{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:12:21Z","timestamp":1772172741334,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008437","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T00:00:00Z","timestamp":1609200000000}}],"reference-count":94,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T00:00:00Z","timestamp":1607990400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000154","name":"Division of Integrative Organismal Systems","doi-asserted-by":"publisher","award":["National Science Foundation IOS 1353914"],"award-info":[{"award-number":["National Science Foundation IOS 1353914"]}],"id":[{"id":"10.13039\/100000154","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000154","name":"Division of Integrative Organismal Systems","doi-asserted-by":"publisher","award":["National Science Foundation IOS 1353914"],"award-info":[{"award-number":["National Science Foundation IOS 1353914"]}],"id":[{"id":"10.13039\/100000154","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000053","name":"National Eye Institute","doi-asserted-by":"publisher","award":["National Institutes of Health NEI P30 EY07003"],"award-info":[{"award-number":["National Institutes of Health NEI P30 EY07003"]}],"id":[{"id":"10.13039\/100000053","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000082","name":"Division of Graduate Education","doi-asserted-by":"publisher","award":["National Science Foundation DGE 1256260"],"award-info":[{"award-number":["National Science Foundation DGE 1256260"]}],"id":[{"id":"10.13039\/100000082","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>\n                    The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called \u201cY-Junctions\u201d, form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the\n                    <jats:italic>Drosophila<\/jats:italic>\n                    compound eye. Since defects can provide insight into cell-cell interactions responsible for pattern formation, here we characterize the arrangement of cones in individual Y-Junction cores as well as the spatial distribution of Y-junctions across entire retinae. We find that for individual Y-junctions, the distribution of cones near the core corresponds closely to structures observed in physical crystals. In addition, Y-Junctions are organized into lines, called grain boundaries, from the retinal center to the periphery. In physical crystals, regardless of the initial distribution of defects, defects can coalesce into grain boundaries via the mobility of individual particles. By imaging in live fish, we demonstrate that grain boundaries in the cone mosaic instead appear during initial mosaic formation, without requiring defect motion. Motivated by this observation, we show that a computational model of repulsive cell-cell interactions generates a mosaic with grain boundaries. In contrast to paradigmatic models of fate specification in mostly motionless cell packings, this finding emphasizes the role of cell motion, guided by cell-cell interactions during differentiation, in forming biological crystals. Such a route to the formation of regular patterns may be especially valuable in situations, like growth on a curved surface, where the resulting long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.\n                  <\/jats:p>","DOI":"10.1371\/journal.pcbi.1008437","type":"journal-article","created":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T14:58:12Z","timestamp":1608044292000},"page":"e1008437","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":11,"title":["Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation"],"prefix":"10.1371","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4634-9422","authenticated-orcid":true,"given":"Hayden","family":"Nunley","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0993-0012","authenticated-orcid":true,"given":"Mikiko","family":"Nagashima","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7848-6352","authenticated-orcid":true,"given":"Kamirah","family":"Martin","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8633-2692","authenticated-orcid":true,"given":"Alcides","family":"Lorenzo Gonzalez","sequence":"additional","affiliation":[]},{"given":"Sachihiro C.","family":"Suzuki","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5383-0874","authenticated-orcid":true,"given":"Declan A.","family":"Norton","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5089-6296","authenticated-orcid":true,"given":"Rachel O. 