半群的Cayley图在化学原子追踪中的应用
Cayley Graphs of Semigroups Applied to Atom Tracking in Chemistry
摘要：
虽然用同位素标记的化合物进行原子跟踪是一种必要且复杂的湿实验室工具，阐明反应机制，只存在有限数量的正式方法来处理这个问题。特别是当考虑大型（生物）化学网络时，其中反应是立体特异性的，严格的技术是不可避免的。我们提出了一种方法，使用右凯莱图的幺半群，以跟踪原子同时通过一系列的反应，并预测其潜在的产品分子的位置。这不仅可以用于系统地建立假设或拒绝反应机制（我们将使用ANRORC机制“亲核体的添加，开环和闭环”作为示例），而且还可以推断（生物）化学系统的自然发生的子系统。我们的研究结果包括TCA循环内的碳痕迹的分析和推断子系统的基础上的一组相关的原子上的右凯莱图的投影。
英文摘要：
While atom tracking with isotope-labeled compounds is an essential and sophisticated wet-lab tool in order to, e.g., illuminate reaction mechanisms, there exists only a limited amount of formal methods to approach the problem. Specifically when large (bio-)chemical networks are considered where reactions are stereo-specific, rigorous techniques are inevitable. We present an approach using the right Cayley graph of a monoid in order to track atoms concurrently through sequences of reactions and predict their potential location in product molecules. This can not only be used to systematically build hypothesis or reject reaction mechanisms (we will use the ANRORC mechanism "Addition of the Nucleophile, Ring Opening, and Ring Closure" as an example), but also to infer naturally occurring subsystems of (bio-)chemical systems. Our results include the analysis of the carbon traces within the TCA cycle and infer subsystems based on projections of the right Cayley graph onto a set of relevant atoms.
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