was calculated to be 330 μmol ATP/g chlorophyll/min, and the transport was not affected by light or temperature between 4 and 22°C. Adenine nucleotide uptake was inhibited only slightly by carboxyatractylate, whereas bongkrekic acid was nearly as effective an inhibitor of the translocator in pea chloroplasts as it was in mammalian mitochondria. There was no counter-transport of adenine nucleotides with substrates carried on the phosphate translocator including inorganic phosphate, 3-phosphoglycerate and dihydroxyacetone phosphate. However, internal or external phosphoenolpyruvate, normally considered to be transported on the phosphate carrier in chloroplasts, was able to exchange readily with adenine nucleotides. Furthermore, inorganic pyrophosphate which is not transported by the phosphate carrier initiated efflux of phosphoenolpyruvate as well as ATP from the chloroplast. These findings illustrate some interesting similarities as well as differences between the various plant phosphate and nucleotide transport systems which may relate to their role in photosynthesis.     

Dependence of the membrane potential on intracellular ATP concentration in tonoplast-free cells of Nitellopsis obtusa

Intact chloroplasts were obtained from mesophyll protoplasts isolated from Mesembryanthemum crystallinum in the C₃ or Crassulacean acid metabolism (CAM) photosynthetic mode, and examined for the influence of inorganic phosphate (Pi) on aspects of bicarbonate-dependent O₂ evolution and CO₂ fixation. While the chloroplasts from both modes responded similarly to varying Pi, some features appear typical of chloroplasts from species capable of CAM, including a relatively high capacity for photosynthesis in the absence of Pi, a short induction period, and resistance to inhibition of photosynthesis by high levels of Pi. In the absence of Pi the chloroplasts retained 75–85% of the ¹⁴CO₂ fixed and the total export of dihydroxyacetone phosphate was low compared with the rate of photosynthesis. In CAM plants the ability to conduct photosynthesis and retain most of the fixed carbon in the chloroplasts at low external Pi concentrations may enable storage of carbohydrates which are essential for providing a carbon source for the nocturnal synthesis of malic acid. At high external Pi concentrations (e.g. 10 25 mM), the amount of total dihydroxyacetone phosphate exported to the assay medium relative to the rate of photosynthesis was high while the products of ¹⁴CO₂ fixation were largely retained in the chloroplasts which indicates starch degradation is occurring at high Pi levels. Starch degradation normally occurs in CAM plants in the dark; high levels of Pi may induce starch degradation in the light which has the effect of limiting export of the immediate products of photosynthesis and thus the degree of Pi inhibition of photosynthesis with the isolated chloroplast.     

On the regulatory significance of inhibitors acting on non-equilibrium enzymes in the Calvin photosynthesis cycle

Control analyses and kinetic model studies have been performed in order to obtain quantitative information on the regulatory significance of 12 experimentally well-documented inhibitory interactions of Calvin cycle intermediates with the four non-equilibrium cycle enzymes. Evidence is presented to show that none of these interactions contributes significantly to the cycle flux control over the range of external orthophosphate concentrations where the reaction cycle shows close to optimal activity. Contrary to what has been generally supposed, the examined inhibitions appear to be of little interest for our understanding of the biological regulation of the Calvin photosynthesis cycle under conditions of light and carbon dioxide saturation.     

Functional characterization of the plastidic phosphate translocator gene family from the thermo-acidophilic red alga Galdieria sulphuraria reveals specific adaptations of primary carbon partitioning in green plants and red algae

In chloroplasts of green plants and algae, CO₂ is assimilated into triose-phosphates (TPs); a large part of these TPs is exported to the cytosol by a TP/phosphate translocator (TPT), whereas some is stored in the plastid as starch. Plastidial phosphate translocators have evolved from transport proteins of the host endomembrane system shortly after the origin of chloroplasts by endosymbiosis. The red microalga Galdieria sulphuraria shares three conserved putative orthologous transport proteins with the distantly related seed plants and green algae. However, red algae, in contrast to green plants, store starch in their cytosol, not inside plastids. Hence, due to the lack of a plastidic starch pool, a larger share of recently assimilated CO₂ needs to be exported to the cytosol. We thus hypothesized that red algal transporters have distinct substrate specificity in comparison to their green orthologs. This hypothesis was tested by expression of the red algal genes in yeast (Saccharomyces cerevisiae) and assessment of their substrate specificities and kinetic constants. Indeed, two of the three red algal phosphate translocator candidate orthologs have clearly distinct substrate specificities when compared to their green homologs. GsTPT (for G. sulphuraria TPT) displays very narrow substrate specificity and high affinity; in contrast to green plant TPTs, 3-phosphoglyceric acid is poorly transported and thus not able to serve as a TP/3-phosphoglyceric acid redox shuttle in vivo. Apparently, the specific features of red algal primary carbon metabolism promoted the evolution of a highly efficient export system with high affinities for its substrates. The low-affinity TPT of plants maintains TP levels sufficient for starch biosynthesis inside of chloroplasts, whereas the red algal TPT is optimized for efficient export of TP from the chloroplast.     