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I. Location of germinal cells and numbers of neurons produced","volume":"3","author":"PA Raymond","year":"1983","journal-title":"J Neurosci"},{"key":"pcbi.1008437.ref019","first-page":"280","article-title":"Cellular pattern formation in the retina: retinal regeneration as a model system","volume":"8","author":"DL Stenkamp","year":"2002","journal-title":"Mol Vis"},{"issue":"20","key":"pcbi.1008437.ref020","doi-asserted-by":"crossref","first-page":"4182","DOI":"10.1002\/cne.22447","article-title":"Ontogeny of cone photoreceptor mosaics in zebrafish","volume":"518","author":"WT Allison","year":"2010","journal-title":"J Comp Neurol"},{"issue":"8","key":"pcbi.1008437.ref021","doi-asserted-by":"crossref","first-page":"e1002618","DOI":"10.1371\/journal.pcbi.1002618","article-title":"Coupling mechanical deformations and planar cell polarity to create regular patterns in the zebrafish retina","volume":"8","author":"G Salbreux","year":"2012","journal-title":"PLoS Comput Biol"},{"issue":"5","key":"pcbi.1008437.ref022","doi-asserted-by":"crossref","first-page":"795","DOI":"10.2108\/zsj.14.795","article-title":"Three-Dimensional Reconstitution of Cone Arrangement on the Spherical Surface of the Retina in the Medaka Eyes","volume":"14","author":"Y Nishiwaki","year":"1997","journal-title":"Zoological Science"},{"issue":"18","key":"pcbi.1008437.ref023","doi-asserted-by":"crossref","first-page":"185502","DOI":"10.1103\/PhysRevLett.89.185502","article-title":"Crystalline order on a sphere and the generalized Thomson problem","volume":"89","author":"M Bowick","year":"2002","journal-title":"Phys Rev Lett"},{"issue":"13","key":"pcbi.1008437.ref024","doi-asserted-by":"crossref","first-page":"8738","DOI":"10.1103\/PhysRevB.62.8738","article-title":"Interacting topological defects on frozen topographies","volume":"62","author":"MJ Bowick","year":"2000","journal-title":"Physical Review B"},{"key":"pcbi.1008437.ref025","first-page":"186","author":"G. Flegg","year":"2001","edition":"1"},{"issue":"22","key":"pcbi.1008437.ref026","doi-asserted-by":"crossref","first-page":"224115","DOI":"10.1103\/PhysRevB.79.224115","article-title":"Defect motifs for spherical topologies","volume":"79","author":"DJ Wales","year":"2009","journal-title":"Physical Review B"},{"issue":"6337","key":"pcbi.1008437.ref027","doi-asserted-by":"crossref","DOI":"10.1126\/science.aai7407","article-title":"Self-organized Notch dynamics generate stereotyped sensory organ patterns in Drosophila","volume":"356","author":"F Corson","year":"2017","journal-title":"Science"},{"issue":"1","key":"pcbi.1008437.ref028","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1038\/nphys3876","article-title":"Topological defects in confined populations of spindle-shaped cells","volume":"13","author":"G Duclos","year":"2017","journal-title":"Nature Physics"},{"issue":"7654","key":"pcbi.1008437.ref029","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1038\/nature22321","article-title":"Topological defects control collective dynamics in neural progenitor cell cultures","volume":"545","author":"K Kawaguchi","year":"2017","journal-title":"Nature"},{"issue":"7649","key":"pcbi.1008437.ref030","doi-asserted-by":"crossref","first-page":"212","DOI":"10.1038\/nature21718","article-title":"Topological defects in epithelia govern cell death and extrusion","volume":"544","author":"TB Saw","year":"2017","journal-title":"Nature"},{"key":"pcbi.1008437.ref031","first-page":"821","author":"FRN Nabarro","year":"1967"},{"key":"pcbi.1008437.ref032","first-page":"213","author":"J Weertman","year":"1964"},{"issue":"22","key":"pcbi.1008437.ref033","doi-asserted-by":"crossref","first-page":"225502","DOI":"10.1103\/PhysRevLett.112.225502","article-title":"Emergent structure of multidislocation ground States in curved crystals","volume":"112","author":"A Azadi","year":"2014","journal-title":"Phys Rev Lett"},{"issue":"1\u20131","key":"pcbi.1008437.ref034","doi-asserted-by":"crossref","first-page":"013003","DOI":"10.1103\/PhysRevE.94.013003","article-title":"Neutral versus charged defect patterns