{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T11:38:43Z","timestamp":1767181123017,"version":"build-2238731810"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1007508","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000}}],"reference-count":40,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T00:00:00Z","timestamp":1575244800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["R01 GM121888"],"award-info":[{"award-number":["R01 GM121888"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["376198"],"award-info":[{"award-number":["376198"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["P50 GM085764"],"award-info":[{"award-number":["P50 GM085764"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000011","name":"Howard Hughes Medical Institute","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000011","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.1007508","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T14:12:41Z","timestamp":1575295961000},"page":"e1007508","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":7,"title":["Statistics of correlated percolation in a bacterial community"],"prefix":"10.1371","volume":"15","author":[{"given":"Xiaoling","family":"Zhai","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5660-0246","authenticated-orcid":true,"given":"Joseph W.","family":"Larkin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3051-3689","authenticated-orcid":true,"given":"Kaito","family":"Kikuchi","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2227-4806","authenticated-orcid":true,"given":"Samuel E.","family":"Redford","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3059-6661","authenticated-orcid":true,"given":"Ushasi","family":"Roy","sequence":"additional","affiliation":[]},{"given":"G\u00fcrol M.","family":"S\u00fcel","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9367-7026","authenticated-orcid":true,"given":"Andrew","family":"Mugler","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2019,12,2]]},"reference":[{"issue":"2","key":"pcbi.1007508.ref001","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1007\/s40484-013-0013-3","article-title":"Predictive power of cell-to-cell variability","volume":"1","author":"B Li","year":"2013","journal-title":"Quantitative Biology"},{"issue":"5","key":"pcbi.1007508.ref002","doi-asserted-by":"crossref","first-page":"788","DOI":"10.1016\/j.molcel.2016.05.023","article-title":"What\u2019s Luck Got to Do with It: Single Cells, Multiple Fates, and Biological Nondeterminism","volume":"62","author":"O Symmons","year":"2016","journal-title":"Molecular Cell"},{"issue":"1842","key":"pcbi.1007508.ref003","doi-asserted-by":"crossref","first-page":"1299","DOI":"10.1098\/rsta.2006.1771","article-title":"The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue","volume":"364","author":"BE Steinberg","year":"2006","journal-title":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences"},{"issue":"12","key":"pcbi.1007508.ref004","doi-asserted-by":"crossref","first-page":"932","DOI":"10.1038\/nrn2023","article-title":"Axonal conduction and injury in multiple sclerosis: the role of sodium channels","volume":"7","author":"SG Waxman","year":"2006","journal-title":"Nature Reviews Neuroscience"},{"issue":"2","key":"pcbi.1007508.ref005","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.cels.2018.06.005","article-title":"Signal Percolation within a Bacterial Community","volume":"7","author":"JW Larkin","year":"2018","journal-title":"Cell systems"},{"key":"pcbi.1007508.ref006","volume-title":"Introduction to percolation theory","author":"D Stauffer","year":"1994"},{"issue":"4","key":"pcbi.1007508.ref007","doi-asserted-by":"crossref","first-page":"042409","DOI":"10.1103\/PhysRevE.99.042409","article-title":"Disruption of microbial communication yields a two-dimensional percolation transition","volume":"99","author":"KPT Silva","year":"2019","journal-title":"Physical Review E"},{"issue":"18","key":"pcbi.1007508.ref008","doi-asserted-by":"crossref","first-page":"188102","DOI":"10.1103\/PhysRevLett.97.188102","article-title":"Percolation in living neural networks","volume":"97","author":"I Breskin","year":"2006","journal-title":"Physical review letters"},{"issue":"1-3","key":"pcbi.1007508.ref009","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.physrep.2007.02.014","article-title":"The physics of living neural networks","volume":"449","author":"JP Eckmann","year":"2007","journal-title":"Physics Reports"},{"issue":"12","key":"pcbi.1007508.ref010","doi-asserted-by":"crossref","first-page":"e15571","DOI":"10.1371\/journal.pone.0015571","article-title":"Viral