Effects of nonlinear degradation of protein on the oscillatory dynamics in a simple gene regulatory network

Fengpan Zhang, Jinrui Lu, Zhiguang Liu, Aimin Chen and Jianwei Shen

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 6, 1286-1295

Abstract: Cooperative stability of protein is here defined as the tendency for the oligomers to be more stable than their monomeric components and to perform their physiological functions. In this paper, we incorporate nonlinear degradation of protein induced by cooperative stability into a simple model which has been previously presented in the biological literature. Linear analysis gives a critical time delay beyond which a periodic solution is born in a Hopf bifurcation. Lindstedt’s method is applied to the nonlinear system, resulting in closed form approximate expressions for the amplitude and frequency of oscillation. Our findings indicate that cooperative stability can cause periodic dynamics through reducing the critical time delay. In addition, we show that cooperative stability may increase the amplitude of oscillation. Our study contributes to the theoretical demonstration of the effect of cooperative stability in the simple gene regulatory network.

Keywords: Gene regulatory network; Cooperative stability; Lindstedt’s method; Holf bifurcation; Oscillation (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:6:p:1286-1295

DOI: 10.1016/j.physa.2009.11.040

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