The CO2-concentrating mechanism in the physiological context: lowering the CO2 supply diminishes culture growth and economises starch utilisation in Chlamydomonas reinhardtii.

In a synchronously grown Chlamydomonas reinhardtii (Chlorophyceae) culture the CO2-concentrating mechanism (CCM) was induced by lowering the CO2 level from 4% to 0.036% CO2 (culture HL). The effects of the reduced carbon supply on starch levels were studied over a period of up to 100 h and compared with control cultures kept either at 4% CO2 (culture H) or continuously at ambient air (0.036% CO2, culture L). Lowering the CO2 supply reduced culture growth as estimated by chlorophyll, protein and cell density. The starch level continued to show diurnal variations with an initially reduced rate of starch synthesis at reduced or abolished culture growth. Subsequently, starch maxima and minima increased. After 4 days the resulting pattern for culture HL was similar to that of culture L, which possessed higher minima but identical maxima to culture H. The intracellular starch localisation was examined on electron micrographs. Cell extracts were assayed for ADP-glucose pyrophosphorylase (EC 2.7.7.27) and starch phosphorylase (EC 2.4.1.1) activities. Over the assayed period of 2 days, there was a good correlation between the observed changes in the starch levels and the measured enzyme activities. The rate of CO2-dependent oxygen evolution of culture HL declined from 100% to 60% of the control over the day. This indicates that the diminished or abolished growth and the impairment of starch accumulation upon CO2 depletion are not simply consequences of the lowered level of the substrate CO2. The diminished growth and the peculiar starch accumulation pattern with higher positions of the starch minima in low-CO2 cells are interpreted as economised starch utilisation as long-term aspects of induction of the CCM.

Starchless mutants of Chlamydomonas reinhardtii lack the small subunit of a heterotetrameric ADP-glucose pyrophosphorylase.

ADP-glucose synthesis through ADP-glucose pyrophosphorylase defines the major rate-controlling step of storage polysaccharide synthesis in both bacteria and plants. We have isolated mutant strains defective in the STA6 locus of the monocellular green alga Chlamydomonas reinhardtii that fail to accumulate starch and lack ADP-glucose pyrophosphorylase activity. We show that this locus encodes a 514-amino-acid polypeptide corresponding to a mature 50-kDa protein with homology to vascular plant ADP-glucose pyrophosphorylase small-subunit sequences. This gene segregates independently from the previously characterized STA1 locus that encodes the large 53-kDa subunit of the same heterotetramer enzyme. Because STA1 locus mutants have retained an AGPase but exhibit lower sensitivity to 3-phosphoglyceric acid activation, we suggest that the small and large subunits of the enzyme define, respectively, the catalytic and regulatory subunits of AGPase in unicellular green algae. We provide preliminary evidence that both the small-subunit mRNA abundance and enzyme activity, and therefore also starch metabolism, may be controlled by the circadian clock.

Mathematical modelling of metabolism.

Modelling of metabolism attempts to improve our understanding of metabolic regulation by quantifying essential parts or aspects of the metabolic system. Three areas in which modelling has recently made considerable contributions toward this aim can be identified. First, the more detailed description of individual reactions and pathways; second, the analysis of relative flux limitations within a pathway by means of metabolic control analysis; and third, in vivo flux analysis using nuclear magnetic resonance or mass spectroscopic analysis in combination with positionally labelled carbon compounds.

Metabolic Control Analysis: Separable Matrices and Interdependence of Control Coefficients.

A central quantity for the analysis of the interdependence of control coefficients is the Jacobian H of the pathway. For a simple metabolic chain, H is known to be tridiagonal. Its inverse H-1, which is required to calculate control coefficients, is semi-separable. A semi-separable nxn matrix (aij) has the characteristic property that it is decomposable into two triangles for each of which there are vectors r=(r1, . . . ,rn) and t=(t1, . . . ,tn) with aij=ritj. The exact definitions of semi-separability and the related separability of matrices are given in Appendix B. Owing to the semi-separability of H-1, the determinants of all 2x2 sub-matrices of elements located within one of the triangles are zero. Therefore, these triangles are regions of vanishing two-minors. The flux control coefficient matrix CJ is hown to be separable and the concentration control coefficient matrix Cs to be semi separable. Cs has, in addition, the peculiarity that the row vector is the same for both its upper and lower triangle. A feedback loop gives rise to a new sub-region of vanishing two-minors, thereby disturbing the semi-separability of the upper triangle of Cs. A recipe is given to graphically construct the regions of vanishing two-minors of concentration control coefficients. The notion of (semi-)separability allows assessment of all dependences of control coefficients for metabolic pathways.Copyright 1998 Academic Press

