Stability of delay induced oscillations in gene expression of Hes1 protein model

详细信息	查看全文 | 推荐本文 |

• 作者：Marek Bodnar^a ; ^{mbodnar@mimuw.edu.pl} ; Agnieszka Bartł ; omiejczyk^b ; ^{agnes@mif.pg.gda.pl}
• 关键词：Biochemical reaction ; Delay differential equations ; Asymptotic analysis ; The Hopf bifurcation ; The Hill coefficient ; Hes1 protein
• 刊名：Nonlinear Analysis ; Real World Applications
• 出版年：2012
• 期刊代码：44_14681218
• 类别：mt
• 出版时间：October, 2012
• 卷：13
• 期：5
• 页码：2227-2239
• 文件大小：684 K

摘要

Mathematical analysis of the Hes1 genetic oscillator system is presented. The considered model is a聽modification of the model proposed by Monk [N.A. Monk, Oscillatory expression of Hes1, p53, and NF- B driven by transcriptional time delays, Curr. Biol. 13 (2003) 1409-1413]. In this paper we model separately time delays connected with transcription and translation processes. Global existence, uniqueness and non-negativity of solutions are proved. The existence of a聽unique positive steady state is shown. The stability of the steady state is studied and it is shown that it depends on the sum of time delays. Conditions guaranteeing the occurrence of the Hopf bifurcation as well as its stability are proved. Presented analysis partially confirms the results obtained numerically by Jensen et聽al. [M. Jensen, K. Sneppen, G. Tiana, Sustained oscillations and time delays in gene expression of protein Hes1, FEBS Lett. 541 (2003) 176-177].