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	Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond
	Zhou, Peijie ; Li, Tiejun
	2016
关键词	WADDINGTONS EPIGENETIC LANDSCAPE ONSAGER-MACHLUP FUNCTION NONEQUILIBRIUM ROBUSTNESS FRAMEWORK NETWORKS BIOLOGY CELL
英文摘要	Motivated by the famous Waddington's epigenetic landscape metaphor in developmental biology, biophysicists and applied mathematicians made different proposals to construct the landscape for multi-stable complex systems. We aim to summarize and elucidate the relationships among these theories from a mathematical point of view. We systematically investigate and compare three different but closely related realizations in the recent literature: the Wang's potential landscape theory from steady state distribution of stochastic differential equations (SDEs), the Freidlin-Wentzell quasi-potential from the large deviation theory, and the construction through SDE decomposition and A-type integral. We revisit that the quasi-potential is the zero noise limit of the potential landscape, and the potential function in the third proposal coincides with the quasi-potential. We compare the difference between local and global quasi-potential through the viewpoint of exchange of limit order for time and noise amplitude. We argue that local quasi-potentials are responsible for getting transition rates between neighboring stable states, while the global quasi-potential mainly characterizes the residence time of the states as the system reaches stationarity. The difference between these two is prominent when the transitivity property is broken. The most probable transition path by minimizing the Onsager-Machlup or Freidlin-Wentzell action functional is also discussed. As a consequence of the established connections among different proposals, we arrive at the novel result which guarantees the existence of SDE decomposition while denies its uniqueness in general cases. It is, therefore, clarified that the A-type integral is more appropriate to be applied to the decomposed SDEs rather than its primitive form as believed by previous researchers. Our results contribute to a deeper understanding of landscape theories for biological systems. (C) 2016 AIP Publishing LLC.; NSFC [11171009, 11421101, 91530322]; National Science Foundation for Excellent Young Scholars [11222114]; SCI(E); PubMed; ARTICLE; cliffzhou@pku.edu.cn; tieli@pku.edu.cn; 9; 094109; 144
语种	中文
出处	PubMed ; SCI
出版者	JOURNAL OF CHEMICAL PHYSICS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/434575]
专题	数学科学学院
推荐引用方式 GB/T 7714	Zhou, Peijie,Li, Tiejun. Construction of the landscape for multi-stable systems: Potential landscape, quasi-potential, A-type integral and beyond. 2016-01-01.

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