(484c) Simultaneous Estimation of Reaction Fluxes and Metabolite Levels Using Instationary 13C Metabolic Flux Analysis

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.