Modeling framework for isotopic labeling of heteronuclear moieties

Mark I Borkum,Ronald C Taylor,Nancy G Isern,Patrick N Reardon

doi:10.1186/s13321-017-0201-7

Mark I Borkum, Ronald C Taylor + Show 2 more

Open Access

https://doi.org/10.1186/s13321-017-0201-7

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Abstract

BackgroundIsotopic labeling is an analytic technique that is used to track the movement of isotopes through reaction networks. In general, the applicability of isotopic labeling techniques is limited to the investigation of reaction networks that consider homonuclear moieties, whose atoms are of one tracer element with two isotopes, distinguished by the presence of one additional neutron.ResultsThis article presents a reformulation of the modeling framework for isotopic labeling, generalized to arbitrarily large, heteronuclear moieties, arbitrary numbers of isotopic tracer elements, and arbitrary numbers of isotopes per element, distinguished by arbitrary numbers of additional neutrons.ConclusionsWith this work, it is now possible to simulate the isotopic labeling states of metabolites in completely arbitrary biochemical reaction networks.

Highlights

Isotopic labeling is an analytic technique that is used to track the movement of isotopes through reaction networks
The applicability of isotopic labeling techniques is limited to the investigation of reaction networks that consider homonuclear moieties, whose atoms are of one isotopic tracer element with two isotopes, distinguished by the presence of one additional neutron
Representing isotopic labeling states of carbon atoms in backbones of metabolites as vectors of placeholder variables, which they referred to as “cumomers”, using 1 and x to denote, respectively, determinate (13C-labeled) and indeterminate (12C-unlabeled or 13C-labeled) isotopic labeling states, with a total ordering given by x < 1, they showed that Malloy et al.’s construction could be reformulated as a cascade system of linear functions of relative abundances of cumomers, which they referred to as “cumomer fractions,” with the original construction being recovered via a “suitable variable transformation” [2, Eq 7] in the form of an invertible square matrix

Summary

Results

Definitions The indeterminacy which still prevails on a number of fundamental points in the theory of isotopic labeling compels us to make some prefatory remarks about the concept of an isotopic labeling state and the scope of its validity. We have shown that the EMU method can be “done” because the function that interprets a set of isotopic atoms (with determinate isotopic labeling states) as a mass distribution is a homomorphism, and because the set of mass distributions is a commutative monoid (when sets of isotopic atoms are pairwise disjoint) From this new perspective, the cumomer method can be “done” for two reasons: because cumomer fraction vectors are a valid codomain of the homomorphism and EMU-based flux balance equations can be transformed into cumomer-based flux balance equations by elementary algebraic manipulations: replacement of flux variable coefficients by coefficient matrices; transposition of row vectors and subsequent construction of a block column vector; and, permutation of rows and columns. What are the “translations” of laminar flow and friction? can a biological reaction network be embedded in an arbitrary manifold, thereby allowing the model to account for the spatial characteristics of the compartment?

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