Control of the rate of photosynthetic carbon dioxide fixation

A simplified model of the reductive pentose phosphate pathway of photosynthesis is analysed in order to quantify the degree to which each of the constituent reactions controls the rate of CO₂ fixation (given by the control coefficient). The analysis focuses on the four largely irreversible reactions of the cycle together with the first irreversible reaction in the sucrose and starch synthetic pathways. The model assumes that the other reactions are at equilibrium. The photorespiratory and electron transport systems are not included in the model. The analysis demonstrates that: (1) an analytical approach can be used to investigate the distribution of flux control in autocatalytic and moiety-conserved cycles; (2) measurements of enzyme kinetic parameters and certain fluxes and substrate concentrations can be used to solve the equations defining the enzyme control coefficients; (3) the conservation of total stromal phosphate and the intricate regulatory mechanisms of the photosynthetic system result in a relationship between the control coefficients that is complex and may defy any intuitive assessment of ‘rate limitation’; (4) ribulose-1,5-bisphosphate carboxylase / oxygenase may, under certain conditions, be a major controller of the rate of CO₂ fixation and, by regulating the concentration of ribulose 1,5-bisphosphate, may be important in governing the ratio of organic to inorganic phosphate in the stroma; (5) the other enzymes may also serve an important role in determining the distribution of phosphate between organic and inorganic species because they catalyze reactions at the branch points between starch and sucrose synthesis and ribulose 1,5-bisphosphate regeneration; (6) these enzymes that catalyze ‘branch-pint’ reactions may have negative control coefficients because of their ability to reduce the total concentration of cycle intermediates; (7) an approach combining the use of the equations presented in this paper and flux and substrate concentration measurements may be adequate for determining the control coefficients of several enzymes of the reductive pentose phosphate pathway.     

Control and regulation of metabolic fluxes in microbes by substrates and enzymes

The control of enzymes and substrates on the flux through microbial metabolic pathways can be quantified in terms of flux control coefficients. In pathways involving group transfer, the summation theorem for flux control by the enzymes has to be modified: the sum of control by all enzymes is between 1 and 2. The phosphoenolpyruvate:glucose phosphotransferase system is such a pathway. Experimental determination of the control by the enzymes in this pathway is under way. The control of the enzymes on the glycolytic flux in yeast is low, with the possible exception of the uptake step. InKlebsiella pneumoniae potassium and ammonium ions can simultaneously be limiting, (i.e. have significant control on growth) at pH 6, but not at pH 8. This may be due to the fact that at pH 8 the high-affinity potassium uptake system is absent.     

On describing microbial growth kinetics from continuous culture data: Some general considerations,observations, and concepts

Analysis of continuous culture methodology suggests that this potentially powerful tool for kinetic analysis can be improved by minimizing several inherent shortcomings. Medium background substrates — organic carbon, phosphate, and manganese — were shown to dominate kinetic observations at concentrations below chemical detection methods. Reactor wall growth, culture size distribution changes, sample removal-induced steady state perturbations, and limiting substrate leakage from organisms are treated in terms of kinetic measurement errors. Large variations in maximal growth rates and substrate uptake rates found are attributed to experimental protocol-induced transient states. Relationships are presented for correcting limiting substrate concentrations for lability during sampling, contamination with unreacted medium, and background substrate effects. Analytical procedures are discussed for improved measurement of limiting substrate kinetics involving enzymes, isotopes, and material balance manipulation. Relaxation methods as applied to continuous culture are introduced as a means for isolating separate rate constants describing net substrate transport and for evaluating cellular metabolite leakage. Low velocity growth, multiple substrate metabolism, and endogenous metabolism are discussed along with measurements showing that 1-month generation times for aquatic microorganisms can be quite normal and that the kinetics are compatible withμg/liter limiting substrate concentrations. The concept of regarding growth kinetics as the sum of several net accumulation processes is suggested.     

