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Control analysis provides a simple means of understanding the control structure of a metabolic pathway.

In a recent paper, Crabtree & Newsholme (1987) present a method for deriving control coefficients which is based on a somewhat different approach from that proposed by Kacser & Burns (1973) and Heinrich & Rapoport (1974). We wish to comment on several important points raised by Crabtree & Newsholme (1987). Crabtree & Newsholme (1987) conclude that knowledge of the values of flux control coefficients of enzymes in a specific steady state does not provide much information about the control structure of a metabolic pathway. We agree completely. It is hazardous to conclude that external control of pathway flux must be exerted via a step with a high flux control coefficient. An example of an erroneous interpretation of this nature can be found in a recent paper of Pryor et al. (1987). They conclude that flux control of the gluconeogenic pathway by the respiratory chain must be exerted via pyruvate carboxylase because this is the step with the highest flux control coefficient. This could be the case in the presence of glucagon, when pyruvate kinase is inhibited. However, in the absence of the hormone the gluconeogenic pathway is branched and flux is very sensitively controlled via pyruvate kinase (Groen et al., 1986). Although this enzyme has a relatively low flux control coefficient it plays an important role in controlling gluconeogenic flux via its very high elasticity coefficient towards phosphoenolpyruvate, i.e. a small change in the phosphoenolpyruvate concentration has a large effect on pyruvate kinase flux and hence gluconeogenic flux. Therefore all steps that have a signficant concentration control coefficient on cytosolic phosphoenolpyruvate (for instance the respiratory chain) also control gluconeogenic flux [see Groen et al. (1986) for a discussion of how the respiratory chain can control the phosphoenolpvruvate concentration]. This demonstrates nicely that not only flux or concentration control coefficients but also elasticity coefficients are important for understanding the control structure of a metabolic pathway. Indeed the elasticity coefficients generate the control coefficients (for a discussion see Kacser & Burns, 1979). We have shown that the elasticity coefficients of most enzymes can be calculated relatively simply from enzyme kinetic data and the value of the ratio between the mass action ratio and the equilibrium constant (F/Keq.) (Groen et al., 1982). In the absence of enzyme kinetic data, elasticity coefficients can be determined experimentally (Kacser & Burns, 1973, 1979; Groen et al., 1982; Salter et al., 1986). Calculation of flux control coefficients and concentration control coefficients from the elasticity coefficients and the flux distribution through the pathway has become very simple since the development of the matrix method (Fell & Sauro, 1985; Sauro et al., 1987; Westerhoff & Kell, 1987). We agree with Crabtree & Newsholme (1987) that the use of the summation theorem in this method imposes the risk of missing as yet unknown steps. Therefore the flux control coefficient of at least one step in the pathway should be determined directly, for instance by using a wellcharacterized effector of enzyme activity (Groen et al., 1982). Crabtree & Newsholme (1987) repeatedly claim that we have failed to do so in our study on control of gluconeogenesis. This must be a misunderstanding. In our paper we explicitly discussed the danger of using the summation theorem (Groen et al., 1986). In order to check the calculated values of the flux control coefficients of the gluconeogenic enzymes we measured the combined flux control coefficient of the enzymes located between pyruvate and phosphoenolpyruvate directly by varying the external substrate pyruvate. Excellent agreement was observed between calculated and measured values. In an earlier study we determined the flux control coefficient of phosphoenolpyruvate carboxykinase using published data on the effect of mercaptopicolinic acid on gluconeogenic flux (Groen et al., 1982). Also in this case there was good agreement between measured and calculated values. Crabtree & Newsholme (1987) suggest that quantification of control does not provide much information about the control structure of a metabolic pathway, since the values obtained apply only under one particular set of conditions. This is, of course, the case. We also agree with Crabtree & Newsholme (1987) that the absolute values of control coefficients are not important because they hold only for one steady state. However, Crabtree & Newsholme (1987) are in error in suggesting that determination of the control distribution in one steady state does not allow one to predict what will happen under other conditions. If the values for the elasticity coefficients of the enzymes in a pathway under certain conditions are known, it is in general not difficult to predict what will happen to these values under other conditions. This also applies to the effect of external effectors. For instance, when flux through a pathway increases, the elasticity coefficients of most non-equilibrium enzymes to their substrate(s) will decrease. This can have a profound but predictable influence on the distribution of control. Since it is now very simple to calculate values for flux control coefficients and concentration control coefficients from the elasticity coefficients, it has also become easy to simulate the influence of changes in the values of elasticity coefficients on the distribution of control in a pathway. In conclusion, control analysis, if applied in the correct way does, indeed, provide a simple and convenient means of establishing the control structure of a metabolic pathway.