in curved crystals","volume":"94","author":"A Azadi","year":"2016","journal-title":"Phys Rev E"},{"issue":"26","key":"pcbi.1008437.ref035","doi-asserted-by":"crossref","first-page":"12076","DOI":"10.1021\/la0517383","article-title":"Grain boundary scars on spherical crystals","volume":"21","author":"T Einert","year":"2005","journal-title":"Langmuir"},{"issue":"39","key":"pcbi.1008437.ref036","doi-asserted-by":"crossref","first-page":"15544","DOI":"10.1073\/pnas.1300787110","article-title":"Dislocation reactions, grain boundaries, and irreversibility in two-dimensional lattices using topological tweezers","volume":"110","author":"WT Irvine","year":"2013","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"7326","key":"pcbi.1008437.ref037","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1038\/nature09620","article-title":"Pleats in crystals on curved surfaces","volume":"468","author":"WT Irvine","year":"2010","journal-title":"Nature"},{"issue":"5","key":"pcbi.1008437.ref038","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1038\/nmat1376","article-title":"Direct visualization of dislocation dynamics in grain-boundary scars","volume":"4","author":"P Lipowsky","year":"2005","journal-title":"Nat Mater"},{"issue":"5","key":"pcbi.1008437.ref039","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1039\/C4SM02234C","article-title":"Defect formation and coarsening in hexagonal 2D curved crystals","volume":"11","author":"NA Garcia","year":"2015","journal-title":"Soft Matter"},{"issue":"1","key":"pcbi.1008437.ref040","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1186\/s13064-017-0096-z","article-title":"Anisotropic Muller glial scaffolding supports a multiplex lattice mosaic of photoreceptors in zebrafish retina","volume":"12","author":"M Nagashima","year":"2017","journal-title":"Neural Dev"},{"issue":"6","key":"pcbi.1008437.ref041","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1016\/j.devcel.2012.03.007","article-title":"Crb apical polarity proteins maintain zebrafish retinal cone mosaics via intercellular binding of their extracellular domains","volume":"22","author":"J Zou","year":"2012","journal-title":"Dev Cell"},{"issue":"37","key":"pcbi.1008437.ref042","doi-asserted-by":"crossref","first-page":"15109","DOI":"10.1073\/pnas.1303551110","article-title":"Cone photoreceptor types in zebrafish are generated by symmetric terminal divisions of dedicated precursors","volume":"110","author":"SC Suzuki","year":"2013","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"22","key":"pcbi.1008437.ref043","doi-asserted-by":"crossref","first-page":"5069","DOI":"10.1242\/dev.02075","article-title":"Targeting of amacrine cell neurites to appropriate synaptic laminae in the developing zebrafish retina","volume":"132","author":"L Godinho","year":"2005","journal-title":"Development"},{"issue":"8","key":"pcbi.1008437.ref044","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1016\/S0960-9822(03)00207-0","article-title":"Dendrites of distinct classes of Drosophila sensory neurons show different capacities for homotypic repulsion","volume":"13","author":"WB Grueber","year":"2003","journal-title":"Curr Biol"},{"issue":"1","key":"pcbi.1008437.ref045","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1038\/nn.2236","article-title":"Transient neurites of retinal horizontal cells exhibit columnar tiling via homotypic interactions","volume":"12","author":"RM Huckfeldt","year":"2009","journal-title":"Nat Neurosci"},{"issue":"2","key":"pcbi.1008437.ref046","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S1350-9462(01)00024-6","article-title":"The role of tangential dispersion in retinal mosaic formation","volume":"21","author":"BE Reese","year":"2002","journal-title":"Prog Retin Eye Res"},{"issue":"8","key":"pcbi.1008437.ref047","doi-asserted-by":"crossref","first-page":"2965","DOI":"10.1046\/j.1460-9568.1999.00712.x","article-title":"Clonal expansion and cell dispersion in the developing mouse retina","volume":"11","author":"BE Reese","year":"1999","journal-title":"Eur J Neurosci"},{"issue":"5","key":"pcbi.1008437.ref048","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1101\/gad.7.5.723","article-title":"Cell interactions and gene interactions in peripheral neurogenesis","volume":"7","author":"A