| One of the most ubiquitous feature of complex biological systems is that theygenerally output signals with long-range correlations. As Boolean networks has beensuccessfully used to model a number of biomolecular systems. In this paper, we studiedthe long-range correlation behaviors of this model. Our results show that Booleannetworks can undergo a regular transfer from Brownian noise to1/f process, andfinally come to the regime of white noise. This provides a theoretical support thatBoolean networks are appropriate for modeling genetic regulatory networks.In physiology, free-running healthy systems typically generate complex outputsignals that have long-range correlations. Deviations from the1/f pattern have beenassociated with disease or aging in various contexts. We find that networks withmultiple attractors prefer to generate the1/f dynamics and systems with large basinentropy tend to sustain such dynamics in a wide noise range. Further study show thatnetworks with1/f dynamics are easier to intervent.The existing theoretical analysis reveals that order functions play an important roleon the running and dynamical behavior of networks. Post function has been known asone ordered function with the maximum numeber, however it has the drawback that it only possesses the positive regulatory mechanism. In this paper we extend the Postfunction to a class contains both the positive and negative regulatory mechanism.Simulation results show that this extended Post class functions have the similarcharacters as the previous Post class and Canalizing functions on maintaining theordered and long-range correlated dynamics. And the number of the extended Post classfunctions is the biggest comparing with the remaining ordered functions. From the pointof view of the evolution, such abundant and with ordered dynamics functions are easierto be selected as the regulatory mechanism between genes. Finally, the distribution offunctions for eight real systems also supports this hypothesis. |
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