Mathematical and Theoretical Physics Unit, Okinawa Institute of Science and Technology Graduate University, 1919-1 Tancha, Onna-son, Kunigami-gun, Okinawa, 904-0495, Japan.
Sci Rep. 2018 Jul 13;8(1):10607. doi: 10.1038/s41598-018-28954-1.
Investigations of topological uniqueness of gene interaction networks in cancer cells are essential for understanding the disease. Although cancer is considered to originate from the topological alteration of a huge molecular interaction network in cellular systems, the theoretical study to investigate such complex networks is still insufficient. It is necessary to predict the behavior of a huge complex interaction network from the behavior of a finite size network. Based on the random matrix theory, we study the distribution of the nearest neighbor level spacings P(s) of interaction matrices of gene networks in human cancer cells. The interaction matrices are computed using the Cancer Network Galaxy (TCNG) database which is a repository of gene interactions inferred by a Bayesian network model. 256 NCBI GEO entries regarding gene expressions in human cancer cells have been used for the inference. We observe the Wigner distribution of P(s) when the gene networks are dense networks that have more than ~38,000 edges. In the opposite case, when the networks have smaller numbers of edges, the distribution P(s) becomes the Poisson distribution. We investigate relevance of P(s) both to the sparseness of the networks and to edge frequency factor which is the reliance (likelihood) of the inferred gene interactions.
研究癌细胞中基因相互作用网络的拓扑唯一性对于理解这种疾病至关重要。尽管癌症被认为起源于细胞系统中巨大分子相互作用网络的拓扑改变，但对这种复杂网络进行理论研究仍然不足。有必要从有限大小的网络的行为来预测巨大复杂相互作用网络的行为。基于随机矩阵理论，我们研究了人类癌细胞中基因网络相互作用矩阵的最近邻能级间距 P(s)的分布。这些相互作用矩阵是使用 Cancer Network Galaxy (TCNG)数据库计算的，该数据库是一个由贝叶斯网络模型推断出的基因相互作用的存储库。我们使用了 256 个与人类癌细胞基因表达有关的 NCBI GEO 条目进行推断。当基因网络是密集网络，即具有超过~38000 个边时，我们观察到 P(s)的维格纳分布。在相反的情况下，当网络具有较少的边时，分布 P(s)变为泊松分布。我们研究了 P(s)与网络的稀疏性以及边缘频率因子（推断出的基因相互作用的可靠性）之间的相关性。
