Limits...
An analytic approximation of the feasible space of metabolic networks

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.


Comparison of the results of HR versus EP.HR vs. EP prediction for three large-scale metabolic reconstructions: iJR904 (a), CHOLnorm (b), and RECON1 models (c). The top-left plot shows the Pearson correlation coefficients between variances and means estimated through EP and HR. The bottom-left panel reports the computing time of EP and HR for different values of T. The plots on the right are scatter plots of the means and variances of the approximated marginals computed via EP against the ones estimated via HR for an increasing number of explored configurations T.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC5384209&req=5

f2: Comparison of the results of HR versus EP.HR vs. EP prediction for three large-scale metabolic reconstructions: iJR904 (a), CHOLnorm (b), and RECON1 models (c). The top-left plot shows the Pearson correlation coefficients between variances and means estimated through EP and HR. The bottom-left panel reports the computing time of EP and HR for different values of T. The plots on the right are scatter plots of the means and variances of the approximated marginals computed via EP against the ones estimated via HR for an increasing number of explored configurations T.

Mentions: The three large subplots in Fig. 2 show the results for E. coli, C. neuron and Homo sapiens, respectively. For each organism, we report on the top-left panel the time spent by EP (straight line) and by HR (cyan points) and on the bottom-left panel the Pearson correlation coefficients. Both measures of time and correlation are plotted as functions of the number of configuration T obtained from the HR algorithm. As shown in these plots, we can notice that to reach a high correlation regime a very large number of explored configurations, employing a computing time that is always several orders of magnitude larger than the EP running time. This is particularly strinking in the case of the RECON1 model, for which we needed to run HR for about 20 days in order to reach results similar to the outcomes of EP, that converges in less than 1 h on the same machine.


An analytic approximation of the feasible space of metabolic networks
Comparison of the results of HR versus EP.HR vs. EP prediction for three large-scale metabolic reconstructions: iJR904 (a), CHOLnorm (b), and RECON1 models (c). The top-left plot shows the Pearson correlation coefficients between variances and means estimated through EP and HR. The bottom-left panel reports the computing time of EP and HR for different values of T. The plots on the right are scatter plots of the means and variances of the approximated marginals computed via EP against the ones estimated via HR for an increasing number of explored configurations T.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: Comparison of the results of HR versus EP.HR vs. EP prediction for three large-scale metabolic reconstructions: iJR904 (a), CHOLnorm (b), and RECON1 models (c). The top-left plot shows the Pearson correlation coefficients between variances and means estimated through EP and HR. The bottom-left panel reports the computing time of EP and HR for different values of T. The plots on the right are scatter plots of the means and variances of the approximated marginals computed via EP against the ones estimated via HR for an increasing number of explored configurations T.
Mentions: The three large subplots in Fig. 2 show the results for E. coli, C. neuron and Homo sapiens, respectively. For each organism, we report on the top-left panel the time spent by EP (straight line) and by HR (cyan points) and on the bottom-left panel the Pearson correlation coefficients. Both measures of time and correlation are plotted as functions of the number of configuration T obtained from the HR algorithm. As shown in these plots, we can notice that to reach a high correlation regime a very large number of explored configurations, employing a computing time that is always several orders of magnitude larger than the EP running time. This is particularly strinking in the case of the RECON1 model, for which we needed to run HR for about 20 days in order to reach results similar to the outcomes of EP, that converges in less than 1 h on the same machine.

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.