Calculation errors of time-varying flux control coefficients obtained from elasticity coefficients by means of summation and connectivity theorems in metabolic control analysis

Metabolic control analysis is a powerful technique for the evaluation of flux control within biochemical pathways. Its foundation is the elasticity coefficients and the flux control coefficients (FCCs). On the basis of a thermokinetic description of reaction rates it is here shown that the elasticity coefficients can be calculated directly from the pool levels of metabolites at steady state. The only requirement is that one thermodynamic parameter be known, namely the reaction affinity at the intercept of the tangent in the inflection point of the curve of reaction rate against reaction affinity. This parameter can often be determined from experiments in vitro. The methodology is applicable only to the analysis of simple two-step pathways, but in many cases larger pathways can be lumped into two overall conversions. In cases where this cannot be done it is necessary to apply an extension of the thermokinetic description of reaction rates to include the influence of effectors. Here the reaction rate is written as a linear function of the logarithm of the metabolite concentrations. With this type of rate function it is shown that the approach of Delgado and Liao [Biochem. J. (1992) 282, 919–927] can be much more widely applied, although it was originally based on linearized kinetics. The methodology of determining elasticity coefficients directly from pool levels is illustrated with an analysis of the first two steps of the biosynthetic pathway of penicillin. The results compare well with previous findings based on a kinetic analysis.

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Metabolic Control Analysis of glycolysis in tuber tissue of potato (Solanum tuberosum): explanation for the low control coefficient of phosphofructokinase over respiratory flux

Biochemical Journal ◽

10.1042/bj3220119 ◽

1997 ◽

Vol 322 (1) ◽

pp. 119-127 ◽

Cited By ~ 49

Author(s):

Simon THOMAS ◽

Peter J. F. MOONEY ◽

Michael M. BURRELL ◽

David A. FELL

Keyword(s):

Potato Tuber ◽

Metabolic Control ◽

Kinetic Data ◽

Metabolic Control Analysis ◽

Glycolytic Flux ◽

Control Analysis ◽

Tuber Tissue ◽

Flux Control ◽

Calculated Concentration ◽

Control Coefficients

We have applied Metabolic Control Analysis (MCA) in an attempt to determine the distribution of glycolytic flux control between the steps of glycolysis in aged disks of potato tuber under aerobic conditions, using concentrations of glycolytic metabolites in tuber tissue from a range of transgenic potato plants and published enzyme kinetic data. We modelled the substrate and effector kinetics of potato tuber phosphofructokinase (PFK) by reanalysing published results. Despite the scarcity of reliable kinetic data, our results are in agreement with experimental findings namely that, under the conditions described, PFK has little control over glycolytic flux. Furthermore our analysis predicts that under these conditions far more control lies in the dephosphorylation of phosphoenolpyruvate and/or in the steps beyond. We have validated the results of our analysis in two ways. First, predictions based on calculated concentration control coefficients from the analysis show generally good agreement with observed metabolite deviation indices discussed in the preceding paper [Thomas, Mooney, Burrell, and Fell (1997) Biochem. J.322, 111Ő117]. Second, sensitivity analysis of our results shows that the calculated control coefficients are robust to errors in the elasticities used in the analysis, of which relatively few need to be known accurately. Experimental and control analysis results agree with previous predictions of MCA that strong co-operative feedback inhibition of enzymes serves to move flux control downstream of the inhibiting metabolite. We conclude that MCA can successfully model the outcome of experiments in the genetic manipulation of enzyme amounts.

