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A bi-objective network design approach for discovering functional modules linking Golgi apparatus fragmentation and neuronal death

  • S.I.: OR in Neuroscience
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Abstract

Experimental records show the existence of a biological linkage between neuronal death and Golgi apparatus fragmentation. The comprehension of such linkage should help to understand the dynamics undergoing neurological damage caused by diseases such as Alzheimer’s disease or amyotrophic lateral sclerosis. In this paper, the bi-objective minimum cardinality bottleneck Steiner tree problem along with an ad-hoc exact algorithm are proposed to study such phenomena. The proposed algorithm is based on integer programming and the so-called \(\epsilon \)-constraint method. A key feature of the devised approach is that it allows an efficient integer programming formulation of the problem. The obtained results show that it is possible to obtain additional evidence supporting the hypothesis that alterations of the Golgi apparatus structure and neuronal death interact through the biological mechanisms underlying the outbreak and progression of neurodegenerative diseases. Moreover, the function of cellular response to stress as a biological linkage between these phenomena is also further investigated. Complementary, computational results on a synthetic dataset are also provided with the aim of reporting the performance of the proposed algorithm.

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Notes

  1. KEGG network diagrams are manually drawn detailed molecular interaction/reaction schemes corresponding to different processes of interest; they are made available by the Kyoto Encyclopedia of Genes and Genome (KEGG 2015).

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Acknowledgments

The authors would like to acknowledge the anonymous reviewers for their insightful and constructive comments which helped to improve the quality of the paper. E. Álvarez-Miranda acknowledges the support of the Chilean Council of Scientific and Technological Research, CONICYT, through the grant FONDECYT N.11140060 and through the Complex Engineering Systems Institute (ICM:P-05-004-F, CONICYT:FBO16). H. Farhan is supported by the Swiss National Science Foundation, the German Science Foundation, the Young Scholar Fund of the University of Konstanz and by the Canton of Thurgau. M. Sinnl is supported by the Austrian Research Fund (FWF, Project P 26755-N19). M. Luipersbeck acknowledges the support of the University of Vienna through the uni:docs fellowship programme.

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, Universidad de Talca, Curicó, Chile

    Eduardo Álvarez-Miranda

  2. Biotechnology Institute Thurgau, Kreuzlingen, Switzerland

    Hesso Farhan

  3. Department of Biology, University of Konstanz, Konstanz, Germany

    Hesso Farhan

  4. Department of Statistics and Operations Research, Faculty of Business, Economics and Statistics, University of Vienna, Vienna, Austria

    Martin Luipersbeck & Markus Sinnl

Authors
  1. Eduardo Álvarez-Miranda
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  2. Hesso Farhan
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Corresponding author

Correspondence to Eduardo Álvarez-Miranda.

Appendix

Appendix

See Figs. 5, 6, 7, and 8, Tables 2, 3, 4, 5, Fig. 9, Table 6.

Fig. 5
figure 5

Pathways in which the neuronal death hits appear to be statiscally meaningful

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Fig. 6
figure 6

Pathways in which the Golgi fragmentation hits appear to be statiscally meaningful

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Fig. 7
figure 7

KEGG pathway associated with ALS (obtained from KEGG 2015)

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Fig. 8
figure 8

KEGG pathway associated with Alzheimer’s disease (dobtained from KEGG 2015)

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Table 2 Proteins associated with neuronal death Gene (2015)
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Table 3 Proteins regulating Golgi apparatus fragmentation Simpson et al. (2012)
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Table 4 Proteins regulating Golgi apparatus fragmentation Chia et al. (2012)
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Table 5 Proteins regulating Golgi apparatus fragmentation Millarte et al. (2015)
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Fig. 9
figure 9

Network associated with the response to stress pathway (obtained via BiNGO analysis Maere et al. (2005) and displayed using STRING (2015) web tool)

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Table 6 Proteins associated with the response to stress
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Álvarez-Miranda, E., Farhan, H., Luipersbeck, M. et al. A bi-objective network design approach for discovering functional modules linking Golgi apparatus fragmentation and neuronal death. Ann Oper Res 258, 5–30 (2017). https://doi.org/10.1007/s10479-016-2188-2

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