Thermodynamics of the control of metabolism

A theory is presented, describing the control analysis of metabolic systems in terms of Gibbs free energies, extending earlier work of Kacser and Burns (25), and Heinrich and Rapoport (29). It is shown that relationships exist between flux control coefficients (the degree to which enzymes control steady-state fluxes) and free-energy elasticity coefficients, defined as the fractional change in the rate of a reaction induced by a standard change in one free-energy difference, while all the other free-energy differences are kept constant. Application of this extended control analysis to some biochemical reactions, including proton translocation, demonstrates that 1. Problems arising in the control analysis because of conservation (sum concentration of substrate and product constant) can be circumvented. 2. Although free-energy elasticity coefficients are maximal when the reaction is close to equilibrium, they can also be significant when the reaction is not close to equilibrium. 3. Problems in the control analysis caused by compartmentation can be resolved by defining control parameters that refer to the organelle as a whole. 4. These latter control parameters obey the above-mentioned relationships.