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Control analysis of photosynthetic sucrose synthesis: assignment of elasticity coefficients and flux-control coefficients to the cytosolic fructose 1,6-bisphosphatase and sucrose phosphate synthase

Philosophical Transactions of the Royal Society of London Series B Biological Sciences ◽

10.1098/rstb.1989.0014 ◽

1989 ◽

Vol 323 (1216) ◽

pp. 327-338 ◽

Cited By ~ 20

Keyword(s):

Sucrose Phosphate Synthase ◽

Control Analysis ◽

Sucrose Synthesis ◽

Flux Control ◽

Fructose 1,6 Bisphosphatase ◽

Flux Control Coefficients ◽

Sucrose Phosphate ◽

Control Coefficients ◽

Phosphate Synthase

The use of elasticity coefficients and flux-control coefficients in a quantitative treatment of control is discussed, with photosynthetic sucrose synthesis as an example. Experimental values for elasticities for the cytosolic fructose 1,6-bisphosphatase and sucrose phosphate synthase are derived from their in vitro properties, and from an analysis of the in vivo relation between fluxes and metabolite levels. An empirical factor α , describing the response of the fructose 2,6-bisphosphate regulator cycle to fructose 6-phosphate is described, and an expression is derived relating α to the elasticities of the enzymes involved in this regulator cycle. The in vivo values for elasticities and α are then used in a modified form of the connectivity theorem to estimate the flux control coefficients of the cytosolic fructose 1,6-bisphosphatase and sucrose phosphate synthase during rapid photosynthetic sucrose synthesis.

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Metabolic Control Analysis: Separable Matrices and Interdependence of Control Coefficients

Journal of Theoretical Biology ◽

10.1006/jtbi.1998.0728 ◽

1998 ◽

Vol 193 (4) ◽

pp. 649-661 ◽

Cited By ~ 8

Author(s):

Ludwig Elsner ◽

Christoph Giersch

Keyword(s):

Metabolic Control ◽

Metabolic Control Analysis ◽

Control Analysis ◽

Control Coefficients

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Metabolic control analysis using transient metabolite concentrations. Determination of metabolite concentration control coefficients

Biochemical Journal ◽

10.1042/bj2850965 ◽

1992 ◽

Vol 285 (3) ◽

pp. 965-972 ◽

Cited By ~ 26

Author(s):

J Delgado ◽

J C Liao

Keyword(s):

Theoretical Basis ◽

Metabolic Control Analysis ◽

Metabolite Concentration ◽

Quasi Equilibrium ◽

Control Analysis ◽

Algebraic Equations ◽

Metabolite Concentrations ◽

Flux Control Coefficients ◽

Control Coefficients

The methodology previously developed for determining the Flux Control Coefficients [Delgado & Liao (1992) Biochem. J. 282, 919-927] is extended to the calculation of metabolite Concentration Control Coefficients. It is shown that the transient metabolite concentrations are related by a few algebraic equations, attributed to mass balance, stoichiometric constraints, quasi-equilibrium or quasi-steady states, and kinetic regulations. The coefficients in these relations can be estimated using linear regression, and can be used to calculate the Control Coefficients. The theoretical basis and two examples are discussed. Although the methodology is derived based on the linear approximation of enzyme kinetics, it yields reasonably good estimates of the Control Coefficients for systems with non-linear kinetics.

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Quantification of the control of carbohydrate catabolism in the tapeworm Hymenolepis diminuta

Biochemistry and Cell Biology ◽

10.1139/o93-048 ◽

1993 ◽

Vol 71 (7-8) ◽

pp. 315-323 ◽

Cited By ~ 4

Author(s):

Wendy Y. Precious ◽

John Barrett

Keyword(s):

Phosphoenolpyruvate Carboxykinase ◽

Glycogen Synthase ◽

Hymenolepis Diminuta ◽

Rate Equations ◽

Control Analysis ◽

Control Coefficient ◽

Flux Control ◽

Flux Control Coefficients ◽

Carbohydrate Catabolism ◽

Control Coefficients

The elasticities for the different steps of carbohydrate catabolism in the tapeworm Hymenolepis diminuta were estimated from perturbation experiments. These data were then used to calculate flux and metabolite control coefficients. Enzyme elasticities were also calculated from the rate equations and an independent estimate of the flux control coefficients for phosphoenolpyruvate carboxykinase was made by inhibitor titration. The values obtained for the flux control coefficients for carbohydrate breakdown in H. diminuta are consistent with how the pathway is thought to be controlled in vivo. A sensitivity analysis of the flux control coefficients of the important regulatory enzymes in the pathway shows that for hexokinase, phosphofructokinase, pyruvate kinase, and phosphoenolpyruvate carboxykinase there are three or four key elasticities which have a significant effect on the coefficient. For glycogen synthase, the major factor in determining the magnitude of the flux control coefficient is the relative flux through the branch.Key words: Hymenolepis diminuta, metabolic control analysis, control coefficient, enzyme elasticity.