大肠杆菌苏氨酸合成途径动力学模型的构建与分析

动力学模型分析有利于理解生物系统的调控机制,从而为高效细胞工厂的理性设计提供指导。基于以往发表的相关途径动力学模型和测量的酶动力学数据,开发了大肠杆菌苏氨酸合成途径的动力学模型。模型包含从天冬氨酸至苏氨酸的合成途径及葡萄糖开始的为合成途径提供前体以及能量的代谢途径。与以往模型不同的是新模型中考虑了能量和还原力的平衡,从而使模型模拟的系统自身成为一个不需要从外界提供能量和还原力的自洽系统。模型稳态分析的结果表明PTS、G6PDH和HDH等反应对苏氨酸合成反应的通量控制系数较大,通过过表达这些反应的酶可以有效增加苏氨酸合成反应的通量。     

Metabolic regulation: A control analytic perspective

A possible basis for a quantitative theory of metabolic regulation is outlined. Regulation is defined here as the alteration of reaction properties to augment or counteract the mass-action trend in a network reactions. In living systems the enzymes that catalyze these reactions are the handles through which such alteration is effected. It is shown how the elasticity coefficients of an enzyme-catalyzed reaction with respect to substrates and products are the sum of a massaction term and a regulatory kinetic term; these coefficients therefore distinguish between massaction effects and regulatory effects and are recognized as the key to quantifying regulation. As elasticity coefficients are also basic ingredients of metabolic control analysis, it is possible to relate regulation to such concepts as control, signalling, stability, and homeostasis. The need for care in the choice of relative or absolute changes when considering questions of metabolic regulation is stressed. Although the concepts are illustrated in terms of a simple coupled reaction system, they apply equally to more complex systems. When such systems are divided into reaction blocks, co-response coefficients can be used to measure the elasticities of these blocks.I dedicate this paper to Henrik Kacser, co-founder of and guiding light in the field of metabolic control analysis. His recent death leaves us bereft of a fount of wisdom and kindness, but his work remains as a monument along the path of our search for an understanding of metabolic behavior.     

Metabolic control and its analysis. Additional relationships between elasticities and control coefficients

Existing theorems from the analysis of metabolic control have been taken and embedded in a simple matrix algebra procedure for calculating the flux control coefficients of enzymes (formerly known as sensitivities) in a metabolic pathway from their kinetic properties (their elasticities). New theorems governing the flux control coefficients of branched pathways and substrate cycles have been derived to allow the procedure to be applied to complex pathway configurations. Modifications to the elasticity terms used in the equations have been theoretically justified so that the method remains valid for pathways with conserved metabolites (for example, the adenine nucleotide pool or the intermediates of a catalytic cycle such as the tricarboxylic acid cycle) or with pools of metabolites kept very near to equilibrium by very rapid reactions. The matrix equations generated using these theorems and relationships may be solved algebraically or numerically. Algebraic solutions have been used to determine the factors responsible for the degree of amplification of flux control coefficients by substrate cycles and to show that it is possible to derive expressions for the elasticities of a group of enzymes.     

Design of substrate label for steady state flux measurements in plant systems using the metabolic network of Brassica napus embryos

Steady state metabolic flux analysis using (13)C labeled substrates is of growing importance in plant physiology and metabolic engineering. The quality of the flux estimates in (13)C metabolic flux analysis depend on the: (i) network structure; (ii) flux values; (iii) design of the labeling substrate; and (iv) label measurements performed. Whereas the first two parameters are facts of nature, the latter two are to some extent controlled by the experimenter, yet they have received little attention in most plant studies. Using the metabolic flux map of developing Brassica napus (Rapeseed) embryos, this study explores the value of optimal substrate label designs obtained with different statistical criteria and addresses the applicability of different optimal designs to biological questions. The results demonstrate the value of optimizing the choice of labeled substrates and show that substrate combinations commonly used in bacterial studies can be far from optimal for mapping fluxes in plant systems. The value of performing additional experiments and the inclusion of measurements is also evaluated.     

Flux control analysis for biphenyl metabolism by Rhodococcus pyridinovorans R04

The flux control coefficients of the four enzymes involved in the upper pathway of biphenyl degradation were determined from transient metabolite concentrations. The first enzyme was indicated as the major rate-limiting step of the pathway with a control coefficient of 0.48. The flux control coefficients of the other three enzymes were 0.03, 0.23 and 0.27, respectively. This is the first experimental evidence of the control step in the pathway of biphenyl degradation using metabolic control analysis.     

