Maximum number of fixed points in regulatory Boolean networks
1Departamento Ingeniería Matemática, Universidad de Concepción, Av. Esteban Iturra s/n, Casilla 160-C, Concepción, Chile. jaracena@ing-mat.udec.cl
Bulletin of Mathematical Biology
|March 1, 2008
Summary
Boolean networks model genetic regulation. This study finds an upper bound for the number of stable states (fixed points) in regulatory Boolean networks, aiding in their design.
Area of Science:
- Computational Biology
- Systems Biology
- Network Theory
Background:
- Boolean networks (BNs) are widely employed as mathematical models for genetic regulatory networks.
- The number of fixed points in a BN is a critical determinant of its dynamic behavior.
Purpose of the Study:
- To investigate the maximum number of fixed points in regulatory Boolean networks (RBNs).
- To establish relationships between network cycles and the count of fixed points.
Main Methods:
- Analysis of interaction graphs in RBNs, distinguishing between activation and inhibition.
- Identification of positive and negative cycles within the network structure.
Main Results:
- Established relationships between positive/negative cycles and the number of fixed points.
- Derived an upper bound for fixed points based on the minimum set of vertices intersecting all positive cycles.
Conclusions:
- The findings provide a theoretical upper bound for fixed points in RBNs.
- This bound is applicable to the rational design of genetic regulatory networks.
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