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Metabolites 2013, 3(4), 946-966; doi:10.3390/metabo3040946

Counting and Correcting Thermodynamically Infeasible Flux Cycles in Genome-Scale Metabolic Networks

1,2, 1, 1, 1,2,3,†,*  and 1,2,†,*
1 Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, Roma 00185, Italy 2 Center for Life Nano Science@Sapienza, Istituto Italiano di Tecnologia, v. Regina Elena 291, Roma 00151, Italy 3 CNR-IPCF, UOS di Roma, Dipartimento di Fisica, Sapienza Universit`a di Roma, Roma 00185, Italy These authors contributed equally to this work.
* Authors to whom correspondence should be addressed.
Received: 6 August 2013 / Revised: 18 September 2013 / Accepted: 24 September 2013 / Published: 14 October 2013
(This article belongs to the Special Issue Data Processing in Metabolomics)
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Thermodynamics constrains the flow of matter in a reaction network to occur through routes along which the Gibbs energy decreases, implying that viable steady-state flux patterns should be void of closed reaction cycles. Identifying and removing cycles in large reaction networks can unfortunately be a highly challenging task from a computational viewpoint. We propose here a method that accomplishes it by combining a relaxation algorithm and a Monte Carlo procedure to detect loops, with ad hoc rules (discussed in detail) to eliminate them. As test cases, we tackle (a) the problem of identifying infeasible cycles in the E. coli metabolic network and (b) the problem of correcting thermodynamic infeasibilities in the Flux-Balance-Analysis solutions for 15 human cell-type-specific metabolic networks. Results for (a) are compared with previous analyses of the same issue, while results for (b) are weighed against alternative methods to retrieve thermodynamically viable flux patterns based on minimizing specific global quantities. Our method, on the one hand, outperforms previous techniques and, on the other, corrects loopy solutions to Flux Balance Analysis. As a byproduct, it also turns out to be able to reveal possible inconsistencies in model reconstructions.
Keywords: thermodynamics; infeasible cycles; genome-scale metabolic networks; flux-balance analysis thermodynamics; infeasible cycles; genome-scale metabolic networks; flux-balance analysis
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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De Martino, D.; Capuani, F.; Mori, M.; De Martino, A.; Marinari, E. Counting and Correcting Thermodynamically Infeasible Flux Cycles in Genome-Scale Metabolic Networks. Metabolites 2013, 3, 946-966.

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