Periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbations.
In this paper, we derive new criteria for evaluating the global stability of periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbation, which appear in many biological systems at biomolecular or cellular levels due to the weak coupling and signal diffusion (or transport) process. Our results rely on the Lipschtiz conditions of Hill function, topology of gene networks and delay kernels. In particular, Our method based on the proposed model transforms the original network into matrix analysis problem, thereby not only significantly reducing the computational complexity but also making analysis of periodic oscillation tractable for even large-scale nonlinear networks.
Shanghai University College of Science, Shanghai University, Shanghai, China. wangyihzh@hotmail.com
Yi
Y
Wang
Zhongjun
Z
Ma
Jianwei
J
Shen
Zengrong
Z
Liu
Luonan
L
Chen
D000465:Algorithms; D001693:Biological Transport, Active / Q000502:physiology; D004058:Diffusion; D004926:Escherichia coli / Q000502:physiology; D025461:Feedback, Physiological / Q000502:physiology; D053263:Gene Regulatory Networks / Q000502:physiology*; D008957:Models, Genetic; D010507:Periodicity; D011506:Proteins / Q000378:metabolism; D012333:RNA, Messenger / Q000378:metabolism; D012441:Saccharomyces cerevisiae / Q000502:physiology; D014157:Transcription Factors / Q000378:metabolism
D011506:Proteins; D012333:RNA, Messenger; D014157:Transcription Factors