Consequences of detailed balance in a model for sensory adaptation based on ligand-induced receptor modification

A model for exact sensory adaptation has been published by Segel and co-workers in several papers [e.g., Knox, B. E., Devreotes, P. N., Goldbeter, A. & Segel, L. A. (1986) Proc. Natl. Acad. Sci. USA 83, 2345-2349]. The model comprises a pair of states whose relative probabilities are determined by the binding of a ligand. A second pair of states related by the same ligand binding is accessible as a consequence of either a conformational change or a "covalent modification." By taking proper account of detailed balance, we show that the notion of covalent modification in this context includes three cases, two of which involve dissipation of metabolic energy. The condition for exact adaptation is dependent on metabolite concentrations in all cases of covalent modification. The performance of the model is critically examined on thermodynamic and kinetic grounds.