Flux control coefficient

In both intermediate and maximum rates of respiration, control is distributed between several different steps, including the activity of the adenine nucleotide translocator (Groen et al., 1983). It is now recognized that the idea of a simple rate-limiting step for a metabolic pathway is simplistic and that control is shared by all steps although to different extents (Kacserand Bums, 1978 Fell, 1992). Each step in a pathway has a flux control coefficient (FCC) defined as ... 

Metabolic control analysis (MCA) assigns a flux control coefficient (FCC) to each step in the pathway and considers the sum of the coefficients. Competing pathway components may have negative FCCs. To measure FCCs, a variety of experimental techniques including radio isotopomers and pulse chase experiments are necessary in a tissue culture system. Perturbation of the system, for example, with over-expression of various genes can be applied iteratively to understand and optimize product accumulation. 

Correspondingly, the normalized flux control coefficient CJ is defined as... 

For a lucid account of the kinetics of multi-enzyme systems, the reader should consult Cornish-Bowden who defines such related parameters as flux control coefficients, summation relationships, and response coefficients. 

The formalized application of metabolic control analysis deals with several parameters (a) The flux control coefficient is defined as the fractional change in pathway flux... 

Quantitative data obtained as described in Figure 15-33 can be used to calculate a flux control coefficient,... 

C, for each enzyme in a pathway. This coefficient expresses the relative contribution of each enzyme to setting the rate at which metabolites flow through the pathway—that is, the flux, J. C can have any value from 0.0 (for an enzyme with no impact on the flux) to 1.0 (for an enzyme that wholly determines the flux). An enzyme can also have a negative flux control coefficient. In a branched pathway, an enzyme in one branch, by drawing intermediates away from the other branch, can have a negative impact on the flux through that other branch (Fig. 15-34). C is not a constant, and it is not... 

FIGURE 15-34 Flux control coefficient, C, in a branched metabolic pathway. In this simple pathway, the intermediate B has two alternative fates. To the extent that reaction B —> E draws B away from the pathway A —> D, it controls that pathway, which will result in a negative flux control coefficient for the enzyme that catalyzes step B —> E. Note that the sum of all four coefficients equals 1.0, as it must. 

When real data from the experiment on glycolysis in a rat liver extract (Fig. 15-33) were subjected to this kind of analysis, investigators found flux control coefficients (for enzymes at the concentrations found in the extract) of 0.79 for hexoldnase, 0.21 for PFK-1, and 0.0 for phosphohexose isomerase. It is not just fortuitous that these values add up to 1.0 we can show that for any complete pathway, the sum of the flux control coefficients must equal unity. 

FIGURE 2 The flux control coefficient, (a) Typical variation of the pathway flux, )ymeasured at the step catalyzed by the enzyme ydh, as a function of the amount of the enzyme xase, xase, which catalyzes an earlier step in the pathway. The flux control coefficient at (e,j) is the slope of the product of the tangent to the curve, d/ydh/3 xase/ and the ratio (scaling factor), e/j. (b) On a double-logarithmic plot of the same curve, the flux control coefficient is the slope of the tangent to the curve. 

The flux control coefficient, C, is an experimentally determined measure of the effect of an enzyme s concentration on flux through a multienzyme pathway. It is characteristic of the whole system, not intrinsic to the enzyme. 

Report of the experimental determination of the flux control coefficients for glucokinase and the glucokinase regulatory protein in hepatocytes. 

The Flux Summation Theorem states that the sum of all the flux control coefficients of any pathway is equal to unity ... 

In linear pathways, individual flux control coefficient will normally lie between zero (no control) and 1 (full control). But in branched pathways, negative flux control coefficients arise where the stimulation of an enzyme in one branch may decrease the flux through a competing branch. This gives rise to values greater than 1 occurring in that pathway. 

The Connectivity Theorem states that the flux control coefficient and elasticity are related, that is,... 

The increasing availability of mutant and transgenic plants now facilitates the study of how plant metabolism is controlled. In particular, control analysis involves asking how much a flux changes for a given change in enzyme activity, such that the flux control coefficient. 

Kruckeberg, A. L., Neuhaus, H. E., Feil, R.. Gottlieb, L. D., and Stitt, M. 1989. Decreased-activity mutants of phosphoglucose isomerase in the cytosol and chloroplast of Clarkia xantiana Impact on mass-action ratios and fluxes to sucrose and starch and estimation of flux control coefficients and elasticity coefficients. Biochem. J. 261, 457-467. 

One of the many important consequences of these summation theorems is that, in the case where all flux control coefficients are positive, all coefficients have values between 0 and 1. In this case, the reaction for which C,1 is greatest represents the reaction to which the flux Jj is most sensitive. In the limit that one flux control coefficient has a value close to 1 and all others have values close to 0, we can say that there exists a rate-limiting step a change in activity of the rate-limiting enzyme would be expected to elicit a proportional change in the flux Jj. 

Finally, the steady state fluxes J, stoichiometric matrix S, and flux control coefficient matrix C satisfy... 

The effect of a change of the activity of an enzyme i on the steady-state flux J is quantified by the corresponding flux control coefficient Cj. Cf is the percentage change of the flux J upon a 1% change of the enzyme activity v,- causing the change of the flux. Or, in more precise mathematical terms ... 

In simple metabolic pathways, with only one independent flux, the value of Cj is usually between zero and 1. Partial inhibition of an enzyme with zero flux control does not affect the flux, while an enzyme with a flux control coefficient of 1 is completely rate-limiting. Flux control coefficients between 0 and 1 have often been found (Groen et al. 1982 Ruijter et al. 1991 Snoep et al. 1996). In ideal metabolic pathways, for example, in the absence of metabolite channelling and coenzyme sequestration (Kholodenko et al. 1995), the sum of the flux control coefficients of all enzymes in the pathway must equal 1 ... 

It has been demonstrated that for a given flux the sum of its flux-control coefficients of all steps in the metabolic network obeys the theorem [Heinrich and Rapoport 1974 Giersch 1988 Reder 1988] ... 

The connectivity theorems are another important feature of MCA. Through these theorems, one can relate the control coefficients to the elasticity coefficients. The connectivity theorem for flux-control coefficients states that, for a common metabolite S, the sum of the products of the flux-control coefficient of all (i) steps affected by S and its elasticity coefficients toward S, is zero [Kacser, Bums, and Davies 1973],... 

The Kacser—Burns approach has been used in the analysis of starch synthesis by mutants of Arabidopsis thaliana that studied leaf ADP-Glc PPase, and the significance of 3-PGA regulation in vivo A. thaliana mutant strains containing only 7% of the wild-type activity of ADP-Glc PPase and a hybrid of mutant and wild type with 50% activity, had 10% and 61% of the wild type s starch synthetic rate, respectively, at high light intensity. This is a fairly good correlation between the activity of the ADP-Glc PPase and the rate of synthesis of starch. The flux control coefficient was determined to be 0.64. 

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