The sum of the control coefficients of all enzymes on the flux through a group‐transfer pathway can be as high as two

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Abstract
In simple metabolic pathways the control exerted by enzyme concentrations on the pathway flux adds up to one when the control is quantified in terms of control coefficients. In this paper we demonstrate that this classical summation theorem has to be modified in pathways where the enzymes participate by transferring a group between each other. We derive the corresponding new control theorem and show how it is consistent with standard metabolic control analysis. In group-transfer pathways lacking enzyme complexes, the sum of the flux control by enzyme concentrations and by the donor and acceptor couples of the pathway, equals two. In group-transfer pathways with enzyme-enzyme interactions the flux control by the dissociation rate constants of the enzyme-enzyme complexes must be added to obtain this sum of two. In all cases, the sum of the controls by all reaction activities remains one. Both by using the new theorem and by numerical simulations, we then demonstrate that, in group-transfer pathways with or without enzyme interactions, the sum of the control of enzymes on the pathway flux is higher than one and can reach a value of two. The total control of all enzymes on the concentration of any intermediate either with or without the transferred group can be equal to one, rather than to the zero found in the classical case. Examples of group-transfer pathways are the bacterial phosphoenolpyruvate:sugar phosphotransferase system, the main pathway for uptake of sugars in Enterobacteriaceae, and the electron-transfer chain in free-energy transducing membranes.