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Reconstructing biochemical cluster networks

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Abstract

Motivated by fundamental problems in chemistry and biology we study cluster graphs arising from a set of initial states \({S\subseteq\mathbb{Z}^n_+}\) and a set of transitions/reactions \({M\subseteq\mathbb{Z}^n_+\times\mathbb{Z}^n_+}\). The clusters are formed out of states that can be mutually transformed into each other by a sequence of reversible transitions. We provide a solution method from computational commutative algebra that allows for deciding whether two given states belong to the same cluster as well as for the reconstruction of the full cluster graph. Using the cluster graph approach we provide solutions to two fundamental questions: (1) Deciding whether two states are connected, e.g., if the initial state can be turned into the final state by a sequence of transition and (2) listing concisely all reactions processes that can accomplish that. As a computational example, we apply the framework to the permanganate/oxalic acid reaction.

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Authors and Affiliations

  1. ETH Zurich, Zurich, Switzerland

    Utz-Uwe Haus

  2. Technische Universität Munich, Munich, Germany

    Raymond Hemmecke

  3. University of Erlangen-Nürnberg, Erlangen, Germany

    Sebastian Pokutta

Authors
  1. Utz-Uwe Haus
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  2. Raymond Hemmecke
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  3. Sebastian Pokutta
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Correspondence to Raymond Hemmecke.

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Haus, UU., Hemmecke, R. & Pokutta, S. Reconstructing biochemical cluster networks. J Math Chem 49, 2441–2456 (2011). https://doi.org/10.1007/s10910-011-9892-6

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  • DOI: https://doi.org/10.1007/s10910-011-9892-6

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