ScienceDirect® Home Skip Main Navigation Links
You have guest access to ScienceDirect. Find out more.
 
Home
Browse
My Settings
Alerts
Help
 Quick Search
 Search tips (Opens new window)
    Clear all fields    
Biosystems
Volume 84, Issue 2, May 2006, Pages 153-174
Dynamical Modeling of Biological Regulatory Networks
 
Font Size: Decrease Font Size  Increase Font Size
 Abstract - selected
Article
Purchase PDF (537 K)

Article Toolbox
 
 
 
Related Articles in ScienceDirect
View More Related Articles
 
View Record in Scopus
 
doi:10.1016/j.biosystems.2005.10.006    
How to Cite or Link Using DOI (Opens New Window)

Copyright © 2006 Elsevier Ireland Ltd All rights reserved.

Qualitative analysis of the relation between DNA microarray data and behavioral models of regulation networks

Purchase the full-text article



References and further reading may be available for this article. To view references and further reading you must purchase this article.

A. Siegela, Corresponding Author Contact Information, E-mail The Corresponding Author, O. Radulescub, M. Le Borgnea, P. Vebera, J. Ouya and S. Lagarriguec

aIRISA, Symbiose, Campus de Beaulieu, 35042 Rennes Cedex, France

bIRMAR-Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France

cUMR Génétique Animale, Agrocampus Rennes-INRA, 65 Rue de Saint-Brieuc, CS 84215 Rennes, France


Received 22 August 2005; 
revised 20 September 2005; 
accepted 4 October 2005. 
Available online 23 March 2006.

Abstract

We introduce a mathematical framework that allows to test the compatibility between differential data and knowledge on genetic and metabolic interactions. Within this framework, a behavioral model is represented by a labeled oriented interaction graph; its predictions can be compared to experimental data. The comparison is qualitative and relies on a system of linear qualitative equations derived from the interaction graph. We show how to partially solve the qualitative system, how to identify incompatibilities between the model and the data, and how to detect competitions in the biological processes that are modeled. This approach can be used for the analysis of transcriptomic, metabolic or proteomic data.

Keywords: Systems biology; Qualitative analysis; Steady state shift; Sign algebra

Article Outline

1. Introduction
1.1. Systems biology: models and data
1.2. Steady state shift experiments and microarray data
1.3. Qualitative analysis
2. Working example: regulation of the synthesis of fatty acids
2.1. Variables in the model
2.2. Interactions in the model
2.3. Working data set: virtual fasting protocol
3. Steady state shift: qualitative description
3.1. Interaction graph
3.1.1. Qualitative graph
3.1.2. Exterior and parameters
3.1.3. Extracting an interaction graph from biological facts described in the literature
3.1.4. Example: fasting protocol (Fig. 1)
3.1.5. Paths and loops on graph
3.1.6. Analyzed subgraph, observed nodes
3.1.7. Entrance boundary
3.1.8. Predecessors
3.2. Qualitative linear equations
3.2.1. Steady state shift
3.2.2. Small variation and self-susceptivity
3.2.3. Sign algebra
3.2.4. Generalization to large variations
3.2.5. Qualitative system of equations
3.3. Influences and their transmission across a boundary
3.3.1. Transmission of influences on graphs
3.3.2. Influence of the boundary on the interior
3.4. Moduli and sign algebra
3.4.1. Path modulus
3.4.2. Signs of moduli
4. Model and data compatibility
4.1. Solving qualitative systems
4.1.1. Compatible system
4.1.2. Competitions
4.2. Hand solving of qualitative equations
4.3. Graph valuation algorithm
4.3.1. Basic ideas underlying the algorithm
4.3.2. The graph valuation algorithm
4.3.3. Application to the detection of incompatibilities
4.3.4. Criterion to compare model and data 1
4.3.5. Working example
5. Assessment of competitions
5.1. Competitions
5.2. Set of equations describing the sign of variation of a variable Xi0
5.3. Example of SREBP
5.4. Paths appearing in an Eq. (13)
5.5. Example of SREBP-a
5.6. Influences
5.7. Examples of SREBP and SREBP-a
5.8. Counterbalanced influences
5.9. Redundant and essential influences
5.10. Essentially balanced nodes
5.11. Complementarity with the graph valuation algorithm
5.12. Working example and biological discussion
5.13. Improvements
6. Application to an extended model of the synthesis of fatty acids
6.1. Backward–forward algorithm
6.2. Essential balances
6.3. Backward–forward algorithm on a corrected set of data
7. Remarks and conclusion
Acknowledgements
Appendix A. Proofs
References



Corresponding Author Contact InformationCorresponding author. Tel.: +33 299847448; fax: +33 299847171.

Biosystems
Volume 84, Issue 2, May 2006, Pages 153-174
Dynamical Modeling of Biological Regulatory Networks
 
Home
Browse
My Settings
Alerts
Help
Elsevier.com (Opens new window)
About ScienceDirect  |  Contact Us  |  Information for Advertisers  |  Terms & Conditions  |  Privacy Policy
Copyright © 2008 Elsevier B.V. All rights reserved. ScienceDirect® is a registered trademark of Elsevier B.V.