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Algebraic Models and Their Use in Systems Biology

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Discrete and Topological Models in Molecular Biology

Part of the book series: Natural Computing Series ((NCS))

Abstract

Progress in systems biology relies on the use of mathematical and statistical models for system-level studies of biological processes. Several different modeling frameworks have been used successfully, including traditional differential-equation-based models, a variety of stochastic models, agent-based models, and Boolean networks, to name some common ones. This chapter focuses on discrete models, and describes a mathematical approach to the construction and analysis of discrete models which relies on combinatorics and computational algebraic geometry. The underlying mathematical concept is that of a polynomial dynamical system over a finite field. Examples are given of the advantages of this approach, and several applications are discussed.

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Authors and Affiliations

  1. Center for Quantitative Medicine, University of Connecticut Health Center, 195 Farmington Ave., Farmington, CT, 06030, USA

    Reinhard Laubenbacher

  2. C/o Renzelmann, Kurfürstenstr. 35, 80801, München, Germany

    Franziska Hinkelmann

  3. School of Mathematics, Georgia Tech, Atlanta, GA, USA

    David Murrugarra

  4. 606 PGH, Department of Mathematics, University of Houston, Houston, TX, 77004, USA

    Alan Veliz-Cuba

  5. 312 Keck Hall, Department of Biochemistry and Cell Biology, Rice University, Houston, TX, 77251, USA

    Alan Veliz-Cuba

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  1. Reinhard Laubenbacher
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  2. Franziska Hinkelmann
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  3. David Murrugarra
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  4. Alan Veliz-Cuba
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Correspondence to Reinhard Laubenbacher .

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Editors and Affiliations

  1. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Nataša Jonoska

  2. Dept. Mathematics & Statistics, University of South Florida, Tampa, Florida, USA

    Masahico Saito

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Laubenbacher, R., Hinkelmann, F., Murrugarra, D., Veliz-Cuba, A. (2014). Algebraic Models and Their Use in Systems Biology. In: Jonoska, N., Saito, M. (eds) Discrete and Topological Models in Molecular Biology. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40193-0_21

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