Ghysen","year":"1993","journal-title":"Genes Dev"},{"issue":"2","key":"pcbi.1008437.ref049","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1016\/S0025-5564(98)10034-2","article-title":"Mathematical modelling of juxtacrine cell signalling","volume":"153","author":"MR Owen","year":"1998","journal-title":"Math Biosci"},{"issue":"5613","key":"pcbi.1008437.ref050","doi-asserted-by":"crossref","first-page":"1716","DOI":"10.1126\/science.1081160","article-title":"Grain boundary scars and spherical crystallography","volume":"299","author":"AR Bausch","year":"2003","journal-title":"Science"},{"issue":"3","key":"pcbi.1008437.ref051","doi-asserted-by":"crossref","first-page":"036110","DOI":"10.1103\/PhysRevE.72.036110","article-title":"Ground state of a large number of particles on a frozen topography","volume":"72","author":"A. Travesset","year":"2005","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"13","key":"pcbi.1008437.ref052","doi-asserted-by":"crossref","first-page":"135502","DOI":"10.1103\/PhysRevLett.116.135502","article-title":"Stress Induced Branching of Growing Crystals on Curved Surfaces","volume":"116","author":"C Kohler","year":"2016","journal-title":"Phys Rev Lett"},{"issue":"6171","key":"pcbi.1008437.ref053","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1126\/science.1244827","article-title":"Elastic instability of a crystal growing on a curved surface","volume":"343","author":"G Meng","year":"2014","journal-title":"Science"},{"issue":"12","key":"pcbi.1008437.ref054","doi-asserted-by":"crossref","first-page":"2329","DOI":"10.1039\/C7SM02233F","article-title":"Defect formation dynamics in curved elastic surface crystals","volume":"14","author":"N Stoop","year":"2018","journal-title":"Soft Matter"},{"key":"pcbi.1008437.ref055","first-page":"699","author":"PM Chaikin","year":"1995"},{"issue":"5","key":"pcbi.1008437.ref056","doi-asserted-by":"crossref","first-page":"053021","DOI":"10.1088\/1367-2630\/10\/5\/053021","article-title":"Juan Fd, Vozmediano MAH. Dislocations in graphene","volume":"10","author":"A Carpio","year":"2008","journal-title":"New Journal of Physics"},{"issue":"1","key":"pcbi.1008437.ref057","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1103\/RevModPhys.81.109","article-title":"The electronic properties of graphene","volume":"81","author":"AH Castro Neto","year":"2009","journal-title":"Reviews of Modern Physics"},{"issue":"17","key":"pcbi.1008437.ref058","doi-asserted-by":"crossref","first-page":"1819","DOI":"10.1103\/PhysRevLett.56.1819","article-title":"Consequences of bond-orientational order on the macroscopic orientation patterns of thin tilted hexatic liquid-crystal films","volume":"56","author":"SB Dierker","year":"1986","journal-title":"Phys Rev Lett"},{"key":"pcbi.1008437.ref059","first-page":"377","author":"DR Nelson","year":"2002"},{"issue":"1","key":"pcbi.1008437.ref060","doi-asserted-by":"crossref","first-page":"e85325","DOI":"10.1371\/journal.pone.0085325","article-title":"Patterning the cone mosaic array in zebrafish retina requires specification of ultraviolet-sensitive cones","volume":"9","author":"PA Raymond","year":"2014","journal-title":"PLoS One"},{"issue":"5","key":"pcbi.1008437.ref061","doi-asserted-by":"crossref","first-page":"051605","DOI":"10.1103\/PhysRevE.70.051605","article-title":"Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals","volume":"70","author":"KR Elder","year":"2004","journal-title":"Physical Review E"},{"issue":"6","key":"pcbi.1008437.ref062","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1080\/00018732.2012.737555","article-title":"Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview","volume":"61","author":"H Emmerich","year":"2012","journal-title":"Advances in Physics"},{"issue":"24","key":"pcbi.1008437.ref063","doi-asserted-by":"crossref","first-page":"245701","DOI":"10.1103\/PhysRevLett.88.245701","article-title":"Modeling elasticity in crystal growth","volume":"88","author":"KR Elder","year":"2002","journal-title":"Phys Rev Lett"},{"issue":"5","key":"pcbi.1008437.ref064","doi-asserted-by":"crossref","first-page":"055004","DOI":"10.1088\/1361-651X\/aa6e48","article-title":"Application of the anisotropic phase-field crystal model to investigate the lattice systems of different anisotropic parameters and orientations","volume":"25","author":"J