Bayesian stationary state flux balance analysis for a skeletal muscle metabolic model

Cellular metabolism can be modelled as a multi-compartment dynamical system, the compartments representing the circulatory system consisting of blood and interstitial fluid, and different subcellular structures. The inverse problem in cellular metabolism is to obtain information about the state of the system based on few measured concentrations of metabolites or intermediates either in the blood or in the tissue. In this article, we first discuss a new three compartment metabolic model for human skeletal muscle metabolism and the corresponding inverse problem of determining the metabolic reaction and transport rates given blood concentration data under sustained exercise. We introduce the concept of a metabolic stationary state, describe a Bayesian methodology to analyze it and apply it to study the stationary state of human leg skeletal muscles under exercise. Our analysis demonstrates that the system is fairly well identified if the concentrations of certain species in the blood are known, and that the lack of oxygen concentration data can be replaced by prescribing either the ATP hydrolysis level or the glycogen depletion rate.