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The complex fluctuations of probabilistic Boolean networks.

Yuan-ming Gao¹, Peng Xu, Xiang-hong Wang

¹Department of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, Zhejiang, China.

|July 23, 2013

Summary

Probabilistic Boolean networks (PBNs) exhibit long-range correlations and 1/f dynamics, outperforming Boolean networks (BNs) across broader noise ranges. Constituent BNs and homogeneous steady-state distributions are key to sustaining these dynamics.

Keywords:

1/f dynamics Long-range correlation Probabilistic Boolean network

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Area of Science:

Systems Biology
Computational Biology
Network Dynamics

Background:

Boolean networks (BNs) and Probabilistic Boolean networks (PBNs) are established models for biological systems.
Understanding long-range correlations and 1/f dynamics is crucial for analyzing complex biological network behavior.

Purpose of the Study:

To investigate the long-range correlations and 1/f dynamics of Probabilistic Boolean networks (PBNs).
To compare the noise tolerance and dynamic properties of PBNs against traditional Boolean networks (BNs).

Main Methods:

Modeling PBNs using their corresponding Markov chains.
Quantifying PBN states via the deviation of their steady-state distributions.
Analyzing the impact of constituent BNs and steady-state distribution homogeneity on 1/f dynamics.

Main Results:

PBNs demonstrate 1/f dynamics over a wider and higher noise range compared to BNs.
The specific Boolean networks composing a PBN significantly influence the generation of 1/f dynamics.
PBNs with homogeneous steady-state distributions are more effective at sustaining 1/f dynamics across varying noise levels.

Conclusions:

PBNs offer enhanced capabilities for modeling complex biological dynamics, particularly concerning long-range correlations and 1/f noise.
The architecture of constituent BNs and the nature of steady-state distributions are critical factors in PBN dynamic behavior.
PBNs present a more robust framework than BNs for simulating biological systems under noisy conditions.