epidemics in a cell culture: novel high resolution data and their interpretation by a percolation theory based model","volume":"5","author":"B G\u00f6nci","year":"2010","journal-title":"PloS one"},{"issue":"10","key":"pcbi.1007508.ref011","doi-asserted-by":"crossref","first-page":"108103","DOI":"10.1103\/PhysRevLett.115.108103","article-title":"Percolation model of sensory transmission and loss of consciousness under general anesthesia","volume":"115","author":"DW Zhou","year":"2015","journal-title":"Physical review letters"},{"issue":"11","key":"pcbi.1007508.ref012","doi-asserted-by":"crossref","first-page":"5048","DOI":"10.1529\/biophysj.108.140863","article-title":"Gap Junction Coupling and Calcium Waves in the Pancreatic Islet","volume":"95","author":"RKP Benninger","year":"2008","journal-title":"Biophysical Journal"},{"key":"pcbi.1007508.ref013","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1038\/s41586-019-1387-9","article-title":"Collective intercellular communication through ultra-fast hydrodynamic trigger waves","volume":"571","author":"A Mathijssen","year":"2019","journal-title":"Nature"},{"key":"pcbi.1007508.ref014","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1038\/nature14660","article-title":"Metabolic co-dependence gives rise to collective oscillations within biofilms","volume":"523","author":"J Liu","year":"2015","journal-title":"nature"},{"key":"pcbi.1007508.ref015","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1038\/nature15709","article-title":"Ion channels enable electrical communication in bacterial communities","volume":"527","author":"A Prindle","year":"2015","journal-title":"nature"},{"issue":"1-2","key":"pcbi.1007508.ref016","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.cell.2016.12.014","article-title":"Species-independent attraction to biofilms through electrical signaling","volume":"168","author":"J Humphries","year":"2017","journal-title":"Cell"},{"issue":"7","key":"pcbi.1007508.ref017","doi-asserted-by":"crossref","first-page":"e1005679","DOI":"10.1371\/journal.pcbi.1005679","article-title":"Growth of bacteria in 3-d colonies","volume":"13","author":"X Shao","year":"2017","journal-title":"PLoS computational biology"},{"issue":"1","key":"pcbi.1007508.ref018","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1103\/PhysRevB.29.387","article-title":"Long-range correlated percolation","volume":"29","author":"A Weinrib","year":"1984","journal-title":"Physical Review B"},{"issue":"4","key":"pcbi.1007508.ref019","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1137\/070710111","article-title":"Power-law distributions in empirical data","volume":"51","author":"A Clauset","year":"2009","journal-title":"SIAM review"},{"issue":"7","key":"pcbi.1007508.ref020","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1088\/0034-4885\/43\/7\/001","article-title":"Percolation theory","volume":"43","author":"JW Essam","year":"1980","journal-title":"Reports on progress in physics"},{"key":"pcbi.1007508.ref021","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/978-3-0346-0030-9_5","volume-title":"Fractal geometry and stochastics IV","author":"JE Steif","year":"2009"},{"key":"pcbi.1007508.ref022","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2015.03.003","article-title":"Recent advances in percolation theory and its applications","volume":"578","author":"AA Saberi","year":"2015","journal-title":"Physics Reports"},{"key":"pcbi.1007508.ref023","doi-asserted-by":"crossref","DOI":"10.1201\/9780429493492","volume-title":"Lectures on phase transitions and the renormalization group","author":"N Goldenfeld","year":"2018"},{"issue":"4","key":"pcbi.1007508.ref024","doi-asserted-by":"crossref","first-page":"1116","DOI":"10.1073\/pnas.1109261108","article-title":"Osmotic spreading of Bacillus subtilis biofilms driven by an extracellular matrix","volume":"109","author":"A Seminara","year":"2012","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"5","key":"pcbi.1007508.ref025","doi-asserted-by":"crossref","first-page":"052107","DOI":"10.1103\/PhysRevE.87.052107","article-title":"Bond and site percolation in three dimensions","volume":"87","author":"J Wang","year":"2013","journal-title":"Physical Review E"},{"issue":"7312","key":"pcbi.1007508.ref026","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1038\/nature09326","article-title":"Functional roles for noise in genetic circuits","volume":"467","author":"A Eldar","year":"2010","journal-title":"Nature"},{"issue":"18","key":"pcbi.1007508.ref027","doi-asserted-by":"crossref","first-page":"5775","DOI":"10.1128\/JB.00521-09","article-title":"Role