{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,27]],"date-time":"2026-02-27T06:12:45Z","timestamp":1772172765351,"version":"3.50.1"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1008440","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T00:00:00Z","timestamp":1608076800000}}],"reference-count":32,"publisher":"Public Library of Science (PLoS)","issue":"12","license":[{"start":{"date-parts":[[2020,12,4]],"date-time":"2020-12-04T00:00:00Z","timestamp":1607040000000},"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>Cells assemble microns-long filamentous structures from protein monomers that are nanometers in size. These structures are often highly dynamic, yet in order for them to function properly, cells maintain them at a precise length. Here we investigate length-dependent depolymerization as a mechanism of length control. This mechanism has been recently proposed for flagellar length control in the single cell organisms Chlamydomonas and Giardia. Length dependent depolymerization can arise from a concentration gradient of a depolymerizing protein, such as kinesin-13 in Giardia, along the length of the flagellum. Two possible scenarios are considered: a linear and an exponential gradient of depolymerizing proteins. We compute analytically the probability distributions of filament lengths for both scenarios and show how these distributions are controlled by key biochemical parameters through a dimensionless number that we identify. In Chlamydomonas cells, the assembly dynamics of its two flagella are coupled via a shared pool of molecular components that are in limited supply, and so we investigate the effect of a limiting monomer pool on the length distributions. Finally, we compare our calculations to experiments. While the computed mean lengths are consistent with observations, the noise is two orders of magnitude smaller than the observed length fluctuations.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1008440","type":"journal-article","created":{"date-parts":[[2020,12,4]],"date-time":"2020-12-04T15:20:45Z","timestamp":1607095245000},"page":"e1008440","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":7,"title":["Control of filament length by a depolymerizing gradient"],"prefix":"10.1371","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7474-1720","authenticated-orcid":true,"given":"Arnab","family":"Datta","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3288-5926","authenticated-orcid":true,"given":"David","family":"Harbage","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7522-7144","authenticated-orcid":true,"given":"Jane","family":"Kondev","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2020,12,4]]},"reference":[{"key":"pcbi.1008440.ref001","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1038\/nature08908","article-title":"Cell mechanics and the cytoskeleton","volume":"463","author":"DA Fletcher","year":"2010","journal-title":"Nature"},{"key":"pcbi.1008440.ref002","doi-asserted-by":"crossref","first-page":"R359","DOI":"10.1016\/j.cub.2010.02.054","article-title":"Mitosis: Taking the Measure of Spindle Length","volume":"20","author":"DJ Needleman","year":"2010","journal-title":"Current Biology"},{"key":"pcbi.1008440.ref003","doi-asserted-by":"crossref","first-page":"e1004160","DOI":"10.1371\/journal.pcbi.1004160","article-title":"Antenna Mechanism of Length Control of Actin Cables","volume":"11","author":"L Mohapatra","year":"2015","journal-title":"PLoS Comput Biol"},{"key":"pcbi.1008440.ref004","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1146\/annurev.cellbio.20.012103.094437","article-title":"CELLULAR LENGTH CONTROL SYSTEMS","volume":"20","author":"WF Marshall","year":"2004","journal-title":"Annu Rev Cell Dev Biol"},{"key":"pcbi.1008440.ref005","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/S0074-7696(06)60004-1","article-title":"Flagellar Length Control in Chlamydomonas\u2014A Paradigm for Organelle Size Regulation","author":"KA Wemmer","year":"2007","journal-title":"International Review of