Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology
Fumito Mori1, Atsushi Mochizuki1,2
1Theoretical Biology Laboratory, RIKEN, Wako 351-0198, Japan.
Physical Review Letters
|July 29, 2017
Summary
Boolean network models reveal a consistent expected number of fixed points, crucial for understanding cell types. This count remains independent of network complexity under specific conditions, highlighting key dynamics in genetic regulatory networks.
Area of Science:
- Computational Biology
- Network Science
- Systems Biology
Background:
- Boolean network models are utilized to simulate dynamics in genetic, neural, and social systems.
- Fixed points in genetic regulatory networks often represent distinct cell types.
- Network topology generally influences system dynamics.
Purpose of the Study:
- To determine the expected number of fixed points in Boolean networks.
- To investigate the influence of network topology and feedback on fixed points.
- To analyze Boolean networks with non-uniform and non-identical probability distributions for Boolean functions.
Main Methods:
- Mathematical proof for expected number of fixed points.
- Analysis of Boolean functions drawn from general probability distributions.
- Investigation of stochastic neutrality conditions on feedback arc sets.
- Examination of the impact of positive feedback within cycles.
Main Results:
- The expected number of fixed points in a Boolean network is proven to be one.
- This expected number is independent of network topology when a feedback arc set meets stochastic neutrality conditions.
- Predominance of positive feedback in a cycle increases the expected number of fixed points.
Conclusions:
- A universal expected number of fixed points exists in Boolean networks, irrespective of topology under stochastic neutrality.
- Network topology and feedback mechanisms significantly modulate the number of stable states (fixed points).
- Findings provide insights into cell-type determination and dynamics within biological regulatory systems.
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