Use and limitations of modular metabolic control analysis in medicine and biotechnology

By Metabolic Control Analysis (MCA), it has been shown that control on flux is in most cases shared by several enzymes rather than concentrated on one "rate-limiting step." This analysis also allows the quantification of the control exerted by groups (modules) of enzymes. The modules may correspond to spatial compartments or to functional units. A brief outline of the modular approach to MCA is given. The criteria by which the system can be modularized and the concept of monofunctional unit are explained. Various studies in which control analysis was applied to biotechnological and medical issues are reviewed. In particular, MCA has turned out to be helpful in the assessment of the severity of enzyme deficiencies. Another application is the search for target enzymes or enzyme groups where pharmaceuticals can suppress the metabolism of pathogenic microorganisms most. In biotechnology, modular and "traditional" control analyses are valuable tools for choosing the most promising targets for genetic manipulation so as to increase a biosynthetic flux. As control coefficients are linear approximations, the effect of enhancing the activities of enzymes to a larger extent is often overestimated. Further limitations such as the restriction to stationary states, uncertainties due to spatial heterogeneities and the impact of experimental error are discussed.     

Dependence of control coefficient distribution on the boundaries of a metabolic system: a generalized analysis of the effects of additional input and output reactions to a linear pathway

Both experimental and theoretical studies of metabolism are likely to relate to a segment that has been isolated for analytical purposes. In practice, it will be embedded in the whole of cellular metabolism. Thus, it is necessary to consider how conclusions about the control of an isolated pathway may be modified in this wider context where the input and output metabolites are considered as variables of cellular metabolism. Here, we analyse the effect of expanding a linear metabolic pathway by adding an extra input or an extra output. In particular, we analyse the effect of the elasticities of the extra steps on control coefficients. We derive matrix algebraic relationships for obtaining flux and concentration control coefficients from expressions depending on these extra elasticities and on parameters (elasticities and control coefficients) of the original pathway. These equations can be shown in certain cases to be generalized versions of earlier rescaling relationships and to be related to top-down analysis, but also apply where the new variable metabolite of the expanded pathway is an effector of more than one step of the original pathway. We use our relationships to analyse the dependence or independence of control coefficients upon these extra elasticities for the published analyses of the pathway of mammalian serine biosynthesis (Fell & Snell, 1988) and Escherischia coli threonine biosynthesis (Chassagnole et al., 2001). The same analysis can be applied to determine whether the transport reactions of substrates and products of a pathway in and out of a cell need to be included in estimations of the control coefficients of the enzymes.     

The dependence of flux,sensitivity and response of the flux on the concentrations of substrate and modifiers for cooperative enzymes

The sensitivity (change of flux per unit change in the concentration of substrate) and response (change of flux per unit change in the concentration of modifier) are studied for a two-site Adair model in which cooperativity arises from both binding and catalytic interactions. For positive cooperativity, the sensitivity is weakly dependent on the Hill coefficient for the binding case, but can increase without limit for the catalytic case. Negatively cooperative enzymes (binding only) give very large sensitivities compared with positively or non-interacting systems, but the sensitivity rapidly decreases as the saturation increases above 25%. Modifiers greatly enhance the sensitivity; large changes in flux can be obtained for small changes in the concentrations of substrates and modifiers. In general, increasing the degree of kinetic cooperativity decreases the degree of binding cooperativity; selective pressure to maximize the sensitivity and response of allosteric enzymes may act to optimize cooperativity of binding modifiers and kinetic cooperativity of substrate turnover. The initial velocity equations including modifiers can be extended to bi-substrate, cooperative kinetics. The kinetics of methanol dehydrogenase are discussed.     

Experimental determination of flux control distribution in biochemical systems: in vitro model to analyze transient metabolite concentrations

Determination of the control coefficients allows the identification of rate-controlling steps in a reaction system. However, the measurement of the flux control coefficients in a biochemical system is not a trivial task, except for some special cases. We have developed a theoretical basis for the direct determination of these coefficients from dynamic responses. In order to show the validity of this methodology experimentally, the dynamic approach is applied to an in vitro reconstituted partial glycolytic pathway to determine the flux control coefficients of hexokinase and phosphofructokinase. It is shown that the dynamic approach gives consistent results, which agree well with values obtained by the direct enzyme titration method. The detailed procedure and potential applications to other systems, such as immobilized enzyme or cell reactors, are discussed. (c) 1993 Wiley & Sons, Inc.     

Control of gluconeogenesis in rat liver cells. Flux control coefficients of the enzymes in the gluconeogenic pathway in the absence and presence of glucagon.

