Skip to main content

Advertisement

SpringerLink
Log in

A mathematical approach to solve the network reconstruction problem

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

The reconstruction of biochemical and genetic networks from experimental data is an important challenge in biology and medical basic research. We formalize this problem mathematically and present an exact algorithm for its solution. Our procedure yields either a complete list of all alternative network structures that explain the observed phenomena or proves that no solution exists using the given data set.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Andrec M, Kholodenko B, Levy R, Sontag E (2005) Interference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy. J Theor Biol 232:427–441

    MathSciNet  Google Scholar 

  • Bertsimas D, Weismantel R (2005) Optimization over integers. Dynamic ideas. Belmont, Massachusetts

    Google Scholar 

  • Goss PJE, Peccoud J (1998) Quantitative modelling of stochastic systems in molecular biology by using stochastic Petri nets. Proc Natl Acad Sci USA 6750–6755

  • Heiner M, Koch I (2004) Petri net based model validation in systems biology. In: Proceedings of 25th international conference on application and theory of petri nets, Bologna, Springer, Berlin

  • Heiner M, Koch I, Will J (2004) Model validation of biological pathways using Petri nets—demonstrated for apoptosis. BioSystems 75:15–28

    Article  Google Scholar 

  • Hofestädt R (1994) A Petri net application of metabolic processes. J Syst Anal Modell Simul 16:113–122

    MATH  Google Scholar 

  • Laubenbacher R, Stigler B (2005) A computational algebra approach to reverse engineering of gene regulatory networks. J Theor Biol 229:523–537

    Article  MathSciNet  Google Scholar 

  • Marwan W, Sujatha A, Starostzik C (2005) Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri Net modeling and simulation. J Theor Biol 236:349–365

    Article  Google Scholar 

  • Pinney JW, Westhead RD, McConkey GA (2003) Petri net representations in systems biology. Biochem Soc Trans 31:1513–1515

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Magdeburg Center of Systems Biology (MaCS), Otto-von-Guericke Universität Magdeburg, Magdeburg, Germany

    Wolfgang Marwan, Annegret Wagler & Robert Weismantel

Authors
  1. Wolfgang Marwan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Annegret Wagler
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert Weismantel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Robert Weismantel.

Additional information

This work was supported by the German Ministry of Education and Research (BMBF) through the FORSYS initiative.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marwan, W., Wagler, A. & Weismantel, R. A mathematical approach to solve the network reconstruction problem. Math Meth Oper Res 67, 117–132 (2008). https://doi.org/10.1007/s00186-007-0178-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-007-0178-5

Keywords

Search

Navigation