{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:11:30Z","timestamp":1772172690475,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008003","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000}}],"reference-count":63,"publisher":"Public Library of Science (PLoS)","issue":"11","license":[{"start":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T00:00:00Z","timestamp":1606694400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Spatial biological networks are abundant on all scales of life, from single cells to ecosystems, and perform various important functions including signal transmission and nutrient transport. These biological functions depend on the architecture of the network, which emerges as the result of a dynamic, feedback-driven developmental process. While cell behavior during growth can be genetically encoded, the resulting network structure depends on spatial constraints and tissue architecture. Since network growth is often difficult to observe experimentally, computer simulations can help to understand how local cell behavior determines the resulting network architecture. We present here a computational framework based on directional statistics to model network formation in space and time under arbitrary spatial constraints. Growth is described as a biased correlated random walk where direction and branching depend on the local environmental conditions and constraints, which are presented as 3D multilayer grid. To demonstrate the application of our tool, we perform growth simulations of a dense network between cells and compare the results to experimental data from osteocyte networks in bone. Our generic framework might help to better understand how network patterns depend on spatial constraints, or to identify the biological cause of deviations from healthy network function.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008003","type":"journal-article","created":{"date-parts":[[2020,11,30]],"date-time":"2020-11-30T14:21:43Z","timestamp":1606746103000},"page":"e1008003","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":4,"title":["Biological network growth in complex environments: A computational framework"],"prefix":"10.1371","volume":"16","author":[{"given":"Torsten Johann","family":"Paul","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8049-6186","authenticated-orcid":true,"given":"Philip","family":"Kollmannsberger","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2020,11,30]]},"reference":[{"key":"pcbi.1008003.ref001","volume-title":"Lecture Notes in Morphogenesis","author":"M Barth\u00e9lemy","year":"2018"},{"issue":"9","key":"pcbi.1008003.ref002","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1016\/j.tics.2017.05.010","article-title":"Mechanisms of Connectome Development","volume":"21","author":"M Kaiser","year":"2017","journal-title":"Trends in Cognitive Sciences"},{"key":"pcbi.1008003.ref003","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1146\/annurev.bioeng.7.060804.100446","article-title":"Deterministic and stochastic elements of axonal guidance","volume":"7","author":"S Maskery","year":"2005","journal-title":"Annual Review of Biomedical Engineering"},{"issue":"6","key":"pcbi.1008003.ref004","doi-asserted-by":"crossref","DOI":"10.1101\/cshperspect.a001917","article-title":"Wiring the Brain: The Biology of Neuronal Guidance","volume":"2","author":"A Ch\u00e9dotal","year":"2010","journal-title":"Cold Spring Harbor Perspectives in Biology"},{"issue":"1","key":"pcbi.1008003.ref005","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1146\/annurev-conmatphys-031218-013231","article-title":"The Actin Cytoskeleton as an Active Adaptive Material","volume":"11","author":"S Banerjee","year":"2020","journal-title":"Annual Review of Condensed Matter Physics"},{"issue":"9","key":"pcbi.1008003.ref006","doi-asserted-by":"crossref","first-page":"e1002983","DOI":"10.1371\/journal.pcbi.1002983","article-title":"Angiogenesis: An Adaptive Dynamic Biological Patterning Problem","volume":"3","author":"TW Secomb","year":"2013","journal-title":"PLOS Computational Biology"},{"issue":"8","key":"pcbi.1008003.ref007","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1002\/jbmr.1927","article-title":"Architecture of the osteocyte network correlates with bone material quality","volume":"28","author":"M Kerschnitzki","year":"2013","journal-title":"Journal of Bone and Mineral Research: The Official Journal of the American Society for Bone and Mineral Research"},{"issue":"2","key":"pcbi.1008003.ref008","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1162\/artl.2010.16.2.16202","article-title":"Characteristics of pattern formation and evolution in approximations of Physarum transport networks","volume":"16","author":"J Jones","year":"2010","journal-title":"Artificial Life"},{"issue":"1623","key":"pcbi.1008003.ref009","first-page":"2307","article-title":"Biological solutions to transport network design","volume":"274","author":"DP Bebber","year":"2007","journal-title":"Proceedings Biological Sciences"},{"issue":"12","key":"pcbi.1008003.ref010","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.1016\/j.tplants.2017.09.017","article-title":"Bridging Scales in Plant Biology Using Network Science","volume":"22","author":"S Duran-Nebreda","year":"2017","journal-title":"Trends in Plant Science"},{"issue":"7666","key":"pcbi.1008003.ref011","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1038\/nature23455","article-title":"The complete connectome of a learning and memory centre in an insect brain","volume":"548","author":"K Eichler","year":"2017","journal-title":"Nature"},{"issue":"10","key":"pcbi.1008003.ref012","doi-asserted-by":"crossref","first-page":"jeb164954","DOI":"10.1242\/jeb.164954","article-title":"Of what use is connectomics? 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