IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v133y2017icp76-90.html
   My bibliography  Save this article

Graph-theoretic analysis of multistationarity using degree theory

Author

Listed:
  • Conradi, Carsten
  • Mincheva, Maya

Abstract

Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems, since they are large, nonlinear and contain many unknown parameters. Mass action biochemical mechanisms can be represented by a directed bipartite graph with species and reaction nodes. Graph-theoretic methods can then be used to assess the potential of a given biochemical mechanism for multistationarity by identifying structures in the bipartite graph referred to as critical fragments. In this article we present a graph-theoretic method for conservative biochemical mechanisms characterized by bounded species concentrations, which makes the use of degree theory arguments possible. We illustrate the results with an example of a mitogen-activated protein kinases (MAPK) network.

Suggested Citation

  • Conradi, Carsten & Mincheva, Maya, 2017. "Graph-theoretic analysis of multistationarity using degree theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 76-90.
  • Handle: RePEc:eee:matcom:v:133:y:2017:i:c:p:76-90
    DOI: 10.1016/j.matcom.2015.08.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475415001755
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2015.08.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:133:y:2017:i:c:p:76-90. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.