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Metabolic flux control analysis of branch points: an improved approach to obtain flux control coefficients from large perturbation data

Metabolic Engineering ◽

10.1016/j.ymben.2004.07.002 ◽

2004 ◽

Vol 6 (4) ◽

pp. 391-400 ◽

Cited By ~ 25

Author(s):

J.J. Heijnen ◽

W.M. van Gulik ◽

H. Shimizu ◽

G. Stephanopoulos

Keyword(s):

Metabolic Flux ◽

Control Analysis ◽

Branch Points ◽

Flux Control ◽

Large Perturbation ◽

Perturbation Data ◽

Flux Control Coefficients ◽

Control Coefficients

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Control analysis of mammalian serine biosynthesis. Feedback inhibition on the final step

Biochemical Journal ◽

10.1042/bj2560097 ◽

1988 ◽

Vol 256 (1) ◽

pp. 97-101 ◽

Cited By ~ 58

Author(s):

D A Fell ◽

K Snell

Keyword(s):

Feedback Inhibition ◽

Intrinsic Value ◽

Normal Diet ◽

Control Analysis ◽

Flux Control ◽

Low Protein ◽

Flux Control Coefficients ◽

Flux Response ◽

Serine Biosynthesis ◽

Control Coefficients

The flux of serine biosynthesis in the liver of the normal rabbit, and of the rat on a low protein diet, is most sensitive to the activity of phosphoserine phosphatase (flux control coefficient up to 0.97), the last of the three enzymes in the pathway after it branches from glycolysis. The concentration of the pathway product, serine, has a strong controlling influence on the flux (response coefficient up to -0.64) through feedback inhibition at this step. The pathway is therefore controlled primarily by the demand for serine rather than the supply of the pathway precursor, 3-phosphoglycerate. Under conditions where there is a lower biosynthetic flux, the flux control coefficients of the first two enzymes of the pathway are increased, and are probably dominant in the rat on a normal diet. In rabbit liver, when ethanol is used to inhibit serine biosynthesis, control can be distributed between the three enzymes, even though the reactions catalysed by the first two remain close to equilibrium. Apart from their intrinsic value in aiding the understanding of the regulation of mammalian serine metabolism, our findings illustrate the danger of assuming that there are invariant design principles in the regulation of metabolic pathways, such as feedback control on the first step after a branch.

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A computer program for the algebraic determination of control coefficients in Metabolic Control Analysis

Biochemical Journal ◽

10.1042/bj2920351 ◽

1993 ◽

Vol 292 (2) ◽

pp. 351-360 ◽

Cited By ~ 7

Author(s):

S Thomas ◽

D A Fell

Keyword(s):

Computer Program ◽

Metabolic Control ◽

Matrix Method ◽

Metabolic Control Analysis ◽

Control Analysis ◽

Point Distribution ◽

Algebraic Expressions ◽

The Matrix ◽

Control Coefficients

A computer program (MetaCon) is described for the evaluation of flux control, concentration control and branch-point distribution control coefficients of a metabolic pathway. Requiring only the reaction scheme as input, the program produces algebraic expressions for the control coefficients in terms of elasticity coefficients, metabolite concentrations and pathway fluxes. Any of these variables can be substituted by numeric or simple algebraic expressions; the expressions will then be automatically rearranged in terms of the remaining unknown variables. When all variables have been substituted, numeric values will be obtained for the control coefficients. The program is a computerized implementation of the matrix method for the determination of control coefficients. The features of MetaCon are compared with those of other programs available to workers in Metabolic Control Analysis. Potential benefits of, and methods of using, MetaCon are discussed. The mathematical background and validity of the matrix method rules are discussed, and the algorithm used by MetaCon is described. The matrix method is shown to be a specific case of a previously described general formalism for calculating control coefficients.

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