arXiv 2201.016462022-01-05q-bio.MNmath.COmath.MGphysics.chem-ph

是什么让反应网络成为“化学”？

What makes a reaction network "chemical"?

Stefan Müller, Christoph Flamm, Peter F. Stadler

摘要：

反应网络（RN）包括一组物种$X$和一组$\mathscr{R}$，每个将多组离析物$Y\subseteq X$转换为多组产物$Y'\subseteq X$。RN等价于有向超图。然而，并不是所有的RN都必须承认化学解释。相反，它们可能与物理学的基本原理相矛盾，例如能量和质量守恒或化学反应的可逆性。化学计量矩阵$\mathbf{S} \in \mathbb{R}^{X\times\mathscr{R}}$的这些必要条件的后果已在文献中广泛讨论。在这里，我们提供了充分的条件，$\mathbf{S}$，保证解释RN的平衡和公式和结构公式，分别。化学上合理的RN既不允许永久移动，即，一个“徒劳的循环”的反应与不消失的能源生产，也没有创造或湮灭的质量。这样的RN被认为是理论上合理和保守的。对于有限RN，这两个条件可以等价地表示为$\mathbf{S}$的性质。第一个条件对于可逆网络来说是空洞的，但它排除了不可逆的无效循环，而且--在更严格的意义上--甚至包含不可逆反应的无效循环。第二个条件等价于存在严格正的反应不变量。此外，它是足够的存在一个实现方面的总和公式，服从守恒的“原子”。特别地，可以选择这些实现，使得任何两个物质具有不同的和式，除非$\mathbf{S}$暗示它们是“强制异构体”。就结构式而言，每个化合物都是一个标记的多重图，本质上是一个路易斯公式，反应只包括键的重排，这样总的键序就被保留了。

英文摘要：

Reaction networks (RNs) comprise a set $X$ of species and a set $\mathscr{R}$ of reactions $Y\to Y'$, each converting a multiset of educts $Y\subseteq X$ into a multiset $Y'\subseteq X$ of products. RNs are equivalent to directed hypergraphs. However, not all RNs necessarily admit a chemical interpretation. Instead, they might contradict fundamental principles of physics such as the conservation of energy and mass or the reversibility of chemical reactions. The consequences of these necessary conditions for the stoichiometric matrix $\mathbf{S} \in \mathbb{R}^{X\times\mathscr{R}}$ have been discussed extensively in the literature. Here, we provide sufficient conditions for $\mathbf{S}$ that guarantee the interpretation of RNs in terms of balanced sum formulas and structural formulas, respectively. Chemically plausible RNs allow neither a perpetuum mobile, i.e., a "futile cycle" of reactions with non-vanishing energy production, nor the creation or annihilation of mass. Such RNs are said to be thermodynamically sound and conservative. For finite RNs, both conditions can be expressed equivalently as properties of $\mathbf{S}$. The first condition is vacuous for reversible networks, but it excludes irreversible futile cycles and - in a stricter sense - futile cycles that even contain an irreversible reaction. The second condition is equivalent to the existence of a strictly positive reaction invariant. Furthermore, it is sufficient for the existence of a realization in terms of sum formulas, obeying conservation of "atoms". In particular, these realizations can be chosen such that any two species have distinct sum formulas, unless $\mathbf{S}$ implies that they are "obligatory isomers". In terms of structural formulas, every compound is a labeled multigraph, in essence a Lewis formula, and reactions comprise only a rearrangement of bonds such that the total bond order is preserved.

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英文摘要：

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