Jump to ContentJump to Main Navigation
System Modeling in Cellular BiologyFrom Concepts to Nuts and Bolts$
Users without a subscription are not able to see the full content.

Zoltan Szallasi, Jorg Stelling, and Vipul Periwal

Print publication date: 2006

Print ISBN-13: 9780262195485

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262195485.001.0001

Show Summary Details
Page of

PRINTED FROM MIT PRESS SCHOLARSHIP ONLINE (www.mitpress.universitypressscholarship.com). (c) Copyright The MIT Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in MITSO for personal use (for details see http://www.mitpress.universitypressscholarship.com/page/privacy-policy).date: 22 July 2018

Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations

Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations

Chapter:
(p.97) 6. Modeling Molecular Interaction Networks with Nonlinear Ordinary Differential Equations
Source:
System Modeling in Cellular Biology
Author(s):

Emery D. Conrad

John J. Tyson

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262195485.003.0006

This chapter explains how cell biologists can make reliable connections between molecular interaction networks and cell behaviors, when intuition fails in all but the simplest cases. It proposes to make the connection by translating the reaction network into a set of nonlinear differential equations that describe how all the interacting species are changing with time. Differential equations define a vector field in the state space of the network. The vector field points to certain stable attractors, which can be correlated with long-term, stable behavior of the network and of the cell it governs. Transitions from one stable attractor to another represent the responses of the cell to specific perturbations (signals). A natural way to describe the signal-response properties of a regulatory network is in terms of a one-parameter bifurcation diagram, which efficiently displays the stable attractors (steady states and oscillators) and transitions between attractors as signal strength (the “parameter”) varies. These ideas are illustrated with simple examples of linear, hyperbolic, and sigmoidal signal-response curves; bistable switches based on positive feedback or mutual inhibition; and limit cycle oscillators based on substrate depletion, activator-inhibitor interactions, or time-delayed negative feedback.

Keywords:   cell biology, molecular interaction networks, cell behavior, nonlinear differential equations

MIT Press Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs, and if you can't find the answer there, please contact us.