The rate of transport through a phosphate translocator affects delayed luminescence induction: an experiment and a theoretical model

Delayed luminescence (DL) induction curves were studied in leaves from a mutant pea line containing mutations at both the r and rb loci, compared with leaves from wild type plants. Genes at the r and rb loci encode starch branching enzyme and ADP ‐ glucose pyrophosphorylase, respectively. The presence of mutations at both loci, previously known to reduce the starch content in the dry mature seed by 75%, have been shown to lower the starch level in leaves by at least 20%. During induction, the half‐time for the DL intensity decrease from maximum to steady state in the mutant was 1.5 ± 0.2 times longer than for the wild type. It is proposed that the prolongation of the induction period in leaves from the mutant plants is caused by a lack of inorganic phosphate (Pi) restricting the rate of ATP synthesis at the beginning of induction. The reduced Pi would be compensated by triose flow from the chloroplast, via the triose phosphate translocator, being exchanged for Pi from the cytosol. Analysis of our theoretical photosynthesis model confirmed that a decrease in the rate of Pi released from the Calvin cycle could lead to a prolongation of the induction period.     

Identification, purification, and molecular cloning of a putative plastidic glucose translocator

During photosynthesis, part of the fixed carbon is directed into the synthesis of transitory starch, which serves as an intermediate carbon storage facility in chloroplasts. This transitory starch is mobilized during the night. Increasing evidence indicates that the main route of starch breakdown proceeds by way of hydrolytic enzymes and results in glucose formation. This pathway requires a glucose translocator to mediate the export of glucose from the chloroplasts. We have reexamined the kinetic properties of the plastidic glucose translocator and, using a differential labeling procedure, have identified the glucose translocator as a component of the inner envelope membrane. Peptide sequence information derived from this protein was used to isolate cDNA clones encoding a putative plastidic glucose translocator from spinach, potato, tobacco, Arabidopsis, and maize. We also present the molecular characterization of a candidate for a hexose transporter of the plastid envelope membrane. This transporter, initially characterized more than 20 years ago, is closely related to the mammalian glucose transporter GLUT family and differs from all other plant hexose transporters that have been characterized to date.     

Manifestation of a prolonged lag in the photosynthesis of heated spinach chloroplasts

When the time course for CO₂ fixation and O₂ evolution in isolated intact spinach chloroplasts was examined, we found a prolonged lag time in the early phase of photosynthesis after heat-treatment in the dark as well as an expected time-dependent decrease in the rate during the subsequent linear phase. Because the lengthening of the lag period was generally attributed to the depletion of sugar phosphates in the chloroplasts, we tested for the possible involvement of Calvin cycle intermediates in the change of the lag phase by heat-treatment When triose phosphate was added to the heated chloroplasts, the lag time was re-shortened without the rate in the linear phase being elevated to that measured in the control. Mg-ATP or triose phosphate plus oxaloacetate (previously known as protective chemicals) prevented the lengthening of the lag time when added prior to heat-treatment. Quantification of some metabolites in the chloroplasts confirmed that heavy losses had occurred for triose phosphate, fructose-1,6-bis-phosphate, glucose-6-phosphate, and fructose-6-phosphate. However, the level of 3-phosphoglyceric acid was increased. The presence of Mg-ATP during heat-treatment alleviated the losses of those sugar phosphates. Therefore, we conclude that the decrease in sugar phosphates in the chloroplasts, as part of the negative effect from heat-treatment, is the primary cause of the lengthened lag time during the initial phase of photosynthesis.     

