Identification of Minimum Set of Master Regulatory Genes in Gene Regulatory Networks

Identification of master regulatory genes is one of the primary challenges in systems biology. The minimum dominating set problem is a powerful paradigm in analyzing such complex networks. In these models, genes stand as nodes and their interactions are assumed as edges. Here, members of a minimal dominating set could be regarded as master genes. As finitely many minimum dominating sets may exist in a network, it is difficult to identify which one represents the most appropriate set of master genes. In this paper, we develop a weighted gene regulatory network problem with two objectives as a version of the dominating set problem. Collective influence of each gene is considered as its weight. The first objective aims to find a master regulatory genes set with minimum cardinality, and the second objective identifies the one with maximum weight. The model is converted to a single objective using a parameter varying between zero and one. The model is implemented on three human networks, and the results are reported and compared with the existing model of weighted network. Parametric programming in linear optimization and logistic regression are also implemented on the arisen relaxed problem to provide a deeper understanding of the results. Learned from computational results in parametric analysis, for some ranges of priorities in objectives, the identified master regulatory genes are invariant, while some of them are identified for all priorities. This would be an indication that such genes have higher degree of being master regulatory ones, specially on the noisy networks.