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Identifying such a critical point or tipping point is essential for revealing the underlying mechanism of complex biological systems. However, it is difficult to identify the tipping point since few significant differences in the critical state are detected in terms of traditional static measurements.<\/jats:p><\/jats:sec><jats:sec><jats:title>Results<\/jats:title><jats:p>In this study, by exploring the dynamic changes in gene cooperative effects between the before-transition and critical states, we presented a model-free approach, the directed-network rank score (DNRS), to detect the early-warning signal of critical transition in complex biological systems. The proposed method is applicable to both bulk and single-cell RNA-sequencing (scRNA-seq) data. This computational method was validated by the successful identification of the critical or pre-transition state for both simulated and six real datasets, including three scRNA-seq datasets of embryonic development and three tumor datasets. In addition, the functional and pathway enrichment analyses suggested that the corresponding DNRS signaling biomarkers were involved in key biological processes.<\/jats:p><\/jats:sec><jats:sec><jats:title>Availability and implementation<\/jats:title><jats:p>The source code is freely available at https:\/\/github.com\/zhongjiayuan\/DNRS.<\/jats:p><\/jats:sec><jats:sec><jats:title>Supplementary information<\/jats:title><jats:p>Supplementary data are available at Bioinformatics online.<\/jats:p><\/jats:sec>","DOI":"10.1093\/bioinformatics\/btac707","type":"journal-article","created":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T18:24:27Z","timestamp":1666722267000},"page":"5398-5405","source":"Crossref","is-referenced-by-count":21,"title":["Identifying the critical state of complex biological systems by the directed-network rank score method"],"prefix":"10.1093","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0508-1383","authenticated-orcid":false,"given":"Jiayuan","family":"Zhong","sequence":"first","affiliation":[{"name":"School of Mathematics and Big Data, Foshan University , Foshan 528000, China"},{"name":"School of Mathematics, South China University of Technology , Guangzhou 510640, China"}]},{"given":"Chongyin","family":"Han","sequence":"additional","affiliation":[{"name":"School of Biology and Biological Engineering, South China University of Technology , Guangzhou 510640, China"}]},{"given":"Yangkai","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology , Guangzhou 510640, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2017-576X","authenticated-orcid":false,"given":"Pei","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology , Guangzhou 510640, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4547-8695","authenticated-orcid":false,"given":"Rui","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mathematics, South China University of Technology , Guangzhou 510640, China"},{"name":"Pazhou Lab , Guangzhou 510330, China"}]}],"member":"286","published-online":{"date-parts":[[2022,10,25]]},"reference":[{"key":"2022121418404752500_btac707-B1","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1038\/nbt1203","article-title":"Gene prioritization through genomic data fusion","volume":"24","author":"Aerts","year":"2006","journal-title":"Nat. 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