Theory of production rate calculations in steady and non-steady states and its application to glucose metabolism

I present a review and synthesis of the basic theory, steady state, and non-steady state for the calculation of metabolite production rates for systems that have a central well-mixed compartment that is the site of tracer input and sampling. The theory is then applied to the calculation of glucose production. If the only inputs are into the central compartment, an experimental design that involves varying tracer infusion rates to maintain constant specific activity in the central compartment and the same constant specific activity in the peripheral compartments allows calculation of the endogenous production. That holds even if the models are unidentifiable. The correct equation and Steele's pool fraction approximation reduce to the same result for this experimental design. However, that does not justify the use of Steele's equation when there are deviations from the exact experimental design. When the specific activity in the central compartment is not constant, model-dependent correction terms to Steele's equation are needed.