Montoya Andrés, Cruz Elkin, Ágreda Jesús
Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá D. C. 111321, Colombia.
Departamento de Química, Universidad Nacional de Colombia, Bogotá D. C. 111321, Colombia.
Life (Basel). 2019 Sep 15;9(3):74. doi: 10.3390/life9030074.
The goal of our research is the development of algorithmic tools for the analysis of chemical reaction networks proposed as models of biological homochirality. We focus on two algorithmic problems: detecting whether or not a chemical mechanism admits mirror symmetry-breaking; and, given one of those networks as input, sampling the set of racemic steady states that can produce mirror symmetry-breaking. Algorithmic solutions to those two problems will allow us to compute the parameter values for the emergence of homochirality. We found a mathematical criterion for the occurrence of mirror symmetry-breaking. This criterion allows us to compute semialgebraic definitions of the sets of racemic steady states that produce homochirality. Although those semialgebraic definitions can be processed algorithmically, the algorithmic analysis of them becomes unfeasible in most cases, given the nonlinear character of those definitions. We use Clarke's system of convex coordinates to linearize, as much as possible, those semialgebraic definitions. As a result of this work, we get an efficient algorithm that solves both algorithmic problems for networks containing only one enantiomeric pair and a heuristic algorithm that can be used in the general case, with two or more enantiomeric pairs.
我们研究的目标是开发算法工具，用于分析作为生物同手性模型提出的化学反应网络。我们专注于两个算法问题：检测化学机制是否允许镜像对称性破缺；以及，给定其中一个网络作为输入，对可产生镜像对称性破缺的外消旋稳态集进行采样。这两个问题的算法解决方案将使我们能够计算同手性出现的参数值。我们找到了镜像对称性破缺发生的数学标准。该标准使我们能够计算产生同手性的外消旋稳态集的半代数定义。尽管这些半代数定义可以通过算法进行处理，但鉴于这些定义的非线性特征，在大多数情况下对其进行算法分析变得不可行。我们使用克拉克凸坐标系统尽可能地将这些半代数定义线性化。这项工作的结果是，我们得到了一种高效算法，可解决仅包含一对对映体的网络的两个算法问题，以及一种可用于一般情况（包含两对或更多对映体）的启发式算法。