Co-response Coefficients, Monovalent Units, and Combinatorial Rules: Unification of Concepts in Metabolic Control Analysis

The Jacobian H of a linear metabolic pathway without feedback loops is tridiagonal. Its inverse, H-1, which is needed for calculating control coefficients or elasticities, can be decomposed into two regions of mutually dependent rows and columns. For each of these regions of H-1, all sub-determinants of order two are zero. The existence of the two regions is shown to cause certain invariance properties of the ratios of control coefficients that can be expressed as co-response coefficients. Also the concept of monovalent functional units seems to be related to the existence of the regions. Moreover, the combinatorial rules for selecting the right modulations originate from the fact that certain sub-determinants of H-1 are zero when located within the regions. The regions of zero sub-determinants of order two of H-1 are thus a central element for the analysis of the linear pathway. The unifying potential of H-1 is not restricted to the linear chain but is also expected to be valid for complex metabolic systems.Copyright 1997 Academic Press Limited Copyright 1997 Academic Press Limited

Extending double modulation: combinatorial rules for identifying the modulations necessary for determining elasticities in metabolic pathways.

The double modulation method for determining the elasticities of pathway enzymes, originally devised by Kacser & Burns (Biochem. Soc. Trans. 7, 1149-1160, 1979), is extended to pathways of complex topological structure, including branching and feedback loops. An explicit system of linear equations for the unknown elasticities is derived. The constraints imposed on this linear system imply that modulations of more than one enzyme are not necessarily independent. Simple combinatorial rules are described for identifying without using any algebra the set of independent modulations that allow the determination of the elasticities of any enzyme. By repeated application, the minimum numbers of modulations required to determine the elasticities of all enzymes of a given pathway can be determined. The procedure is illustrated with numerous examples.

Concerning the measurement of flux control coefficients by enzyme titration. Steady states, quasi-steady-states, and the role of time in control analytical experiments.

An established method to determine flux control coefficients is the enzyme titration method in which the change in pathway flux upon a change in the enzyme concentration is measured. In this study, the application of this method to a simple reconstituted pathway was investigated by simulated measurements. The pathway was assumed to be in the quasi-steady-state, which is the experimental realization of the mathematical construct 'steady state'. It was shown that flux control coefficients, calculated in a way that mimics their experimental determination, were strongly time dependent. Initially, the calculated flux control coefficient was high for the enzyme adjacent to the reaction monitoring the flux, and the steady-state value was overestimated. Likewise, flux control coefficients were underestimated for enzymes further away from the monitoring reaction. The observed time course of simulated flux control coefficients was shown to reflect the fact that experimental systems are not steady state but quasi-steady-state. For a pathway in the quasi-steady-state, some of the problems with enzyme titration experiments can be overcome by allowing the system to relax for a time interval that is large compared with the turnover time of the pooled pathway intermediates.

Determining elasticities from multiple measurements of flux rates and metabolite concentrations. Application of the multiple modulation method to a reconstituted pathway.

A recently developed method to determine elasticities by multiple measurements of steady-state flux rates and metabolite concentrations [Giersch, C. (1994) J. Theor. Biol. 169, 89-99] is applied to a reconstituted metabolic pathway. The pathway is the section of glycolysis converting glycerate-3-phosphate to pyruvate. The elasticities of the pathway enzymes are determined from the dependence on effector concentrations of measured steady-state flux rates and steady-state metabolite concentrations. To verify assumptions regarding the dependence of reaction rates on metabolites, flux control coefficients calculated from enzyme elasticities are compared with those estimated by means of the usual enzyme titration. The proposed method is shown to allow experimental determination of enzyme elasticities but requires, like other experiments in metabolic control analysis, a high level of reproducibility and experimental accuracy which may be difficult to attain.

Photosynthetic oscillations and the interdependence of photophosphorylation and electron transport as studied by a mathematical model.

