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In this paper, we present analytic criteria for the existence of oscillations in gene regulatory networks with cyclic structure. In particular, inherent time delays in transcription, translation and translocation process are explicitly treated, and the effects of such time delays are quantitatively revealed. We first show that local instability of the unique equilibrium state results in oscillations...
In this paper, we derive an analytic criterion for the existence of periodic oscillations in cyclic gene regulatory networks where each protein represses another gene expression in a cyclic way. We analyze local instability properties of large-scale cyclic gene regulatory networks based on the result which shows that local instability of an equilibrium point globally guarantees the existence of periodic...
This paper investigates the criteria for the existence of protein level oscillations in a class of gene regulatory networks, where a nonlinear differential equation model is considered to analyze its dynamical behavior. There are two steps to derive such criteria: We first employ a Poincare??-Bendixson type theorem to restrict the class of solution trajectories, and then carry out a local stability...
In this paper, we derive an existence condition of periodic oscillations in cyclic gene regulatory networks, of which the dynamical behavior is described by nonlinear differential equations. For this purpose, we first point out that change of the equilibrium point with respect to biochemical parameters is important for comprehensive analysis, and show the properties which the equilibrium point should...
This paper studies analytic robust stability criteria for large-scale cyclic gene-protein regulatory network systems with unstructured or parametric uncertainties. We first consider a class of gene expressions, which is described as uncertain Linear Transcription-Translation Models (LTTMs) with not only feedback loops from translation products to transcription but also degradation properties of proteins...
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