Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations
Hopf bifurcation in a gene regulatory network model: Molecular movement causes oscillations
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DOI：
10.1142/s021820251550030x
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发表时间：
2015-06-15
影响因子：
3.5
通讯作者：
Sturrock, Marc
中科院分区：
文献类型：
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作者：
Chaplain, Mark;Ptashnyk, Mariya;Sturrock, Marc
基因调控网络，即细胞中通过其RNA和蛋白质产物间接相互作用的DNA片段，位于许多重要的细胞内信号转导过程的核心。在本文中，我们分析了一个典型的基因调控网络的数学模型组成的一个单一的负反馈回路之间的蛋白质和它的mRNA（例如Hes 1转录因子系统）。该模型由两个偏微分方程描述的蛋白质和它的mRNA之间的时空相互作用在一个一维域。这样的细胞内负反馈系统是已知的，表现出振荡行为，这是我们的模型的情况下，最初通过计算机模拟显示。为了更深入地研究这种行为，我们对模型的稳态进行了线性化稳定性分析。我们的研究结果表明，蛋白质/mRNA的扩散系数作为一个分支参数，并引起了一个霍普夫分支。这表明mRNA和蛋白质分子的空间运动本身就足以引起振荡。我们的研究结果对转录因子如p53、NF-κ B和热休克蛋白有意义，这些转录因子参与调节重要的细胞过程，如炎症、减数分裂、凋亡和热休克反应，并与关节炎和癌症等疾病有关。
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a one-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NF-kappa B and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.