A simple mathematical model of photosynthetic carbon metabolism as driven by ATP and NADPH has been formulated to analyse photosynthetic oscillations. Two essential assumptions of this model are: (i) reduction of 3-phosphoglycerate to triosephosphate in the Clavin cycle is limited by ATP, not by NADPH, and (ii) photophosphorylation is affected by the availability of both ADP and NADP, while electron transport is limited by NADP only. The model produces oscillations of observed damping and period in ATP and NADP concentrations which are about 180 degrees out of phase, while three alternative proposals regarding coupling of electron transport and photophosphorylation do not produce oscillatory model solutions. The phases of ATP and NADPH are in reasonable agreement with the available experimental data. The model (which assumes that redox control of photophosphorylation is part of the oscillatory mechanism) is compared with an alternative proposal (that oscillations are due to interdependence of turnover of adenylates and Calvin cycle intermediates). From the similarity of the mathematical structures of both models it is inviting to speculate that both models are partial aspects of 'the oscillatory mechanism'.

A simple model relating photoinhibitory fluorescence quenching in chloroplasts to a population of altered Photosystem II reaction centers.

A model is presented describing the relationship between chlorophyll fluorescence quenching and photoinhibition of Photosystem (PS) II-dependent electron transport in chloroplasts. The model is based on the hypothesis that excess light creates a population of inhibited PS II units in the thylakoids. Those units are supposed to posses photochemically inactive reaction centers which convert excitation energy to heat and thereby quench variable fluorescence. If predominant photoinhibition of PS IIα and cooperativity in energy transfer between inhibited and active units are presumed, a quasi-linear correlation between PS II activity and the ratio of variable to maximum fluorescence, FVFM, is obtained. However, the simulation does not result in an inherent linearity of the relationship between quantum yield of PS II and FVFM ratio. The model is used to fit experimental data on photoinhibited isolated chloroplasts. Results are discussed in view of current hypotheses of photoinhibition.

Control analysis of photosynthetic CO2 fixation.

The potential of control analysis to aid our understanding of regulation and control of photosynthetic carbon metabolism is investigated. Methods of metabolic control analysis are used to determine flux control coefficients of photosynthetic reactions from enzyme elasticities. Equations expressing control coefficients symbolically by enzyme elasticities are derived, and general properties of these expressions are analysed. Suggestions for experimental determination of flux control coefficients from enzyme elasticities are given. A simplified model of the Calvin-Benson cycle is used to illustrate interrelations between patterns of photosynthetic metabolites and that of control coefficients.

Control analysis of biochemical pathways: a novel procedure for calculating control coefficients, and an additional theorem for branched pathways.

A novel method for calculating control coefficients of individual enzymes on fluxes and concentrations in metabolic pathways is presented. This method is derived by applying the theorem on implicit functions to the equations defining the steady state metabolite concentrations; it allows verification of the existing summation theorems and connectivity relations, and leads to a novel theorem for flux control coefficients in branched pathways. The method and the novel theorem are illustrated by several examples.

Control analysis of metabolic networks. 1. Homogeneous functions and the summation theorems for control coefficients.

1. The summation theorem CJ1 + ... + CJn = 1 for flux control coefficients CJi is shown to be equivalent to the assumption that flux J is a homogeneous function of degree 1 of enzyme concentrations E1,..., En, that is to the assumption J (tE1,..., tEn) = tJ (E1,..., En) for any t not equal to 0. Likewise, the summation theorem CXj1 + ... + CXjn = 0 for concentration control coefficients CXj1 is equivalent to homogeneity of degree 0 of steady-state metabolite concentrations Xj, or Xj (tE1,..., tEn) = Xj (E1,..., En). From this equivalence it is obvious that metabolic control analysis applies only to homogeneous systems. 2. The summation theorem for flux control coefficients is shown to be equivalent to that for concentration control coefficients, provided all reaction rates vi are homogeneous functions of enzyme concentrations Ei. 3. The equivalence between homogeneity of flux J and the summation theorem for flux control coefficients is used to analyse branching of fluxes in metabolic pathways in terms of flux control coefficients.

Control analysis of metabolic networks. 2. Total differentials and general formulation of the connectivity relations.

