The minimum dominating set (MDSet) comprises the smallest number of graph nodes, where other graph nodes are connected with at least one MDSet node. The MDSet has been successfully applied to extract proteins that control protein-protein interaction (PPI) networks and to reveal the correlation between structural analysis and biological functions. Although the PPI network contains many MDSets, the identification of multiple MDSets is an NP-complete problem, and it is difficult to determine the best MDSets, enriched with biological functions. Therefore, the MDSet model needs to be further expanded and validated to find constrained solutions that differ from those generated by the traditional models. Moreover, by identifying the critical set of the network, the set of nodes common to all MDSets can be time-consuming. Herein, the authors adopted the minimisation of metabolic adjustment (MOMA) algorithm to develop a new framework, called maximisation of interaction adjustment (MOIA). In MOIA, they provide three models; the first one generates two MDSets with a minimum number of shared proteins, the second model generates constrained multiple MDSets ( k -MDSets), and the third model generates user-defined MDSets, containing the maximum number of essential genes and/or other important genes of the PPI network. In practice, these models significantly reduce the cost of finding the critical set and classifying the graph nodes. Herein, the authors termed the critical set as the k -critical set, where k is the number of MDSets generated by the proposed model. Then, they defined a new set of proteins called the ( k - 1 ) -critical set, where each node belongs to ( k - 1 ) MDSets. This set has been shown to be as important as the k -critical set and contains many essential genes, transcription factors, and protein kinases as the k -critical set. The ( k - 1 ) -critical set can be used to extend the search for drug target proteins. Based on the performance of the MOIA models, the authors believe the proposed methods contribute to answering key questions about the MDSets of PPI networks, and their results and analysis can be extended to other network types.

中文翻译：

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用于主导蛋白质相互作用网络的基于约束的模型。

最小支配集（MDSet）由最少数量的图节点组成，其中其他图节点与至少一个MDSet节点相连。MDSet 已成功应用于提取控制蛋白质-蛋白质相互作用 (PPI) 网络的蛋白质，并揭示结构分析与生物功能之间的相关性。虽然 PPI 网络包含许多 MDSet，但多个 MDSet 的识别是一个 NP 完全问题，很难确定最好的 MDSet，并富含生物学功能。因此，MDSet 模型需要进一步扩展和验证，以找到不同于传统模型生成的约束解。此外，通过识别网络的关键集，所有 MDSet 共有的节点集可能非常耗时。在此处，作者采用最小化代谢调整 (MOMA) 算法开发了一个新框架，称为交互调整最大化 (MOIA)。在 MOIA 中，他们提供了三种模型；第一个模型生成两个共享蛋白质最少的 MDSet，第二个模型生成受约束的多个 MDSet ( k -MDSets)，第三个模型生成用户定义的 MDSet，包含最大数量的必需基因和/或其他重要基因PPI 网络。在实践中，这些模型显着降低了查找关键集和对图节点进行分类的成本。在这里，作者将临界集称为 k -临界集，其中 k 是所提出的模型生成的 MDSet 的数量。然后，他们定义了一组新的蛋白质，称为 (k - 1) - 临界集，其中每个节点属于 (k - 1) 个 MDSet。该组已被证明与 k 临界组一样重要，并且与 k 临界组一样包含许多必需基因、转录因子和蛋白激酶。( k - 1 ) 临界集可用于扩展对药物靶蛋白的搜索。基于 MOIA 模型的性能，作者认为所提出的方法有助于回答有关 PPI 网络 MDSet 的关键问题，并且它们的结果和分析可以扩展到其他网络类型。