{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:19:19Z","timestamp":1760231959682,"version":"build-2065373602"},"reference-count":63,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,13]],"date-time":"2022-05-13T00:00:00Z","timestamp":1652400000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["11871238","11931019","61773401","20QD47","3173211205"],"award-info":[{"award-number":["11871238","11931019","61773401","20QD47","3173211205"]}]},{"name":"Science Foundation of Wuhan Institute of Technology","award":["11871238","11931019","61773401","20QD47","3173211205"],"award-info":[{"award-number":["11871238","11931019","61773401","20QD47","3173211205"]}]},{"name":"Foundation of Zhongnan University of Economics and Law","award":["11871238","11931019","61773401","20QD47","3173211205"],"award-info":[{"award-number":["11871238","11931019","61773401","20QD47","3173211205"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>One of the key challenges in systems biology and molecular sciences is how to infer regulatory relationships between genes and proteins using high-throughout omics datasets. Although a wide range of methods have been designed to reverse engineer the regulatory networks, recent studies show that the inferred network may depend on the variable order in the dataset. In this work, we develop a new algorithm, called the statistical path-consistency algorithm (SPCA), to solve the problem of the dependence of variable order. This method generates a number of different variable orders using random samples, and then infers a network by using the path-consistent algorithm based on each variable order. We propose measures to determine the edge weights using the corresponding edge weights in the inferred networks, and choose the edges with the largest weights as the putative regulations between genes or proteins. The developed method is rigorously assessed by the six benchmark networks in DREAM challenges, the mitogen-activated protein (MAP) kinase pathway, and a cancer-specific gene regulatory network. The inferred networks are compared with those obtained by using two up-to-date inference methods. The accuracy of the inferred networks shows that the developed method is effective for discovering molecular regulatory systems.<\/jats:p>","DOI":"10.3390\/e24050693","type":"journal-article","created":{"date-parts":[[2022,5,14]],"date-time":"2022-05-14T09:27:56Z","timestamp":1652520476000},"page":"693","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Inference of Molecular Regulatory Systems Using Statistical Path-Consistency Algorithm"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5833-4607","authenticated-orcid":false,"given":"Yan","family":"Yan","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Wuhan Institute of Technology, Wuhan 430205, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Feng","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6191-0209","authenticated-orcid":false,"given":"Tianhai","family":"Tian","sequence":"additional","affiliation":[{"name":"School of Mathematics, Monash University, Melbourne 3800, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.coisb.2017.08.009","article-title":"Designing and interpreting \u2018multi-omic\u2019 experiments that may change our understanding of biology","volume":"6","author":"Haas","year":"2017","journal-title":"Curr. 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