Kundin","year":"2017","journal-title":"Modelling and Simulation in Materials Science and Engineering"},{"issue":"3","key":"pcbi.1008437.ref065","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1140\/epjst\/e2014-02096-y","article-title":"Bridging the phase-field and phase-field crystal approaches for anisotropic material systems","volume":"223","author":"J Kundin","year":"2014","journal-title":"The European Physical Journal Special Topics"},{"issue":"3","key":"pcbi.1008437.ref066","doi-asserted-by":"crossref","first-page":"035501","DOI":"10.1103\/PhysRevLett.111.035501","article-title":"Exploring the complex world of two-dimensional ordering with three modes","volume":"111","author":"SK Mkhonta","year":"2013","journal-title":"Phys Rev Lett"},{"issue":"46","key":"pcbi.1008437.ref067","first-page":"464110","article-title":"An anisotropic phase-field crystal model for heterogeneous nucleation of ellipsoidal colloids","volume":"21","author":"R Prieler","year":"2009","journal-title":"Journal of Physics: Condensed Matter"},{"issue":"5","key":"pcbi.1008437.ref068","doi-asserted-by":"crossref","first-page":"051404","DOI":"10.1103\/PhysRevE.79.051404","article-title":"Derivation of the phase-field-crystal model for colloidal solidification","volume":"79","author":"S van Teeffelen","year":"2009","journal-title":"Phys Rev E Stat Nonlin Soft Matter Phys"},{"issue":"4","key":"pcbi.1008437.ref069","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1006\/jtbi.1996.0233","article-title":"Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling","volume":"183","author":"JR Collier","year":"1996","journal-title":"J Theor Biol"},{"issue":"13","key":"pcbi.1008437.ref070","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1242\/dev.076406","article-title":"Regulation of neuronal differentiation at the neurogenic wavefront","volume":"139","author":"P Formosa-Jordan","year":"2012","journal-title":"Development"},{"key":"pcbi.1008437.ref071","unstructured":"Formosa-Jordan P, Sprinzak D. Modeling Notch signaling: a practical tutorial. (1940\u20136029 (Electronic))."},{"issue":"3","key":"pcbi.1008437.ref072","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10867-016-9409-4","article-title":"A two-step patterning process increases the robustness of periodic patterning in the fly eye","volume":"42","author":"A Gavish","year":"2016","journal-title":"J Biol Phys"},{"key":"pcbi.1008437.ref073","doi-asserted-by":"crossref","first-page":"10461","DOI":"10.1038\/ncomms10461","article-title":"Periodic patterning of the Drosophila eye is stabilized by the diffusible activator Scabrous","volume":"7","author":"A Gavish","year":"2016","journal-title":"Nat Commun"},{"issue":"6","key":"pcbi.1008437.ref074","doi-asserted-by":"crossref","first-page":"e1002069","DOI":"10.1371\/journal.pcbi.1002069","article-title":"Mutual inactivation of Notch receptors and ligands facilitates developmental patterning","volume":"7","author":"D Sprinzak","year":"2011","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1008437.ref075","article-title":"Ordered Hexagonal Patterns via Notch-Delta Signaling","author":"E Teomy","year":"2019","journal-title":"arXiv e-prints"},{"issue":"1","key":"pcbi.1008437.ref076","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.jtbi.2004.04.024","article-title":"Intra-membrane ligand diffusion and cell shape modulate juxtacrine patterning","volume":"230","author":"SD Webb","year":"2004","journal-title":"J Theor Biol"},{"key":"pcbi.1008437.ref077","first-page":"501","author":"MBA Djamgoz","year":"1995","edition":"1"},{"issue":"4","key":"pcbi.1008437.ref078","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1002\/cne.24354","article-title":"Connectivity of cone photoreceptor telodendria in the zebrafish retina","volume":"526","author":"NCL Noel","year":"2018","journal-title":"J Comp Neurol"},{"key":"pcbi.1008437.ref079","author":"M. Westerfield","year":"1993"},{"issue":"1\u20132","key":"pcbi.1008437.ref080","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/S0014-5793(03)00977-3","article-title":"Fluorescence visualization of ultraviolet-sensitive cone photoreceptor development in living zebrafish","volume":"553","author":"M Takechi","year":"2003","journal-title":"FEBS