  Metabolic fluxes are the rates of life-sustaining chemical reactions within a
cell and metabolites are the components. Determining the changes in these
fluxes is crucial to understanding diseases with metabolic causes and
consequences. Kinetic flux profiling (KFP) is a method for estimating flux that
utilizes data from isotope tracing experiments. In these experiments, the
isotope-labeled nutrient is metabolized through a pathway and integrated into
the downstream metabolite pools. Measurements of proportion labeled for each
metabolite in the pathway are taken at multiple time points and used to fit an
ordinary differential equations model with fluxes as parameters. We begin by
generalizing the process of converting diagrams of metabolic pathways into
mathematical models composed of differential equations and algebraic
constraints. The scaled differential equations for proportions of unlabeled
metabolite contain parameters related to the metabolic fluxes in the pathway.
We investigate flux parameter identifiability given data collected only at the
steady state of the differential equation. Next, we give criteria for valid
parameter estimations in the case of a large separation of timescales with
fast-slow analysis. Bayesian parameter estimation on simulated data from KFP
experiments containing both irreversible and reversible reactions illustrates
the accuracy and reliability of flux estimations. These analyses provide
constraints that serve as guidelines for the design of KFP experiments to
estimate metabolic fluxes.
