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Systems biology towards life in silico: mathematics of the control of living cells

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Abstract

Systems Biology is the science that aims to understand how biological function absent from macromolecules in isolation, arises when they are components of their system. Dedicated to the memory of Reinhart Heinrich, this paper discusses the origin and evolution of the new part of systems biology that relates to metabolic and signal-transduction pathways and extends mathematical biology so as to address postgenomic experimental reality. Various approaches to modeling the dynamics generated by metabolic and signal-transduction pathways are compared. The silicon cell approach aims to describe the intracellular network of interest precisely, by numerically integrating the precise rate equations that characterize the ways macromolecules’ interact with each other. The non-equilibrium thermodynamic or ‘lin–log’ approach approximates the enzyme rate equations in terms of linear functions of the logarithms of the concentrations. Biochemical Systems Analysis approximates in terms of power laws. Importantly all these approaches link system behavior to molecular interaction properties. The latter two do this less precisely but enable analytical solutions. By limiting the questions asked, to optimal flux patterns, or to control of fluxes and concentrations around the (patho)physiological state, Flux Balance Analysis and Metabolic/Hierarchical Control Analysis again enable analytical solutions. Both the silicon cell approach and Metabolic/Hierarchical Control Analysis are able to highlight where and how system function derives from molecular interactions. The latter approach has also discovered a set of fundamental principles underlying the control of biological systems. The new law that relates concentration control to control by time is illustrated for an important signal transduction pathway, i.e. nuclear hormone receptor signaling such as relevant to bone formation. It is envisaged that there is much more Mathematical Biology to be discovered in the area between molecules and Life.

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Authors and Affiliations

  1. Molecular Cell Physiology, Institute of Molecular Cell Biology, Netherlands Institute for Systems Biology, Faculty of Earth and Life Sciences, Vrije Universiteit, De Boelelaan 1085, 1081 HV, Amsterdam, The Netherlands

    Hans V. Westerhoff

  2. Molecular Cell Physiology, Institute of Molecular Cell Biology, BioCentrum Amsterdam, Faculty for Earth and Life Sciences, Vrije Universiteit, De Boelelaan 1085, 1081 HV, Amsterdam, The Netherlands

    Alexey Kolodkin, Frank J. Bruggeman, Klaas Krab, Jan H. van Schuppen, Hanna Hardin, Barbara M. Bakker, Martijn J. Moné, Katja N. Rybakova & Jacky L. Snoep

  3. Manchester Centre for Integrative Systems Biology, Manchester Interdisciplinary Biocentre, School of Chemical Engineering and Analytical Science, The University of Manchester, 131 Princess Street, Manchester, M1 7ND, UK

    Hans V. Westerhoff, Stephen J. Wilkinson & Jacky L. Snoep

  4. Department of Biochemistry, Stellenbosch University, Private Bag X1, Matieland, 7602, South Africa

    Riaan Conradie & Jacky L. Snoep

  5. CWI, 1090 GB, Amsterdam, The Netherlands

    Frank J. Bruggeman, Jan H. van Schuppen & Hanna Hardin

  6. Department of Internal Medicine, Erasmus Medical Centre, 3000 DR, Rotterdam, The Netherlands

    Marco Eijken & Hans J. P. van Leeuwen

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  1. Hans V. Westerhoff
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Correspondence to Hans V. Westerhoff.

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Westerhoff, H.V., Kolodkin, A., Conradie, R. et al. Systems biology towards life in silico: mathematics of the control of living cells. J. Math. Biol. 58, 7–34 (2009). https://doi.org/10.1007/s00285-008-0160-8

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  • DOI: https://doi.org/10.1007/s00285-008-0160-8

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