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A Gröbner fan method for biochemical network modeling

Published: 29 July 2007 Publication History

Abstract

Polynomial dynamical systems (PDSs) have been used successfully as a framework for the reconstruction, or reverse engineering of biochemical networks from experimental data. Within this modeling space, a particular PDS is chosen by way of a Gröbner basis, and using different monomial orders may result in different polynomial models. In this paper, we present a systematic method for selecting most likely polynomial models for a given data set, using the Gröbner fan of the ideal of the input data. We apply the method to reverse engineer two biochemical networks, a Boolean model of lactose metabolism in E. coli and a protein signal transduction network in S. cerevisiae and compare our results to those from two published network-reconstruction methods.

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  • (2023)Boolean Models of the Transport, Synthesis, and Metabolism of Tryptophan in Escherichia coliBulletin of Mathematical Biology10.1007/s11538-023-01122-x85:4Online publication date: 6-Mar-2023
  • (2019)Geometric Characterization of Data Sets with Unique Reduced Gröbner BasesBulletin of Mathematical Biology10.1007/s11538-019-00624-xOnline publication date: 29-Jun-2019
  • (2017)Bistability and Asynchrony in a Boolean Model of the l-arabinose Operon in Escherichia coliBulletin of Mathematical Biology10.1007/s11538-017-0306-179:8(1778-1795)Online publication date: 21-Jun-2017
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  1. A Gröbner fan method for biochemical network modeling

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    cover image ACM Conferences
    ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation
    July 2007
    406 pages
    ISBN:9781595937438
    DOI:10.1145/1277548
    • General Chair:
    • Dongming Wang
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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    Publication History

    Published: 29 July 2007

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    Author Tags

    1. computational algebra
    2. gröbner bases
    3. gröbner fan
    4. model selection
    5. monomial orderings
    6. network inference
    7. polynomial dynamical systems
    8. reverse engineering

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    ISSAC07
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    ISSAC07: International Symposium on Symbolic and Algebraic Computation
    July 29 - August 1, 2007
    Ontario, Waterloo, Canada

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    Overall Acceptance Rate 395 of 838 submissions, 47%

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    View all
    • (2023)Boolean Models of the Transport, Synthesis, and Metabolism of Tryptophan in Escherichia coliBulletin of Mathematical Biology10.1007/s11538-023-01122-x85:4Online publication date: 6-Mar-2023
    • (2019)Geometric Characterization of Data Sets with Unique Reduced Gröbner BasesBulletin of Mathematical Biology10.1007/s11538-019-00624-xOnline publication date: 29-Jun-2019
    • (2017)Bistability and Asynchrony in a Boolean Model of the l-arabinose Operon in Escherichia coliBulletin of Mathematical Biology10.1007/s11538-017-0306-179:8(1778-1795)Online publication date: 21-Jun-2017
    • (2016)Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systemsNonlinear Dynamics10.1007/s11071-016-2715-385:1(675-692)Online publication date: 16-Mar-2016
    • (2014)Polynomial algebra reveals diverging roles of the unfolded protein response in endothelial cells during ischemia-reperfusion injuryFEBS Letters10.1016/j.febslet.2014.05.065588:17(3062-3067)Online publication date: 16-Jun-2014
    • (2014)Data Identification for Improving Gene Network Inference using Computational AlgebraBulletin of Mathematical Biology10.1007/s11538-014-9979-x76:11(2923-2940)Online publication date: 4-Oct-2014
    • (2013)BibliographyHandbook of Finite Fields10.1201/b15006-22(851-1010)Online publication date: 18-Jun-2013
    • (2010)Estimating the Volumes of the Cones in a Gröbner FanMathematics in Computer Science10.1007/s11786-010-0039-03:4(457-463)Online publication date: 13-Apr-2010
    • (2009)List-decoding methods for inferring polynomials in finite dynamical gene network modelsBioinformatics10.1093/bioinformatics/btp28125:13(1686-1693)Online publication date: 28-Apr-2009
    • (2008)Coding-theoretic methods for reverse engineering of gene regulatory networks2008 IEEE Information Theory Workshop10.1109/ITW.2008.4578633(114-118)Online publication date: May-2008
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