Kozdęba Agnieszka, Tomski Andrzej
Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland.
Institute of Mathematics, University of Silesia, Bankowa 14, 40-007 Katowice, Poland.
Math Biosci. 2020 Sep;327:108413. doi: 10.1016/j.mbs.2020.108413. Epub 2020 Jul 4.
In this paper we analyse stochastic expression of a single gene with its dynamics given by the classical Goodwin model with mRNA and protein contribution. We compare the effect of the presence of positive and negative feedback on the transcription regulation. In such cases we observe two qualitatively different types of asymptotic behaviour. In the case of a negative feedback loop, under sufficient conditions, one can find a stationary density for mRNA and protein molecules. In the case of a positive feedback loop we observe extinction of both types of molecules with time.
在本文中，我们分析了单个基因的随机表达，其动力学由具有mRNA和蛋白质贡献的经典古德温模型给出。我们比较了正负反馈对转录调控的影响。在这种情况下，我们观察到两种定性不同的渐近行为类型。在负反馈回路的情况下，在充分条件下，可以找到mRNA和蛋白质分子的平稳密度。在正反馈回路的情况下，我们观察到两种类型的分子随时间灭绝。
