%0 Journal Article
%T Bifurcations and Dynamics of Cancer Signaling Network Regulated by MicroRNA
%A Qianqian Zheng
%A Jianwei Shen
%J Discrete Dynamics in Nature and Society
%D 2013
%I Hindawi Publishing Corporation
%R 10.1155/2013/176956
%X MicroRNAs are currently considered as key regulators of a wide variety of biological pathways and regulate many processes of life and obtained more and more attention in recent years. In this paper, we investigate the dynamics of gene network regulated by miR-34a (microRNA) involved in triple negative feedback loop. As we know that the p53 network involve in cancer, How the cancer arise is unclear. We investigate this negative feedback network by using mathematical model and drive the theoretical results of globally asymptotic stability and provide the sufficient conditions for the periodic oscillation. These results are propitious to understand how p53 network involved in miR-34a induces the cancer. 1. Introduction MicroRNAs (miRNAs) are a family of small regulatory RNAs whose function is to regulate the activity and stability of specific mRNA targets through posttranscriptional regulatory mechanism and play a role in repressing translation of mRNA or degrading mRNAs [1¨C9]. Recent studies show that microRNAs play a central role in many biological (cellular) processes, including developmental timing, cell proliferation, apoptosis, metabolism, cell differentiation, somitogenesis and tumour genesis [1]. In this paper, we focus on miR-34a which may behave as inhibitor depending on biological context. Resecting normal tumor tissues of 25 human hepatocellular carcinoma patients demonstrated an inverse correlation between miR-34a and c-Met-protein [2]. MiR-34a is proposed as a marker for the activity of the p53 pathway in chronic lymphocytic leukemia [3] (Table 1). The induction of miR-34a was most pronounced among all differential regulations. Also expression of the primary miR-34a transcript was induced after p53 activation [4]. MiR-34a may play a cytoprotective role in cell survival [5]. In U87 cell, miR-34a plays a negative role in the regulation of Dll1 target gene through downregulating Dll1 protein but not mRNA [6]. Expression of miR-34a is induced which may mediate the target gene and result in the cells arresting in G1 and G2 phase to repair DNA [7]. Table 1: Notation for species concentrations. In order to understand further the miR-34a involved in the network with p53 and Sirt1, we have planned to model this network with mathematical model. It is well known that the time delay is quite ubiquitous in nature, so we also investigate the relationship between the time delay and the network with miR-34a, p53, and Sirt1. We know that the delay is often caused by a finite signal transmission speed and memory effects, so the time delay can sometimes
%U http://www.hindawi.com/journals/ddns/2013/176956/