We have used control analysis to quantify the distribution of control in the gluconeogenic pathway in liver cells from starved rats. Lactate and pyruvate were used as gluconeogenic substrates. The flux control coefficients of the various enzymes in the gluconeogenic pathway were calculated from the elasticity coefficients of the enzymes towards their substrates and products and the fluxes through the different branches in the pathway. The elasticity coefficients were either calculated from gamma/Keq. ratios (where gamma is the mass-action ratio and Keq. is the equilibrium constant) and enzyme-kinetic data or measured experimentally. It is concluded that the gluconeogenic enzyme pyruvate carboxylase and the glycolytic enzyme pyruvate kinase play a central role in control of gluconeogenesis. If pyruvate kinase is inactive, gluconeogenic flux from lactate is largely controlled by pyruvate carboxylase. The low elasticity coefficient of pyruvate carboxylase towards its product oxaloacetate minimizes control by steps in the gluconeogenic pathway located after pyruvate carboxylase. This situation occurs when maximal gluconeogenic flux is required, i.e. in the presence of glucagon. In the absence of the hormone, when pyruvate kinase is active, control of gluconeogenesis is distributed among many steps, including pyruvate carboxylase, pyruvate kinase, fructose-1,6-bisphosphatase and also steps outside the classic gluconeogenic pathway such as the adenine-nucleotide translocator.     

The mechanism of the phosphoglucomutase reaction. Studies on rabbit muscle phosphoglucomutase with flux techniques

1. The kinetics of phosphoglucomutases from different sources are discussed and it is concluded that on the available evidence there are in all cases three possible mechanisms for the reaction. These are an indirect transfer of phosphate involving the phosphoenzyme (mechanism 1), a direct transfer of phosphate (mechanism 2), and an intermolecular transfer of phosphate from glucose 1,6-diphosphate to the substrate (mechanism 3). Conventional net flux measurements are shown not to differentiate between these mechanisms. 2. Flux equations are developed and it is shown that there are three flux ratios that characterize and distinguish between the mechanisms. 3. To examine these flux ratios induced-transport tests are described with ¹⁴C- and ³²P-labelled substrates. The fluxes determined with ¹⁴C- and ³²P-labelled substrates are also compared at chemical equilibrium. 4. With rabbit muscle phosphoglucomutase the results of these tests were completely consistent with mechanism 1 and unequivocally excluded any substantial part of the reaction proceeding by mechanism 2 or mechanism 3. Evidence was also obtained for an isomerization of the phosphoenzyme with an apparent rate constant about 4·5×10⁷sec.⁻¹. Taking into account the activity coefficients of the substrates the true rate constant appears to be about one-sixth of this value. 5. Isotope effects and non-ideal behaviour of the solutions are discussed and the activity coefficients of the substrates are shown to be equal by measurement of the depression of freezing point. It is concluded that these factors do not influence the tests significantly. 6. Alternative mechanisms are considered and it is concluded that the tests show that the glucose residue is transferred directly, that the phosphate is transferred indirectly with one intermediate phosphate, and that there is an isomerization of the free phosphoenzyme without reference to any other details of the reaction. Further, no assumptions are required about the constancy of rate constants. 7. The relative merits of induced transport and product inhibition for detecting isomerization of the enzyme are discussed. It is concluded that the induced-transport test is more sensitive and that its interpretation is less equivocal. 8. The application of the tests to other enzyme systems is briefly considered.     

The identification of enzyme targets for the optimization of a valine producing Corynebacterium glutamicum strain using a kinetic model

The enzyme targets for the rational optimization of a Corynebacterium glutamicum strain constructed for valine production are identified by analyzing the control of flux in the valine/leucine pathway. The control analysis is based on measurements of the intracellular metabolite concentrations and on a kinetic model of the reactions in the investigated pathway. Data‐driven and model‐based methods are used and evaluated against each other. The approach taken gives a quantitative evaluation of the flux control and it is demonstrated how the understanding of flux control is used to reach specific recommendations for strain optimization. The flux control coefficients (FCCs) with respect to the valine excretion rate were calculated, and it was found that the control is distributed mainly between the acetohydroxyacid synthase enzyme (FCC = 0.32), the branched chain amino acid transaminase (FCC = 0.27), and the exporting translocase (FCC = 0.43). The availability of the precursor pyruvate has substantial influence on the valine flux, whereas the cometabolites are less important as demonstrated by the calculation of the respective response coefficients. The model is further used to make in‐silico predictions of the change in valine flux following a change in enzyme level. A doubling of the enzyme level of valine translocase will result in an increase in valine flux of 31%. By optimizing the enzyme levels with respect to valine flux it was found that the valine flux can be increased by a factor 2.5 when the optimal enzyme levels are implemented. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

