  We build a model for the hepatic fatty acid metabolism and its metabolic and
genetic regulations. The model has two functioning modes: synthesis and
oxidation of fatty acids. We provide a sufficient condition (the strong
lipolytic condition) for the uniqueness of its equilibrium. Under this
condition, modifications of the glucose input produce equilibrium shifts, which
are gradual changes from one functioning mode to the other. We also discuss the
concentration variations of various metabolites during equilibrium shifts. The
model can explain a certain amount of experimental observations, assess the
role of poly-unsaturated fatty acids in genetic regulation, and predict the
behavior of mutants. The analysis of the model is based on block elimination of
variables and uses a modular decomposition of the system dictated by
mathematical global univalence conditions.
