The landscape and flux of a minimum network motif,Wu Xing

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Wu-Xing theory is an ancient philosophy that serves as a guiding principle in the traditional Chinese medicine(TCM).It has been used to explain the unbalance among the TCM organ systems in disease states and provide treatment philosophy qualitatively.Until now,it is still a challenge to explore the Wu-Xing theory beyond its philosophical nature.In this study,we established a quantitative framework using the landscape and flux theory to characterize the nature of the Wu-Xing theory from a perspective of a minimal network motif and leave certain specific functional aspects of Wu-Xing theory for future exploration.We uncovered the irregular ring shape of projection landscape for the Wu-Xing network with several local basins and barriers.We found that the dynamics of the self-organized Wu-Xing system was determined by the underlying negative landscape gradient force and the nonequilibrium rotational flux.While the shape of the Wu-Xing landscape determines the stabilities of the states,the rotational flux guarantees the persistent periodic oscillation and the stability of the flow.This provides a physical and quantitative basis for Yin-Yang duality of the driving forces for determining the dynamics and behaviors of the living systems.Applying landscape and flux analysis,we can identify the key parameter for the dynamics/function of Wu-Xing network.These findings allow us to have a deeper understanding of the scientific merits of the ancient Wu-Xing theory from the network motif perspective.
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