Characterising biochemical reaction network structure in mathematical terms enables the inference of functional biochemical consequences from network structure with existing mathematical techniques and spurs the development of new mathematics that exploits the peculiarities of biochemical network structure. The structure of a biochemical network may be specified by reaction stoichiometry, that is, the relative quantities of each molecule produced and consumed in each reaction of the network. A biochemical network may also be specified at a higher level of resolution in terms of the internal structure of each molecule and how molecular structures are transformed by each reaction in a network. The stoichiometry for a set of reactions can be compiled into a stoichiometric matrix N∈Zm×n, where each row corresponds to a molecule and each column corresponds to a reaction. We demonstrate that a stoichiometric matrix may be split into the sum of m-rank(N) moiety transition matrices, each of which corresponds to a subnetwork accessible to a structurally identifiable conserved moiety. The existence of this moiety matrix splitting is a property that distinguishes a stoichiometric matrix from an arbitrary rectangular matrix.

中文翻译：

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化学计量矩阵的结构保守部分分裂。

用数学术语表征生化反应网络结构，可以利用现有的数学技术从网络结构推断功能生化后果，并刺激利用生化网络结构特性的新数学的发展。生化网络的结构可以通过反应化学计量确定，即在网络的每个反应中产生和消耗的每个分子的相对量。根据每个分子的内部结构以及网络中每个反应如何转化分子结构，还可以更高的分辨率指定一个生化网络。一组反应的化学计量可以编译成化学计量矩阵N∈Zm×n，其中每一行对应一个分子，每一列对应一个反应。我们证明化学计量的矩阵可以分为m-rank（N）部分过渡矩阵的总和，每个矩阵对应于可访问结构可识别的保守部分的子网。该部分矩阵分裂的存在是将化学计量矩阵与任意矩形矩阵区分开的性质。