论文标题
连接不对称蛋白质分离和种群增长的运输方法
A transport approach to relate asymmetric protein segregation and population growth
论文作者
论文摘要
许多单细胞生物在母细胞之间不对称地分配其关键蛋白质，尤其是在压力环境中。一个最近的理论模型能够预测关键蛋白质隔离的不对称性何时增强了种群的适应性，并在隔离完全不对称的两个限制下推断溶液（不对称$ a $ = 1），以及何时不对称的溶液（$ 0 \ leq a \ ll 1 $）。我们通过引入随机性并使用传输方程来获得人口增长率和关键蛋白质量的分布来获得自然方程来概括该模型。我们提供了两种方法来解决自一致方程式：通过扩展分布的矩来迭代和分析，以数值方式更新解决方案。借助这些更强大的工具，我们可以扩展Lin等人的先前模型。包括对隔离不对称的随机性。我们显示随机模型等同于具有修改的有效不对称参数（$ a _ {\ rm eff} $）的确定性模型。我们讨论了模型的生物学意义，并与其他理论模型进行了比较。
Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key proteins enhances the population fitness, extrapolating the solution at two limits where the segregation is perfectly asymmetric (asymmetry $a$ = 1) and when the asymmetry is small ($0 \leq a \ll 1$). We generalize the model by introducing stochasticity and use a transport equation to obtain a self-consistent equation for the population growth rate and the distribution of the amount of key proteins. We provide two ways of solving the self-consistent equation: numerically by updating the solution for the self-consistent equation iteratively and analytically by expanding moments of the distribution. With these more powerful tools, we can extend the previous model by Lin et al. to include stochasticity to the segregation asymmetry. We show the stochastic model is equivalent to the deterministic one with a modified effective asymmetry parameter ($a_{\rm eff}$). We discuss the biological implication of our models and compare with other theoretical models.
