Chaotic motifs in genomic regulatory networks

来源 :The XXIX International Colloquium on Group-Theoretical Metho | 被引量 : 0次 | 上传用户:zq20081979
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  Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations,if their dimensions are no less than 3.It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs.On the other hand,the topic of motifs has attracted great attention in studying biological networks,and network motifs are suggested to be elementary building blocks that carry out some key functions in the network.In this talk,chaotic motifs (subnetworks with chaos) in GRNs are discussed.The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities.Conditions required for chaotic GRNs are found to be very strict,which make chaotic GRNs extremely rare.(ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos,and serve as the intrinsic source of chaos of random fewnode GRNs.Several optimal motifs causing chaos with atypically high probability are figured out.(iii) Moreover,we discovered that a number of special oscillators can never produce chaos.These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms.(iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs.
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