Fluxomers: Efficient New Strategy for 13C Tracer Experiments Analysis

Stoichiometric balance equations provide us with a set of linear constraints describing all the feasible fluxes possible for a given metabolic network. Unfortunately, this set of equations is typically underdetermined, yielding an infinite number of possible values for the metabolic fluxes. In order to estimate the exact value of these fluxes, additional data is required. A variety of experimental procedures have been developed in order to overcome this problem, exposing various hidden features of the metabolic networks. One of these common methods is the $^{13}$C metabolic flux analysis (MFA), in which the isotopic labeling patterns (i.e., isotopomers) of downstream metabolites are measured in response to the introduction of a $^{13}$C-labeled substrate. The traditional mathematical treatment of these experiments uses separate variables representing the fluxes and labeling states of the metabolic system. Unfortunately, analysis of tracer experiments using this set of variables results in a difficult non-convex optimization task, suffering from both implementation complexity and various convergence issues. Furthermore, the error model used by this approach is relaxed in order to ease the optimization process, which detracts from the statistical quality of the results and necessitates estimation of additional measurement normalization factors.

Our work addresses the mathematical and computational problems of tracer experiments analysis using a new set of variables referred to as \emph{fluxomers}. Using fluxomers, a combination of fluxes and isotopomers, several major advantages are obtained: a) the MFA optimization problem can be efficiently solved, b) analysis of incomplete measurement data is possible without the need to estimate additional normalization factors (as required in the traditional approaches), c) there is no need to relax the used error model. A simple yet powerful fluxomers iterative algorithm (FIA) is constructed and implemented in order to solve the MFA optimization problem. The algorithm is shown to outperform the commonly used 13CFLUX algorithm in both convergence time and results variances under different scenarios. The FIA implementation has been developed and published for common usage as an open-source software package in our web-site. This easy-to-use software shows substantial improvements in convergence time and results quality, along with the ability to analyze experiments that were impossible to analyze previously.