Cytology"},{"key":"pcbi.1008440.ref006","doi-asserted-by":"crossref","first-page":"58104","DOI":"10.1103\/PhysRevLett.108.258104","article-title":"Microtubule Length-Regulation by Molecular Motors","volume":"108","author":"A Melbinger","year":"2012","journal-title":"Phys Rev Lett"},{"key":"pcbi.1008440.ref007","doi-asserted-by":"crossref","first-page":"258103","DOI":"10.1103\/PhysRevLett.108.258103","article-title":"Length Regulation of Active Biopolymers by Molecular Motors","volume":"108","author":"D Johann","year":"2012","journal-title":"Phys Rev Lett"},{"key":"pcbi.1008440.ref008","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1126\/science.1243147","article-title":"Cytoplasmic Volume Modulates Spindle Size During Embryogenesis","volume":"342","author":"MC Good","year":"2013","journal-title":"Science"},{"key":"pcbi.1008440.ref009","article-title":"Biophysics of filament length regulation by molecular motors","volume":"28","author":"H-S Kuan","year":"2014"},{"key":"pcbi.1008440.ref010","doi-asserted-by":"crossref","first-page":"6225","DOI":"10.1021\/acs.jpcb.6b02242","article-title":"Exact Length Distribution of Filamentous Structures Assembled from a Finite Pool of Subunits","volume":"120","author":"D Harbage","year":"2016","journal-title":"J Phys Chem B"},{"key":"pcbi.1008440.ref011","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/j.devcel.2011.07.004","article-title":"The Myosin Passenger Protein Smy1 Controls Actin Cable Structure and Dynamics by Acting as a Formin Damper","volume":"21","author":"M Chesarone-Cataldo","year":"2011","journal-title":"Developmental Cell"},{"key":"pcbi.1008440.ref012","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1016\/j.cels.2017.04.011","article-title":"The Limiting-Pool Mechanism Fails to Control the Size of Multiple Organelles","volume":"4","author":"L Mohapatra","year":"2017","journal-title":"Cell Systems"},{"key":"pcbi.1008440.ref013","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1083\/jcb.92.1.170","article-title":"Analysis of flagellar size control using a mutant of Chlamydomonas reinhardtii with a variable number of flagella","volume":"92","author":"MR Kuchka","year":"1982","journal-title":"The Journal of Cell Biology"},{"key":"pcbi.1008440.ref014","doi-asserted-by":"crossref","first-page":"270","DOI":"10.1091\/mbc.e04-07-0586","article-title":"Flagellar Length Control System: Testing a Simple Model Based on Intraflagellar Transport and Turnover","volume":"16","author":"WF Marshall","year":"2005","journal-title":"MBoC"},{"key":"pcbi.1008440.ref015","first-page":"47","article-title":"FLAGELLAR ELONGATION AND SHORTENING IN CHLAMYDOMONAS","author":"B Coyne","year":"1970","journal-title":"The Journal of Cell Biology"},{"key":"pcbi.1008440.ref016","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1038\/nrm3085","article-title":"Ciliogenesis: building the cell\u2019s antenna","volume":"12","author":"H Ishikawa","year":"2011","journal-title":"Nat Rev Mol Cell Biol"},{"key":"pcbi.1008440.ref017","doi-asserted-by":"crossref","first-page":"663","DOI":"10.1016\/j.bpj.2017.11.3784","article-title":"Diffusion as a Ruler: Modeling Kinesin Diffusion as a Length Sensor for Intraflagellar Transport","volume":"114","author":"NL Hendel","year":"2018","journal-title":"Biophysical Journal"},{"key":"pcbi.1008440.ref018","doi-asserted-by":"crossref","first-page":"e42599","DOI":"10.7554\/eLife.42599","article-title":"Length regulation of multiple flagella that self-assemble from a shared pool of components","volume":"8","author":"TG Fai","year":"2019","journal-title":"eLife"},{"key":"pcbi.1008440.ref019","doi-asserted-by":"crossref","first-page":"e48694","DOI":"10.7554\/eLife.48694","article-title":"Length-dependent disassembly maintains four different flagellar lengths in Giardia","volume":"8","author":"SG McInally","year":"2019","journal-title":"eLife"},{"key":"pcbi.1008440.ref020","doi-asserted-by":"crossref","first-page":"1174","DOI":"10.1016\/j.cell.2009.07.032","article-title":"Kinesin-8 Motors Act Cooperatively to Mediate Length-Dependent Microtubule Depolymerization","volume":"138","author":"V