用微分方程组的解析解拟合甲型流感病毒聚合酶酸性蛋白家族的进化过程

Fitting Evolutionary Process of Polymerase Acidic Protein Family from Influenza A Virus with Analytical Solution of System of Differential Equations

关键词:  氨基酸对的可预测性  进化  拟合  甲型流感病毒  聚合酶酸性蛋白  微分方程

Key words:  amino-acid pair predictability  evolution  fitting  influenza A virus  polymerase acidic protein  differential equation

摘要:

用数学模型对甲型流感病毒聚合酶酸性蛋白家族的进化进行拟合:(1)用氨基酸对的可预测性量化1918年至2008年分离的2433个聚合酶酸性蛋白以表示其演变,(2)确定上升半寿期和下降半衰期是否相似作为拟合的前提条件,(3)用微分方程组的解析解拟合进化,(4)用所获得的拟合参数模拟2009年至2018年可能的进化过程。结果呈现了对聚合酶酸性蛋白家族及其不同亚型的良好拟合,这标志着蛋白质进化的研究已经从经验性的实验分析向动力学的数学建模迈进。

Abstract:

We fitted the evolution of polymerase acidic protein family from influenza A virus using a mathematical model:(i) we used the amino-acid pair predictability to quantify 2433 polymerase acidic proteins isolated from 1918 to 2008 to represent their evolution, (ii) we determined if the uphill half-life is similar to the downhill one as a pre-request for fitting, (iii) we used the analytical solution of system of differential equations to fit this evolution, and (iv) we simulated the possible evolutionary process from 2009 to 2018 using the obtained fitted parameters. The results showed a good-of-fit for polymerase acidic protein family and its different subtypes, indicating that the study on protein evolution begins to move forward dynamically mathematical modeling from passively empirical data-collection.