The mathematical background of the connectivity relations of metabolic control theory is analysed. The connectivity relations are shown to reflect general properties of total differentials of reaction rate vi, flux J, and metabolite concentration Xj. Connectivity relations hold for any metabolic network in which all vi are homogeneous functions of enzyme concentration Ei. This notion allows established algebraic methods to be used for the formulation of connectivity relations for metabolic systems in which numerous constraints are imposed on metabolite concentrations. A general procedure to derive connectivity relations for such metabolic systems is given. To encourage a broader audience to apply control theory to physiological systems, an easy-to-use graphical procedure is derived for formulating connectivity relations for biochemical systems in which no metabolite is involved in more than one constraint.

Inactivation of the photosynthetic carbon reduction cycle in isolated mesophyll protoplasts subjected to freezing stress.

Isolated mesophyll protoplasts from Valerianella locusta L. were subjected to freeze-thaw cycles. Subsequently, steady-state pool sizes of (14)C-labeled intermediates of the photosynthetic carbon reduction cycle were determined by high performance liquid chromatography. Protoplasts in which CO2 fixation was inhibited by preceding freezing stress, showed a strong increase in the proportion of fructose-1,6-bisphosphate, sedoheptulose-1,7-bisphosphate and triose phosphates. These results indicate an inhibition of the activities of stromal fructose-1,6-bisphosphatase and sedoheptulose-1,7-bisphosphatase. Furthermore, freezing stress caused a slight increase in the proportion of labeled ribulose-1,5-bisphosphate, which may be based on an inhibition or ribulose bisphosphate carboxylase activity. It was shown earlier (Rumich-Bayer and Krause 1986) that freezing-thawing readily affects photosynthetic CO2 assimilation independently of thylakoid inactivation. The present results are interpreted in terms of an inhibition of the light-activation system of the photosynthetic carbon reduction cycle, caused by freezing stress.

Regulation of photosynthetic carbon metabolism during phosphate limitation of photosynthesis in isolated spinach chloroplasts.

Intact chloroplasts isolated from spinach were illuminated in the absence of inorganic phosphate (Pi) or with optimum concentrations of Pi added to the reaction medium. In the absence of Pi photosynthesis declined after the first 1-2 min and was less than 10% of the maximum rate after 5 min. Export from the chloroplast was inhibited, with up to 60% of the (14)C fixed being retained in the chloroplast, compared to less than 20% in the presence of Pi. Despite the decreased export, chloroplasts depleted of Pi had lower levels of triose phosphate while the percentage of total phosphate in 3-phosphoglycerate was increased. Chloroplast ATP declined during Pi depletion and reached dark levels after 3-4 min in the light without added Pi. At this point, stromal Pi concentration was 0.2 mM, which would be limiting to ATP synthesis. Addition of Pi resulted in a rapid burst of oxygen evolution which was not initially accompanied by net CO2 fixation. There was a large decrease in 3-phosphoglycerate and hexose plus pentose monophosphates in the chloroplast stroma and a lesser decrease in fructose-1,6-bisphosphate. Stromal levels of triose phosphate, ribulose-1,5-bisphosphate and ATP increased after resupply of Pi. There was an increased export of (14)-labelled compounds into the medium, mostly as triose phosphate. Light activation of both fructose-1,6-bisphosphatase and ribulose-1,5-bisphosphate carboxylase was decreased in the absence of Pi but increased following Pi addition.It is concluded that limitation of Pi supply to isolated chloroplasts reduced stromal Pi to the point where it limits ATP synthesis. The resulting decrease in ATP inhibits reduction of 3-phosphoglycerate to triose phosphate via mass action effects on 3-phosphoglycerate kinase. The lack of Pi in the medium also inhibits export of triose phosphate from the chloroplast via the phosphate transporter. Other sites of inhibition of photosynthesis during Pi limitation may be located in the regeneratige phase of the reductive pentose phosphate pathway.

Oscillatory response of photosynthesis in leaves to environmental perturbations: a mathematical model.

Oscillations in the yield of chlorophyll fluorescence, in oxygen evolution, and in CO2 uptake observed with leaves upon perturbation of steady-state conditions are suggested to be due to the interdependence of turnover of adenylates and Calvin cycle intermediates. This suggestion is quantified in a mathematical model; the behavior of the model system in the neighborhood of the singular point of the system is analyzed. The linearized system is solved analytically, a condition for the occurrence of oscillations is given, and explicit expressions for the oscillation period and the damping constant are derived. The model is shown to be capable of exhibiting oscillations with the period observed with algae or leaves, whereas calculated values of the damping constant are higher than those measured for leaves or algae.