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These structural perturbations can cause changes to the reachability of systems\u2019 state spaces. As system structures are related to genotypes and state spaces are related to phenotypes, it is important to study the relationship between structures and state spaces. However, there is still no method can quantitively describe the reachability differences of two state spaces caused by structural perturbations. Therefore, Difference in Reachability between State Spaces (DReSS) is proposed. DReSS index family can quantitively describe differences of reachability, attractor sets between two state spaces and can help find the key structure in a system, which may influence system\u2019s state space significantly. First, basic properties of DReSS including non-negativity, symmetry and subadditivity are proved. Then, typical examples are shown to explain the meaning of DReSS and the differences between DReSS and traditional graph distance. Finally, differences of DReSS distribution between real biological regulatory networks and random networks are compared. Results show most structural perturbations in biological networks tend to affect reachability inside and between attractor basins rather than to affect attractor set itself when compared with random networks, which illustrates that most genotype differences tend to influence the proportion of different phenotypes and only a few ones can create new phenotypes. DReSS can provide researchers with a new insight to study the relation between genotypes and phenotypes.<\/jats:p>","DOI":"10.1093\/bib\/bbaa315","type":"journal-article","created":{"date-parts":[[2020,10,17]],"date-time":"2020-10-17T07:10:03Z","timestamp":1602918603000},"source":"Crossref","is-referenced-by-count":0,"title":["DReSS: a method to quantitatively describe the influence of structural perturbations on state spaces of genetic regulatory networks"],"prefix":"10.1093","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4340-5414","authenticated-orcid":false,"given":"Ziqiao","family":"Yin","sequence":"first","affiliation":[{"name":"Shenyuan Honors College and School of Mathematical Sciences, Beihang University, and Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education. He currently works as a visiting scholar at Yale University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Binghui","family":"Guo","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Institute, Beijing Advanced Innovation Center for Big Data and Brain Computing, LMIB, NLSDE, School of Mathematical Sciences, Beihang University, and Peng Cheng Laboratory"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuangge","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Yale University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yifan","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Statistics, Renmin University of China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhilong","family":"Mi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, and School of Mathematical Sciences from Beihang University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiming","family":"Zheng","sequence":"additional","affiliation":[{"name":"Artificial Intelligence Institute, Beijing Advanced Innovation Center for Big Data and Brain Computing, LMIB, NLSDE, School of Mathematical Sciences, Beihang University, and Peng Cheng Laboratory"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,12,14]]},"reference":[{"issue":"6","key":"2021072117025466300_ref1","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1016\/j.gde.2013.10.003","article-title":"Genotype to phenotype via network analysis","volume":"23","author":"Carter","year":"2013","journal-title":"Curr Opin Genet Dev"},{"issue":"14","key":"2021072117025466300_ref2","doi-asserted-by":"crossref","first-page":"4781","DOI":"10.1073\/pnas.0305937101","article-title":"The yeast cell-cycle network is robustly designed","volume":"101","author":"Li","year":"2004","journal-title":"Proc Natl Acad Sci"},{"key":"2021072117025466300_ref3","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.coisb.2017.11.009","article-title":"Robustness, accuracy, and cell state heterogeneity in biological systems","volume":"8","author":"Wollman","year":"2018","journal-title":"Curr Opin Syst Biol"},{"key":"2021072117025466300_ref4","first-page":"183","article-title":"A robustness analysis of dynamic Boolean models of cellular circuits","author":"Bruner","journal-title":"Bioinformatics Research and Applications. 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