Enumeration and Cartesian Product Decomposition of Alternate Optimal Fluxes in Cellular Metabolism

Onur Şeref (), J. Paul Brooks (), Bernice Huang () and Stephen S. Fong ()
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Onur Şeref: Department of Business Information Technology, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
J. Paul Brooks: Department of Statistical Sciences and Operations Research and the Center for the Study of Biological Complexity, Virginia Commonwealth University, Richmond, Virginia 23284
Bernice Huang: Department of Microbiology and Immunology and the Center for the Study of Biological Complexity, Virginia Commonwealth University, Richmond, Virginia 23298
Stephen S. Fong: Department of Chemical and Life Sciences and the Center for the Study of Biological Complexity, Virginia Commonwealth University, Richmond, Virginia 23284

INFORMS Journal on Computing, 2017, vol. 29, issue 2, 197-210

Abstract: We introduce a framework for finding and analyzing all optimal solutions to a linear-programming-based model for cellular metabolism. The implementation of a pivoting-based method for generating alternate optimal reaction fluxes is described. We present a novel strongly polynomial algorithm to decompose a matrix of alternate optimal solutions of an optimization problem into independent subsets of variables and their respective alternate solutions. The matrix can be reconstructed as a Cartesian product of these subsets of alternate solutions. We demonstrate that our strategy for enumeration is more efficient than other methods, and that our Cartesian product matrix decomposition can quickly recover independent substructures. The framework is applied to analyze the metabolic reconstruction of a disease-causing organism, revealing metabolic pathways that are independently regulated.

Keywords: Cartesian product decomposition; alternate optimal solutions; flux balance analysis (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:29:y:2017:i:2:p:197-210

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