Copyright © 2006 Elsevier Ireland Ltd All rights reserved.
Qualitative analysis of the relation between DNA microarray data and behavioral models of regulation networks
Received 22 August 2005;
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
- 3.4. 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
- 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






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