Abstract
BackgroundWhen studying metabolism at the organ level, a major challenge is to understand the matter exchanges between the input and output components of the system. For example, in nutrition, biochemical models have been developed to study the metabolism of the mammary gland in relation to the synthesis of milk components. These models were designed to account for the quantitative constraints observed on inputs and outputs of the system. In these models, a compatible flux distribution is first selected. Alternatively, an infinite family of compatible set of flux rates may have to be studied when the constraints raised by observations are insufficient to identify a single flux distribution. The precursors of output nutrients are traced back with analyses similar to the computation of yield rates. However, the computation of the quantitative contributions of precursors may lack precision, mainly because some precursors are involved in the composition of several nutrients and because some metabolites are cycled in loops.ResultsWe formally modeled the quantitative allocation of input nutrients among the branches of the metabolic network (AIO). It corresponds to yield information which, if standardized across all the outputs of the system, allows a precise quantitative understanding of their precursors. By solving nonlinear optimization problems, we introduced a method to study the variability of AIO coefficients when parsing the space of flux distributions that are compatible with both model stoichiometry and experimental data. Applied to a model of the metabolism of the mammary gland, our method made it possible to distinguish the effects of different nutritional treatments, although it cannot be proved that the mammary gland optimizes a specific linear combination of flux variables, including those based on energy. Altogether, our study indicated that the mammary gland possesses considerable metabolic flexibility.ConclusionOur method enables to study the variability of a metabolic network with respect to efficiency (i.e. yield rates). It allows a quantitative comparison of the respective contributions of precursors to the production of a set of nutrients by a metabolic network, regardless of the choice of the flux distribution within the different branches of the network.
Highlights
When studying metabolism at the organ level, a major challenge is to understand the matter exchanges between the input and output components of the system
We first investigated the set of flux distributions that are compatible with the stoichiometry of our mammary gland model, without taking datasets into account
They include a control diet (Ctrl), a diet related to an increased protein supply through casein infusion into the duodenum (CN), and a complementary dataset (HB) previously used in a mechanistic model of the mammary metabolism [21]
Summary
When studying metabolism at the organ level, a major challenge is to understand the matter exchanges between the input and output components of the system. In nutrition, biochemical models have been developed to study the metabolism of the mammary gland in relation to the synthesis of milk components These models were designed to account for the quantitative constraints observed on inputs and outputs of the system. The methods developed in this field aim to explore a convex space of plausible flux distributions and to study the extreme flux distributions obtained when optimizing a linear objective function. It allows checking whether an extreme flux distribution is consistent with experimental data and to predict new experimental observations [5,6,7,8]. In flux variability analysis [11], the minimum and the maximum flux for each reaction in the network are computed under some (sub-)optimal conditions
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