Sampling-Based Methods for the Analysis of Isotopomer Labeling Experiments

In constraint-based modeling, the chemical reactions and processes of the metabolism are formalized in terms of their stoichiometries. The operational state of metabolism is formalized via the flux distribution, which describes the rates of the stoichiometric conversions. Basic constraints can be applied to restrict the set of flux distributions which are feasible. The aim of metabolic flux analysis is to identify the flux distribution quantitatively, by combining constraint-based modeling with experimental data.

We provide new theoretical and practical results regarding the parametrization of the set of feasible flux distributions: we (i) formalize the concept of futile cycling and show how to separately parametrize futile cycling fluxes, (ii) we use this result to derive a parametrization with bounded domain space. We further present efficient MCMC-based sampling methods to sample from the domain space of this parametrization. We use these results for the statistical analysis of experimental data which contains information on the flux distribution.

We apply the developed methods to evaluate data from isotopomer labeling experiments. We provide examples which illustrate the necessity of sampling-based methods. We systematically analyze the information gain resulting from mass distribution measurements. We further show how the information gain depends on both the uncertainty in the measured data as well as on the uncertainty in the computation of the mass distributions, i.e. in the forward simulation.