论文标题
一阶频率系统的对称性：符号对称计算，机械模型构建和生物学应用
Symmetries of systems of first order ODEs: Symbolic symmetry computations, mechanistic model construction and applications in biology
论文作者
论文摘要
我们讨论了对称方法在生物系统分析中的作用和优点。特别是，我们考虑了一阶普通微分方程的系统，并对与此类系统的对称性有关的几何基础提供了全面的综述。随后，我们提出了一种用于查找具有合理反应项的系统的无限发生器的算法，并使用符号计算对算法的开源实现。我们讨论了关于机械建模中对称性的两个互补观点。作为分析给定模型的工具或作为在新模型构建中纳入生物学特性的几何原理。通过与生物学建模相关的许多示例，我们证明了对称方法的不同用途，并讨论了如何从实验数据中推断对称性。
We discuss the role and merits of symmetry methods for the analysis of biological systems. In particular, we consider systems of first order ordinary differential equations and provide a comprehensive review of the geometrical foundations pertinent to symmetries of such systems. Subsequently, we present an algorithm for finding infinitesimal generators of symmetries for systems with rational reaction terms, and an open-source implementation of the algorithm using symbolic computations. We discuss two complementary perspectives on symmetries in mechanistic modelling; as tools for the analysis of a given model or as a geometrical principle for incorporating biological properties in the construction of new models. Through numerous examples of relevance to modelling in biology we demonstrate the different uses of symmetry methods, and also discuss how to infer symmetries from experimental data.