of the \u03c3 D-dependent autolysins in Bacillus subtilis population heterogeneity","volume":"191","author":"R Chen","year":"2009","journal-title":"Journal of bacteriology"},{"issue":"7477","key":"pcbi.1007508.ref028","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1038\/nature12804","article-title":"Memory and modularity in cell-fate decision making","volume":"503","author":"TM Norman","year":"2013","journal-title":"Nature"},{"issue":"5","key":"pcbi.1007508.ref029","doi-asserted-by":"crossref","first-page":"1037","DOI":"10.1016\/j.bpj.2017.01.010","article-title":"Signal destruction tunes the zone of activation in spatially distributed signaling networks","volume":"112","author":"KP Silva","year":"2017","journal-title":"Biophysical journal"},{"issue":"18","key":"pcbi.1007508.ref030","doi-asserted-by":"crossref","first-page":"4779","DOI":"10.1073\/pnas.1719317115","article-title":"Spatial determinants of quorum signaling in a Pseudomonas aeruginosa infection model","volume":"115","author":"SE Darch","year":"2018","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"16","key":"pcbi.1007508.ref031","doi-asserted-by":"crossref","first-page":"168104","DOI":"10.1103\/PhysRevLett.104.168104","article-title":"Cell migration driven by cooperative substrate deformation patterns","volume":"104","author":"TE Angelini","year":"2010","journal-title":"Physical review letters"},{"issue":"5-6","key":"pcbi.1007508.ref032","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1387\/ijdb.041821pf","article-title":"Collective cell migration in morphogenesis and cancer","volume":"48","author":"P Friedl","year":"2004","journal-title":"International Journal of Developmental Biology"},{"issue":"13","key":"pcbi.1007508.ref033","doi-asserted-by":"crossref","first-page":"3021","DOI":"10.1242\/dev.01253","article-title":"Parallels between tissue repair and embryo morphogenesis","volume":"131","author":"P Martin","year":"2004","journal-title":"Development"},{"issue":"4","key":"pcbi.1007508.ref034","doi-asserted-by":"crossref","first-page":"R1724","DOI":"10.1103\/PhysRevA.46.R1724","article-title":"Structural and dynamical properties of long-range correlated percolation","volume":"46","author":"S Prakash","year":"1992","journal-title":"Physical Review A"},{"issue":"4","key":"pcbi.1007508.ref035","doi-asserted-by":"crossref","first-page":"3870","DOI":"10.1103\/PhysRevE.54.3870","article-title":"Scaling properties of a percolation model with long-range correlations","volume":"54","author":"M Sahimi","year":"1996","journal-title":"Physical Review E"},{"issue":"6","key":"pcbi.1007508.ref036","doi-asserted-by":"crossref","first-page":"7054","DOI":"10.1103\/PhysRevE.58.7054","article-title":"Modeling urban growth patterns with correlated percolation","volume":"58","author":"HA Makse","year":"1998","journal-title":"Physical Review E"},{"issue":"4-6","key":"pcbi.1007508.ref037","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0370-1573(98)00024-6","article-title":"Non-linear and non-local transport processes in heterogeneous media: from long-range correlated percolation to fracture and materials breakdown","volume":"306","author":"M Sahimi","year":"1998","journal-title":"Physics Reports"},{"issue":"6","key":"pcbi.1007508.ref038","doi-asserted-by":"crossref","first-page":"062133","DOI":"10.1103\/PhysRevE.93.062133","article-title":"Percolation model with an additional source of disorder","volume":"93","author":"S Kundu","year":"2016","journal-title":"Physical Review E"},{"issue":"3","key":"pcbi.1007508.ref039","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1143\/PTP.61.842","article-title":"Percolation in Anisotropic Systems: \u2014Real-Space Renormalization Group\u2014","volume":"61","author":"H Ikeda","year":"1979","journal-title":"Progress of Theoretical Physics"},{"key":"pcbi.1007508.ref040","first-page":"183","volume-title":"Methods in enzymology","author":"E Meijering","year":"2012"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1007508","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1007508","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T13:52:01Z","timestamp":1576158721000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1007508"}},"subtitle":[],"editor":[{"given":"Ned S.","family":"Wingreen","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2019,12,2]]},"references-count":40,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2019,12,2]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1007508","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,2]]}}}