Connectivity theorem, metabolic control

Connectivity theorems allow to relate the control coefficients (systemic properties) to the elasticity coefficients (properties of the network s enzymes individually as if in isolation) (Westerhoff and Van Dam 1987 Heinrich and Schuster 1996 Fell 1997). The connectivity theorems have given us a strong insight into the functioning of metabolic pathways. For example, it follows directly from these theorems that enzymes that are very sensitive to the concentrations of metabolites, such as substrates, products and allosteric effectors, tend to have little control over the flux. This is illustrated by overproduction of phosphofructokinase in bakers yeast, an enzyme often referred to textbooks as rate-limiting. Yet, overproduction of phosphofructokinase does not lead to a significant flux increase, since the cell compensates by lowering the level of its allosteric effector fructose 2,6-bisphosphate (Schaaff et al. 1989 Davies and Brindle 1992). 

Kholodenko, B.N., Sauro, H.M. and Westerhoff, H.V. (1994b) Control by enzymes, coenzymes and conserved moieties. A generalisation of the connectivity theorem of metabolic control analysis. Eur. J. Biochem. 225, 179-186. 

The developed control theory for metabolic systems allows inferring of, for example, the effects of local changes, like the properties of an enzyme on global properties as the flux through the system. Furthermore, general global properties of the systems were captured by summation and connectivity theorems, see [5] for a comprehensive review. 

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