论文标题
fokker-planck基因表达鲁棒性研究的方法
A Fokker-Planck approach to the study of robustness in gene expression
论文作者
论文摘要
我们研究了几个由随机化学动力学系统引起的几个Fokker-Planck方程，该系统对生物学中的基因调节网络进行了建模。求解Fokker-Planck方程的密度描述了细胞中信使RNA和微RNA含量的关节分布。我们提供了理论和数值的证据，即在存在微RNA的情况下，基因表达的鲁棒性增加了。在数学水平上，在存在微RNA的情况下，稳健性增加显示了信使RNA边缘密度变化的较小系数。这些结果来自解决方案的显式公式。此外，由于维度分析和数值模拟，我们为每个参数在模型中的作用提供了定性的见解。随着基因表达水平的增加来自模型中的潜在随机性，我们最终讨论了模型中噪声的选择及其对结果的影响。
We study several Fokker-Planck equations arising from a stochastic chemical kinetic system modeling a gene regulatory network in biology. The densities solving the Fokker-Planck equations describe the joint distribution of the messenger RNA and micro RNA content in a cell. We provide theoretical and numerical evidences that the robustness of the gene expression is increased in the presence of micro RNA. At the mathematical level, increased robustness shows in a smaller coefficient of variation of the marginal density of the messenger RNA in the presence of micro RNA. These results follow from explicit formulas for solutions. Moreover, thanks to dimensional analyses and numerical simulations we provide qualitative insight into the role of each parameter in the model. As the increase of gene expression level comes from the underlying stochasticity in the models, we eventually discuss the choice of noise in our models and its influence on our results.