Varga","year":"2009","journal-title":"Cell"},{"key":"pcbi.1008440.ref021","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1016\/j.devcel.2012.10.016","article-title":"KIF19A Is a Microtubule-Depolymerizing Kinesin for Ciliary Length Control","volume":"23","author":"S Niwa","year":"2012","journal-title":"Developmental Cell"},{"key":"pcbi.1008440.ref022","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1038\/nature04736","article-title":"The depolymerizing kinesin MCAK uses lattice diffusion to rapidly target microtubule ends","volume":"441","author":"J Helenius","year":"2006","journal-title":"Nature"},{"key":"pcbi.1008440.ref023","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1016\/j.cub.2007.03.048","article-title":"A Novel Microtubule-Depolymerizing Kinesin Involved in Length Control of a Eukaryotic Flagellum","volume":"17","author":"C Blaineau","year":"2007","journal-title":"Current Biology"},{"key":"pcbi.1008440.ref024","doi-asserted-by":"crossref","first-page":"5706","DOI":"10.1529\/biophysj.108.143453","article-title":"Protein Localization by Actin Treadmilling and Molecular Motors Regulates Stereocilia Shape and Treadmilling Rate","volume":"95","author":"M Naoz","year":"2008","journal-title":"Biophysical Journal"},{"key":"pcbi.1008440.ref025","article-title":"Dynamics of the IFT machinery at the ciliary tip","volume":"25","author":"A Chien"},{"key":"pcbi.1008440.ref026","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0003-2697(70)90196-X","article-title":"Simple method for quantitive densitometry of polyacrylamide gels using fast green","volume":"35","author":"MA Gorovsky","year":"1970","journal-title":"Analytical Biochemistry"},{"key":"pcbi.1008440.ref027","doi-asserted-by":"crossref","first-page":"1605","DOI":"10.1083\/jcb.119.6.1605","article-title":"Polarity of Flagellar Assembly in Chlamydomonas","volume":"119","author":"KA Johnson","year":"1992","journal-title":"The Journal of Cell Biology"},{"key":"pcbi.1008440.ref028","doi-asserted-by":"crossref","first-page":"29754","DOI":"10.1074\/jbc.M103184200","article-title":"Flagellar Protein Dynamics in Chlamydomonas","volume":"276","author":"L Song","year":"2001","journal-title":"J Biol Chem"},{"key":"pcbi.1008440.ref029","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1083\/jcb.200106141","article-title":"Intraflagellar transport balances continuous turnover of outer doublet microtubules","volume":"155","author":"WF Marshall","year":"2001","journal-title":"The Journal of Cell Biology"},{"key":"pcbi.1008440.ref030","first-page":"111","article-title":",Microtubule dynamics in vitro","volume":"13","author":"PM BAYLEY","year":"1994","journal-title":"Mod cell biol"},{"key":"pcbi.1008440.ref031","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1083\/jcb.201409036","article-title":"Tubulin transport by IFT is upregulated during ciliary growth by a cilium-autonomous mechanism","volume":"208","author":"JM Craft","year":"2015","journal-title":"Journal of Cell Biology"},{"key":"pcbi.1008440.ref032","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/S0021-9258(17)32840-5","article-title":"Microtubular proteins of Chlamydomonas reinhardtii. An immunochemical study based on the use of an antibody specific for the beta-tubulin subunit","volume":"252","author":"G Piperno","year":"1977","journal-title":"Journal of Biological Chemistry"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1008440","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2020,12,16]],"date-time":"2020-12-16T00:00:00Z","timestamp":1608076800000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008440","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,16]],"date-time":"2021-04-16T12:37:18Z","timestamp":1618576638000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1008440"}},"subtitle":[],"editor":[{"given":"Martin","family":"Meier-Schellersheim","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2020,12,4]]},"references-count":32,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1008440","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/2020.06.02.130039","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,4]]}}}