Photosynthesis in Isolated Chloroplasts of the Crassulacean Acid Metabolism Plant Sedum praealtum

Intact chloroplasts were isolated from protoplasts of the Crassulacean acid metabolism plant Sedum praealtum D.C. Typical rates of CO₂ fixation or CO₂-dependent O₂ evolution ranged from 20 to 30 micromoles per milligram chlorophyll per hour and could be stimulated 30 to 50% by several Calvin cycle intermediates. The pH optimum for CO₂ fixation was 7.0 to 7.6 with considerable activity as low as pH 6.4. Low concentrations of orthophosphate (Pi) (optimum 0.4 millimolar) stimulated photosynthesis while high concentrations (5 millimolar) caused some inhibition. Both CO₂ fixation and CO₂-dependent O₂ evolution exhibited a relatively long lag phase (4 to 6 minutes) which remained constant between 0.4 to 5 millimolar Pi. The lag phase could be decreased by addition of dihydroxyacetone-phosphate or ribose 5-phosphate. Further results are presented which suggest these chloroplasts have a functional phosphate translocator.     

Functional differentiation of bundle sheath and mesophyll maize chloroplasts determined by comparative proteomics

Chloroplasts of maize (Zea mays) leaves differentiate into specific bundle sheath (BS) and mesophyll (M) types to accommodate C4 photosynthesis. Consequences for other plastid functions are not well understood but are addressed here through a quantitative comparative proteome analysis of purified M and BS chloroplast stroma. Three independent techniques were used, including cleavable stable isotope coded affinity tags. Enzymes involved in lipid biosynthesis, nitrogen import, and tetrapyrrole and isoprenoid biosynthesis are preferentially located in the M chloroplasts. By contrast, enzymes involved in starch synthesis and sulfur import preferentially accumulate in BS chloroplasts. The different soluble antioxidative systems, in particular peroxiredoxins, accumulate at higher levels in M chloroplasts. We also observed differential accumulation of proteins involved in expression of plastid-encoded proteins (e.g., EF-Tu, EF-G, and mRNA binding proteins) and thylakoid formation (VIPP1), whereas others were equally distributed. Enzymes related to the C4 shuttle, the carboxylation and regeneration phase of the Calvin cycle, and several regulators (e.g., CP12) distributed as expected. However, enzymes involved in triose phosphate reduction and triose phosphate isomerase are primarily located in the M chloroplasts, indicating that the M-localized triose phosphate shuttle should be viewed as part of the BS-localized Calvin cycle, rather than a parallel pathway.     

Effect of antisense repression of the chloroplast triose-phosphate translocator on photosynthetic metabolism in transgenic potato plants

The introduction of an antisense DNA into transgenic potato (Solanum tuberosum L.) plants decreased the expression of the chloroplast triose-phosphate translocator and lowered its activity by 20–30%. With plants propagated from tubers, the effect of the transformation on photosynthetic metabolism was analysed by measuring photosynthesis, the formation of leaf starch, and the total and subcellular metabolite contents in leaves. Although the transformants, in contrast to those propagated from cell cultures, did not differ from the wild-type plants in respect to rates of photosynthesis, plant appearance, growth and tuber production, their photosynthetic metabolism was found to be severely affected. The results show that the decrease in activity of the triose-phosphate translocator in the transformants caused a fourfold increase in the level of 3-phosphoglycerate and a corresponding decrease in inorganic phosphate in the stromal compartment, resulting in a large increase in the synthesis of starch. Whereas during a 12-h day period wild-type plants deposited 43% of their CO₂ assimilate into starch, this value rose to 61–89% in the transformants. In contrast to the wild-type plants, where the rate of assimilate export from the leaves during the night period was about 75% of that during the day, the export rate from leaves of transformants appeared to be much higher during the night than during the day. As the mobilisation of starch occurs in part hydrolytically, resulting in the formation of glucose, the triose-phosphate translocator loses its exclusive function in the export of carbohydrates from the chloroplasts when the photoassimilates are temporarily deposited as starch. It appears that by directing the CO₂ assimilates mainly into starch, the transformants compensate for the deficiency in triose-phosphate translocator activity in such a way that the productivity of the plants is not affected by the transformation.Abbreviations Chl chlorophyll - DHAP dihydroxyacetone phosphate - 3-PGA 3-phosphoglycerate - Rubisco ribulose,1,5-bisphosphate carboxylase/oxygenase - RuBP ribulose-1,5-bisphosphate - trioseP triose phosphate - WT wild type The able technical assistance of Mrs. K. Wildenberger and Mrs. A. Großpietsch is gratefully acknowledged. This work has been supported by the Bundesminister für Forschung und Technologie.