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An analytic approximation of the feasible space of metabolic networks

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ABSTRACT

Assuming a steady-state condition within a cell, metabolic fluxes satisfy an underdetermined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with linear programming (as flux balance analysis), and their marginal distributions can be approximately computed with Monte Carlo sampling. Here we present an approximate analytic method for the latter task based on expectation propagation equations that does not involve sampling and can achieve much better predictions than other existing analytic methods. The method is iterative, and its computation time is dominated by one matrix inversion per iteration. With respect to sampling, we show through extensive simulation that it has some advantages including computation time, and the ability to efficiently fix empirically estimated distributions of fluxes.

No MeSH data available.


Results for a constrained biomass flux.Comparison between the means (a) and variances (b) of the marginal probability densities for all the fluxes computed without the additional constraint (unconstrained case) and with the constrained on the biomass (constrained case). The green point indicates the biomass flux.
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f3: Results for a constrained biomass flux.Comparison between the means (a) and variances (b) of the marginal probability densities for all the fluxes computed without the additional constraint (unconstrained case) and with the constrained on the biomass (constrained case). The green point indicates the biomass flux.

Mentions: We have tested this variant of EP algorithm on the iJR904 model of E. coli for a constrained growth rate. In fact, one of the few fluxes that are experimentally accessible is the biomass flux, often measured in terms of doubling per hour. As a matter of example, we decide to extract one of the growth rates reported in Fig. 3a of ref. 34; the profile labelled as Glc (P5-ori) can be well fitted by a Gaussian probability density of mean 0.92 h−1 and variance 0.0324, h−2. This curve represent single-cell measures of a population of bacteria living in the so-called minimal substrate whose main characteristics are in principle well caught by the iJR904 model. We fixed the bound on the glucose exchange flux EX_glc(e) such that the maximum allowed growth rate (about 2 h−1) contained all experimental values in the profile labelled as Glc (P5-ori) of Fig. 3a of ref. 34. This was easily computed by fixing the biomass flux to the desired value and minimizing the glucose exchange flux using FBA, and gies a the lower bound of the exchanged glucose flux of −43 mmol (g[DW])−1 h−1.


An analytic approximation of the feasible space of metabolic networks
Results for a constrained biomass flux.Comparison between the means (a) and variances (b) of the marginal probability densities for all the fluxes computed without the additional constraint (unconstrained case) and with the constrained on the biomass (constrained case). The green point indicates the biomass flux.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5384209&req=5

f3: Results for a constrained biomass flux.Comparison between the means (a) and variances (b) of the marginal probability densities for all the fluxes computed without the additional constraint (unconstrained case) and with the constrained on the biomass (constrained case). The green point indicates the biomass flux.
Mentions: We have tested this variant of EP algorithm on the iJR904 model of E. coli for a constrained growth rate. In fact, one of the few fluxes that are experimentally accessible is the biomass flux, often measured in terms of doubling per hour. As a matter of example, we decide to extract one of the growth rates reported in Fig. 3a of ref. 34; the profile labelled as Glc (P5-ori) can be well fitted by a Gaussian probability density of mean 0.92 h−1 and variance 0.0324, h−2. This curve represent single-cell measures of a population of bacteria living in the so-called minimal substrate whose main characteristics are in principle well caught by the iJR904 model. We fixed the bound on the glucose exchange flux EX_glc(e) such that the maximum allowed growth rate (about 2 h−1) contained all experimental values in the profile labelled as Glc (P5-ori) of Fig. 3a of ref. 34. This was easily computed by fixing the biomass flux to the desired value and minimizing the glucose exchange flux using FBA, and gies a the lower bound of the exchanged glucose flux of −43 mmol (g[DW])−1 h−1.

View Article: PubMed Central - PubMed

ABSTRACT

Assuming a steady-state condition within a cell, metabolic fluxes satisfy an underdetermined linear system of stoichiometric equations. Characterizing the space of fluxes that satisfy such equations along with given bounds (and possibly additional relevant constraints) is considered of utmost importance for the understanding of cellular metabolism. Extreme values for each individual flux can be computed with linear programming (as flux balance analysis), and their marginal distributions can be approximately computed with Monte Carlo sampling. Here we present an approximate analytic method for the latter task based on expectation propagation equations that does not involve sampling and can achieve much better predictions than other existing analytic methods. The method is iterative, and its computation time is dominated by one matrix inversion per iteration. With respect to sampling, we show through extensive simulation that it has some advantages including computation time, and the ability to efficiently fix empirically estimated distributions of fluxes.

No MeSH data available.