Lett"},{"issue":"46","key":"pcbi.1008437.ref081","doi-asserted-by":"crossref","first-page":"31625","DOI":"10.1074\/jbc.M806226200","article-title":"Identification of cis-acting elements repressing blue opsin expression in zebrafish UV cones and pineal cells","volume":"283","author":"M Takechi","year":"2008","journal-title":"J Biol Chem"},{"issue":"9","key":"pcbi.1008437.ref082","doi-asserted-by":"crossref","first-page":"1383","DOI":"10.1177\/38.9.2201738","article-title":"Improved method for obtaining 3-microns cryosections for immunocytochemistry","volume":"38","author":"LK Barthel","year":"1990","journal-title":"J Histochem Cytochem"},{"issue":"2","key":"pcbi.1008437.ref083","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.ydbio.2004.11.018","article-title":"Notch-Delta signaling is required for spatial patterning and Muller glia differentiation in the zebrafish retina","volume":"278","author":"RL Bernardos","year":"2005","journal-title":"Dev Biol"},{"issue":"3","key":"pcbi.1008437.ref084","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1017\/S0952523899163168","article-title":"Cloning and characterization of six zebrafish photoreceptor opsin cDNAs and immunolocalization of their corresponding proteins","volume":"16","author":"TS Vihtelic","year":"1999","journal-title":"Vis Neurosci"},{"issue":"11","key":"pcbi.1008437.ref085","doi-asserted-by":"crossref","first-page":"3088","DOI":"10.1002\/dvdy.21343","article-title":"The Tol2kit: a multisite gateway-based construction kit for Tol2 transposon transgenesis constructs","volume":"236","author":"KM Kwan","year":"2007","journal-title":"Dev Dyn"},{"issue":"1","key":"pcbi.1008437.ref086","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.devcel.2004.06.005","article-title":"A transposon-mediated gene trap approach identifies developmentally regulated genes in zebrafish","volume":"7","author":"K Kawakami","year":"2004","journal-title":"Dev Cell"},{"issue":"34","key":"pcbi.1008437.ref087","doi-asserted-by":"crossref","first-page":"13904","DOI":"10.1073\/pnas.1308335110","article-title":"Efficient multiplex biallelic zebrafish genome editing using a CRISPR nuclease system","volume":"110","author":"LE Jao","year":"2013","journal-title":"Proc Natl Acad Sci U S A"},{"issue":"2","key":"pcbi.1008437.ref088","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1038\/nmeth.1296","article-title":"A bright and photostable photoconvertible fluorescent protein","volume":"6","author":"SA McKinney","year":"2009","journal-title":"Nat Methods"},{"issue":"1","key":"pcbi.1008437.ref089","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1140\/epje\/i2017-11489-4","article-title":"Vertex stability and topological transitions in vertex models of foams and epithelia","volume":"40","author":"MA Spencer","year":"2017","journal-title":"Eur Phys J E Soft Matter"},{"key":"pcbi.1008437.ref090","first-page":"2018","article-title":"Multicellular actomyosin cables in epithelia under external anisotropic stress","volume":"01","author":"MA Spencer","year":"2018","journal-title":"arXiv e-prints"},{"issue":"6","key":"pcbi.1008437.ref091","doi-asserted-by":"crossref","first-page":"064107","DOI":"10.1103\/PhysRevB.75.064107","article-title":"Phase-field crystal modeling and classical density functional theory of freezing","volume":"75","author":"KR Elder","year":"2007","journal-title":"Physical Review B"},{"issue":"11","key":"pcbi.1008437.ref092","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1080\/09500830701481737","article-title":"Nucleation and growth by a phase field crystal (PFC) model","volume":"87","author":"R Backofen","year":"2007","journal-title":"Philosophical Magazine Letters"},{"issue":"3","key":"pcbi.1008437.ref093","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1137\/0732037","article-title":"Implicit-Explicit Methods for Time-Dependent Partial Differential Equations","volume":"32","author":"UM Ascher","year":"1995","journal-title":"SIAM Journal on Numerical Analysis."},{"key":"pcbi.1008437.ref094","first-page":"341","author":"RJ LeVeque","year":"2007"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1008437","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2020,12,29]],"date-time":"2020-12-29T00:00:00Z","timestamp":1609200000000}}],"container-title":["PLOS Computational 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