On the analysis of substrate cycles in large metabolic systems.

The simultaneous operation of paired, opposing reactions (substrate cycles) or parallel reactions (dual pathways) with seeming wastage of ATP is widespread in cellular metabolism. Analysis of such "futile" pathways has hitherto been limited to loci with only two or three interconnecting fluxes. We introduce here a method that allows straightforward analysis of more complex systems. The method involves the linear superposition of "fundamental" modes, one or more of which may be energetically wasteful. Decomposition of a flux pattern into such modes allows computation of the amount of free energy "wasted" at any locus. Appropriate normalizations of energy wastage yield a number of indices useful for assessing the energetic impact of futile pathways on the cell and for comparing the degree of regulation of substrate cycles or dual pathways under different metabolic conditions. This approach is applied to steady-state flux data obtained in the protozoan Tetrahymena pyriformis and in isolated rat hepatocytes under a variety of conditions.