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DOI: 10.4230/LIPIcs.WABI.2018.1

A Duality-Based Method for Identifying Elemental Balance Violations in Metabolic Network Models

Authors: Hooman Zabeti, Tamon Stephen, Bonnie Berger, and Leonid Chindelevitch

Published in: LIPIcs, Volume 113, 18th International Workshop on Algorithms in Bioinformatics (WABI 2018)

Abstract

Elemental balance, the property of having the same number of each type of atom on both sides of the equation, is a fundamental feature of chemical reactions. In metabolic network models, this property is typically verified on a reaction-by-reaction basis. In this paper we show how violations of elemental balance can be efficiently detected in an entire network, without the need for specifying the chemical formula of each of the metabolites, which enhances a modeler's ability to automatically verify that their model satisfies elemental balance. Our method makes use of duality theory, linear programming, and mixed integer linear programming, and runs efficiently on genome-scale metabolic networks (GSMNs). We detect elemental balance violations in 40 out of 84 metabolic network models in the BiGG database. We also identify a short list of reactions that are candidates for being elementally imbalanced. Out of these candidates, nearly half turn out to be truly imbalanced reactions, and the rest can be seen as witnesses of elemental balance violations elsewhere in the network. The majority of these violations involve a proton imbalance, a known challenge of metabolic network reconstruction. Our approach is efficient, easy to use and powerful. It can be helpful to metabolic network modelers during model verification. Our methods are fully integrated into the MONGOOSE software suite and are available at https://github.com/WGS-TB/MongooseGUI3.

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Hooman Zabeti, Tamon Stephen, Bonnie Berger, and Leonid Chindelevitch. A Duality-Based Method for Identifying Elemental Balance Violations in Metabolic Network Models. In 18th International Workshop on Algorithms in Bioinformatics (WABI 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 113, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{zabeti_et_al:LIPIcs.WABI.2018.1,
  author =	{Zabeti, Hooman and Stephen, Tamon and Berger, Bonnie and Chindelevitch, Leonid},
  title =	{{A Duality-Based Method for Identifying Elemental Balance Violations in Metabolic Network Models}},
  booktitle =	{18th International Workshop on Algorithms in Bioinformatics (WABI 2018)},
  pages =	{1:1--1:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-082-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{113},
  editor =	{Parida, Laxmi and Ukkonen, Esko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2018.1},
  URN =		{urn:nbn:de:0030-drops-93034},
  doi =		{10.4230/LIPIcs.WABI.2018.1},
  annote =	{Keywords: Metabolic network analysis, elemental imbalance, linear programming, model verification}
}

Document

DOI: 10.4230/LIPIcs.SEA.2018.6

Speeding up Dualization in the Fredman-Khachiyan Algorithm B

Authors: Nafiseh Sedaghat, Tamon Stephen, and Leonid Chindelevitch

Published in: LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

Abstract

The problem of computing the dual of a monotone Boolean function f is a fundamental problem in theoretical computer science with numerous applications. The related problem of duality testing (given two monotone Boolean functions f and g, declare that they are dual or provide a certificate that shows they are not) has a complexity that is not yet known. However, two quasi-polynomial time algorithms for it, often referred to as FK-A and FK-B, were proposed by Fredman and Khachiyan in 1996, with the latter having a better complexity guarantee. These can be naturally used as a subroutine in computing the dual of f. In this paper, we investigate this use of the FK-B algorithm for the computation of the dual of a monotone Boolean function, and present practical improvements to its performance. First, we show how FK-B can be modified to produce multiple certificates (Boolean vectors on which the functions defined by the original f and the current dual g do not provide outputs consistent with duality). Second, we show how the number of redundancy tests - one of the more costly and time-consuming steps of FK-B - can be substantially reduced in this context. Lastly, we describe a simple memoization technique that avoids the solution of multiple identical subproblems. We test our approach on a number of inputs coming from computational biology as well as combinatorics. These modifications provide a substantial speed-up, as much as an order of magnitude, for FK-B dualization relative to a naive implementation. Although other methods may end up being faster in practice, our work paves the way for a principled optimization process for the generation of monotone Boolean functions and their duals from an oracle.

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Nafiseh Sedaghat, Tamon Stephen, and Leonid Chindelevitch. Speeding up Dualization in the Fredman-Khachiyan Algorithm B. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{sedaghat_et_al:LIPIcs.SEA.2018.6,
  author =	{Sedaghat, Nafiseh and Stephen, Tamon and Chindelevitch, Leonid},
  title =	{{Speeding up Dualization in the Fredman-Khachiyan Algorithm B}},
  booktitle =	{17th International Symposium on Experimental Algorithms (SEA 2018)},
  pages =	{6:1--6:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-070-5},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{103},
  editor =	{D'Angelo, Gianlorenzo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.6},
  URN =		{urn:nbn:de:0030-drops-89413},
  doi =		{10.4230/LIPIcs.SEA.2018.6},
  annote =	{Keywords: Monotone boolean functions, dualization, Fredman-Khachiyan algorithm, algorithm engineering, metabolic networks}
}

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A Duality-Based Method for Identifying Elemental Balance Violations in Metabolic Network Models

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Speeding up Dualization in the Fredman-Khachiyan Algorithm B

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