31P NMR magnetization-transfer measurements of flux between inorganic phosphate and adenosine 5'-triphosphate in yeast cells genetically modified to overproduce phosphoglycerate kinase

31P NMR magnetization-transfer measurements were used to measure flux between inorganic phosphate and ATP in the reactions catalyzed by phosphoglycerate kinase and glyceraldehyde-3-phosphate dehydrogenase in anaerobic cells of the yeast Saccharomyces cerevisiae. Flux between ATP and Pi and glucose consumption and ethanol production were measured in cells expressing different levels of phosphoglycerate kinase activity. Overexpression of the enzyme was obtained by transforming the cells with a multicopy plasmid containing the phosphoglycerate kinase coding sequence and portions of the promoter element. Fluxes were also measured in cells in which the glyceraldehyde-3-phosphate dehydrogenase activity had been lowered by limited incubation with iodoacetate. These measurements showed that both enzymes have low flux control coefficients for glycolysis but that phosphoglycerate kinase has a relatively high flux control coefficient for the ATP----Pi exchange catalyzed by the two enzymes. The Pi----ATP exchange velocities observed in the cell were shown to be similar to those displayed by the isolated enzymes in vitro under conditions designed to mimic those in the cell with respect to the enzyme substrate concentrations.     

In vitro control analysis of an enzyme system: Experimental and analytical developments

In this paper we describe a flow-through system for reconstituting parts of metabolism from purified enzymes. This involves pumping continuously into a reaction chamber, fresh enzymes and reagents so that metabolic reactions occur in the chamber. The waste products leave the chamber via the outflow so that a steady state can be setup. The system we chose consisted of a single enzyme, lactate dehydrogenase. This enzyme was chosen because it consumes NADH in the chamber which could be monitored spectrophotometrically. The aim of the work was to investigate whether a steady state could be achieved in the flow system and whether a metabolic control analysis could be done. We measured two control coefficients, C_LDH and C_pump for the enzyme flux and NADH concentration and confirmed that the summation theorem applied to this system. The advantage of a flow-through system is that the titrations necessary to estimate the control coefficients can be easily and precisely controlled; this means that accurate estimates for the control coefficients can be obtained. In the paper, we discuss some statistical aspects of the data analysis and some possible applications of the technique, including a method to determine the presence of metabolic channelling between two different enzymes.     

Metabolic network sensitivity analysis

A linear sensitivity analysis of metabolic regulation in nonsteady states is described. This treatment considers the effects of enzymatic and nonenzymatic reactions and spontaneous rapid equilibria. Sensitivity coefficients summarizing the influence of metabolite concentrations on reaction rates and pathway net flux are defined, as are sensitivity coefficients summarizing the effects of enzymes on metabolite concentrations and net flux. The sensitivity analysis is implemented in an easily used set of computer programs. A four-enzyme test model was shown to be resistant to intuitive interpretation. Sensitivity analysis showed a shift of control from the end of the enzymic sequence to the beginning of the sequence with changing metabolic state. The homeostatic behavior of the test system was shown to depend on the nonenzymatic reactions as well as on the enzymes. Under certain conditions metabolic regulation is shared so intimately among enzymes and spontaneous reactions that separation of their effects is impossible.     

Microscopic diffusion-reaction coupling in steady-state enzyme kinetics

The theory of diffusion-controlled processes is applied to describe the steady state of a reversible enzymatic reaction with special emphasis on the effects of enzyme saturation. A standard macroscopic steady-state treatment requires only that the average diffusional influx of substrate equals the net reaction flux as well as the average diffusional efflux of product. In contrast, the microscopic diffusion-reaction coupling used here takes properly into account the conditional concentration distributions of substrate and product: Only when the enzyme is unoccupied will there be a diffusional association flux; when the enzyme is occupied, the concentration distributions will relax towards their homogeneous bulk values. In this way the relaxation effects of the non-steady state will be constantly reoccurring as the enzyme shifts between unoccupied and occupied states. Thus, one is forced to describe the steady state as the weighted sum of properly time-averaged non-stationary conditional distributions. The consequences of the theory for an appropriate assessment of the parameters obtained in Lineweaver-Burk plots are discussed. In general, our results serve to justify the simpler macroscopic coupling scheme. However, considerable deviations between the standard treatment and our analysis can occur for fast enzymes with an essentially irreversible product release.