Department of Computer Science and Information Technology, Faculty of Science, Ibb University, Ibb, Yemen.
Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt.
IET Syst Biol. 2021 Jul;15(5):148-162. doi: 10.1049/syb2.12021. Epub 2021 May 28.
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 ( -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 -critical set, where is the number of MDSets generated by the proposed model. Then, they defined a new set of proteins called the -critical set, where each node belongs to MDSets. This set has been shown to be as important as the -critical set and contains many essential genes, transcription factors, and protein kinases as the -critical set. The -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.
最小支配集（MDSet）由数量最少的图节点组成，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。尽管 PPI 网络包含许多 MDSets，但多个 MDSets 的识别是一个 NP 完全问题，并且很难确定富含生物功能的最佳 MDSets。因此，需要进一步扩展和验证 MDSet 模型，以找到与传统模型生成的约束解决方案不同的解决方案。此外，通过识别网络的关键集，识别所有 MDSets 共有的节点集可能很耗时。在此，作者采用代谢调整最小化（MOMA）算法开发了一种新框架，称为交互调整最大化（MOIA）。在 MOIA 中，他们提供了三种模型；第一种模型生成具有最小共享蛋白质数的两个 MDSets，第二种模型生成约束多个 MDSets（ - MDSets），第三种模型生成用户定义的 MDSets，包含 PPI 网络的最大数量的必需基因和/或其他重要基因。在实践中，这些模型大大降低了寻找关键集和对图节点进行分类的成本。在此，作者将关键集称为 -关键集，其中 是由提出的模型生成的 MDSets 的数量。然后，他们定义了一组新的蛋白质，称为 -关键集，其中每个节点属于 个 MDSets。事实证明，该集合与 -关键集一样重要，并且包含许多必需基因、转录因子和蛋白激酶，与 -关键集一样重要。 -关键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关于 PPI 网络 MDSets 的关键问题，并且他们的结果和分析可以扩展到其他网络类型。
