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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.


Marginal probability densities of nine fluxes of the red blood cell.The blue bars represent the result of Monte Carlo estimate for T ∼108 sampling points. The cyan line is the result of the non-adaptive Gaussian approximation while the red line represents the EP estimate.
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f1: Marginal probability densities of nine fluxes of the red blood cell.The blue bars represent the result of Monte Carlo estimate for T ∼108 sampling points. The cyan line is the result of the non-adaptive Gaussian approximation while the red line represents the EP estimate.

Mentions: Notice that in this approximation fluxes result unbounded. Marginals obtained by this strategy against the HR Monte Carlo estimate are shown in Fig. 1 (cyan line) for nine representative metabolic fluxes of one of the standard model for red blood cell25. Marginals evaluated with this simple non-adaptive strategy differ significantly from the ones evaluated with the Monte Carlo sampling technique. In the following, we will show how we can overcome this limitation by choosing different values for the means a and the variances d in equation (10) making use of the EP algorithm.


An analytic approximation of the feasible space of metabolic networks
Marginal probability densities of nine fluxes of the red blood cell.The blue bars represent the result of Monte Carlo estimate for T ∼108 sampling points. The cyan line is the result of the non-adaptive Gaussian approximation while the red line represents the EP estimate.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Marginal probability densities of nine fluxes of the red blood cell.The blue bars represent the result of Monte Carlo estimate for T ∼108 sampling points. The cyan line is the result of the non-adaptive Gaussian approximation while the red line represents the EP estimate.
Mentions: Notice that in this approximation fluxes result unbounded. Marginals obtained by this strategy against the HR Monte Carlo estimate are shown in Fig. 1 (cyan line) for nine representative metabolic fluxes of one of the standard model for red blood cell25. Marginals evaluated with this simple non-adaptive strategy differ significantly from the ones evaluated with the Monte Carlo sampling technique. In the following, we will show how we can overcome this limitation by choosing different values for the means a and the variances d in equation (10) making use of the EP algorithm.

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.