¹³C metabolic flux analysis (MFA) is typically performed under conditions of metabolic and isotopic steady state, wherein the prevailing reaction fluxes, metabolite pool sizes and the isotopic labeling of those pools have been allowed to fully equilibrate. Instationary metabolic flux analysis (IMFA), on the other hand, involves the introduction of labeled substrate followed by repeated measurements of intracellular label enrichment during the transient period preceding isotopic steady state. Metabolic steady state is maintained throughout the period of label incorporation, so that a single set of reaction fluxes and metabolite concentrations uniquely determines the trajectory of the labeling dynamics. A key advantage of IMFA is its ability to simultaneously extract information on reaction fluxes and metabolite levels from the resulting time-series data, whereas stationary ¹³C MFA only provides information on fluxes. Furthermore, relaxing the requirement for isotopic steady state translates into experiments of shorter duration that consume smaller amounts of labeled substrate in comparison to stationary MFA. This not only reduces the cost of performing tracer experiments but also facilitates work with mammalian systems and especially whole animals, which can be held in a fixed metabolic state for only short periods of time.

It is difficult to extend computational methods based on isotopomer or cumomer balances to the IMFA problem, since they result in a large system of ordinary differential equations (ODE's) which must be solved to simulate the transient response of the network. An alternative method based on a recently developed elementary metabolite unit (EMU) decomposition of the network allows for a reduction in system size by 90% in comparison to the cumomer formulation. This decomposition traces the atom transitions through the network to identify the smallest collection of mass isotopomers that need to be simulated in order to describe the available measurements. An ODE solver has been customized to efficiently handle the cascaded linear systems generated by the EMU treatment. This solver makes use of a partial analytical solution, reducing the integration of ODE's to numerical quadrature. As a result of these developments, computational time can be dramatically reduced such that IMFA is feasible for biochemical reaction networks of realistic size and complexity.

As an illustration of our approach, we report results from applying IMFA to yeast cultures growing on ¹³C labeled glucose. High density fed-batch and chemostat cultures are used to maintain the system at metabolic steady state throughout the course of the experiments. Labeled substrate is introduced by switching the feed glucose from an unlabeled to a labeled supply. Culture samples are withdrawn from the fermentor and quenched immediately using a cold methanol/water solution. The biomass fraction is extracted with a methanol/chloroform/water mixture, and the resulting samples are derivatized to enable analysis by GC/MS. The mass isotopomer distributions of fragments obtained in this manner are used to estimate reaction fluxes and metabolite levels by fitting the IMFA network model to the measurements. Nonlinear statistical methods are applied to characterize the goodness-of-fit and to compute accurate confidence intervals for all estimated parameters.