Energy expenditure in the control of biochemical systems by covalent modification

Regulation by reversible, covalent modification of proteins requires a continuous expenditure of energy, even in a steady-state situation. The cost of this energy drain is evaluated for the case of an effector controlling the modifying enzyme and an effector controlling the demodifying enzyme and for the case of dual control in which an effector activates one of these enzymes and inhibits the other. Energy consumption is determined when the converter enzymes are functioning in the first-order and zero-order domains. The profile of energy expenditure versus fractional protein modification at steady state varies both as a function of the mechanism of control of the converter enzymes and of the kinetic domain in which they operate. This theory allows one to predict the strategies that would minimize energy costs. Dual control appears to provide maximum sensitivity with minimal energy expenditure. The analysis is applied to two experimental systems. Comparison of ATP turnover rates with rates for individual modification enzymes in living systems shows that a significant fraction of the total energy expenditure of an organism is required for the large number of reactions which involve covalent modification of proteins. It is concluded that there will be selection pressure for energy-efficient control of covalent regulation.