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Google matrix analysis of bi-functional SIGNOR network of protein–protein interactions

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  • Frahm, Klaus M.
  • Shepelyansky, Dima L.

Abstract

Directed protein networks with only a few thousand of nodes are rather complex and do not allow to extract easily the effective influence of one protein to another taking into account all indirect pathways via the global network. Furthermore, the different types of activation and inhibition actions between proteins provide a considerable challenge in the frame work of network analysis. At the same time these protein interactions are of crucial importance and at the heart of cellular functioning. We develop the Google matrix analysis of the protein–protein network from the open public database SIGNOR. The developed approach takes into account the bi-functional activation or inhibition nature of interactions between each pair of proteins describing it in the frame work of Ising-spin matrix transitions. We also apply a recently developed linear response theory for the Google matrix which highlights a pathway of proteins whose PageRank probabilities are most sensitive with respect to two proteins selected for the analysis. This group of proteins is analyzed by the reduced Google matrix algorithm which allows to determine the effective interactions between them due to direct and indirect pathways in the global network. We show that the dominating activation or inhibition function of each protein can be characterized by its magnetization. The results of this Google matrix analysis are presented for three examples of selected pairs of proteins. The developed methods work rapidly and efficiently even for networks with several million of nodes and can be applied to various biological networks.

Suggested Citation

  • Frahm, Klaus M. & Shepelyansky, Dima L., 2020. "Google matrix analysis of bi-functional SIGNOR network of protein–protein interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    • Handle: RePEc:eee:phsmap:v:559:y:2020:i:c:s0378437120305318
    DOI: 10.1016/j.physa.2020.125019
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    References listed on IDEAS

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    1. Célestin Coquidé & José Lages & Dima L. Shepelyansky, 2019. "World influence and interactions of universities from Wikipedia networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(1), pages 1-20, January.
    2. Célestin Coquidé & Leonardo Ermann & José Lages & Dima L. Shepelyansky, 2019. "Influence of petroleum and gas trade on EU economies from the reduced Google matrix analysis of UN COMTRADE data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(8), pages 1-14, August.
    3. Frahm, Klaus M. & Shepelyansky, Dima L., 2019. "Ising-PageRank model of opinion formation on social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    4. José Lages & Dima L Shepelyansky & Andrei Zinovyev, 2018. "Inferring hidden causal relations between pathway members using reduced Google matrix of directed biological networks," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-28, January.
    5. C'elestin Coquid'e & Leonardo Ermann & Jos'e Lages & D. L. Shepelyansky, 2019. "Influence of petroleum and gas trade on EU economies from the reduced Google matrix analysis of UN COMTRADE data," Papers 1903.01820, arXiv.org.
    6. Célestin Coquidé & Leonardo Ermann & José Lages & Dima Shepelyansky, 2019. "Influence of petroleum and gas trade on EU economies from the reduced Google matrix analysis of UN COMTRADE data," Working Papers hal-02058766, HAL.
    7. Klaus M. Frahm & Katia Jaffrès-Runser & Dima L. Shepelyansky, 2016. "Wikipedia mining of hidden links between political leaders," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(12), pages 1-21, December.
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    Cited by:

    1. Célestin Coquidé & José Lages & Leonardo Ermann & Dima Shepelyansky, 2022. "COVID-19 impact on the international trade," Post-Print hal-03536528, HAL.

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