{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:10:38Z","timestamp":1760145038882,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,8]],"date-time":"2024-06-08T00:00:00Z","timestamp":1717804800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"publisher","award":["EP\/V008641\/1","EP\/S024344\/1"],"award-info":[{"award-number":["EP\/V008641\/1","EP\/S024344\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The process of end-joining during nonhomologous repair of DNA double-strand breaks (DSBs) after radiation damage is considered. Experimental evidence has revealed that the dynamics of DSB ends exhibit subdiffusive motion rather than simple diffusion with rare directional movement. Traditional models often overlook the rare long-range directed motion. To address this limitation, we present a heterogeneous anomalous diffusion model consisting of subdiffusive fractional Brownian motion interchanged with short periods of long-range movement. Our model sheds light on the underlying mechanisms of heterogeneous diffusion in DSB repair and could be used to quantify the DSB dynamics on a time scale inaccessible to single particle tracking analysis. The model predicts that the long-range movement of DSB ends is responsible for the misrepair of DSBs in the form of dicentric chromosome lesions.<\/jats:p>","DOI":"10.3390\/e26060502","type":"journal-article","created":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T10:08:43Z","timestamp":1718014123000},"page":"502","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Modelling Heterogeneous Anomalous Dynamics of Radiation-Induced Double-Strand Breaks in DNA during Non-Homologous End-Joining Pathway"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7208-4555","authenticated-orcid":false,"given":"Nickolay","family":"Korabel","sequence":"first","affiliation":[{"name":"Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3638-7759","authenticated-orcid":false,"given":"John W.","family":"Warmenhoven","sequence":"additional","affiliation":[{"name":"Division of Cancer Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PL, UK"},{"name":"The Christie NHS Foundation Trust, Manchester M20 4BX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9670-7638","authenticated-orcid":false,"given":"Nicholas T.","family":"Henthorn","sequence":"additional","affiliation":[{"name":"Division of Cancer Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PL, UK"},{"name":"The Christie NHS Foundation Trust, Manchester M20 4BX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1786-349X","authenticated-orcid":false,"given":"Samuel","family":"Ingram","sequence":"additional","affiliation":[{"name":"Division of Cancer Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PL, UK"},{"name":"Christie Medical Physics and Engineering, The Christie NHS Foundation Trust, Manchester M20 4BX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2722-4330","authenticated-orcid":false,"given":"Sergei","family":"Fedotov","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2021-3148","authenticated-orcid":false,"given":"Charlotte J.","family":"Heaven","sequence":"additional","affiliation":[{"name":"Division of Cancer Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PL, UK"},{"name":"The Christie NHS Foundation Trust, Manchester M20 4BX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0901-210X","authenticated-orcid":false,"given":"Karen J.","family":"Kirkby","sequence":"additional","affiliation":[{"name":"Division of Cancer Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PL, UK"},{"name":"The Christie NHS Foundation Trust, Manchester M20 4BX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8718-3684","authenticated-orcid":false,"given":"Michael J.","family":"Taylor","sequence":"additional","affiliation":[{"name":"Division of Cancer Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PL, UK"},{"name":"The Christie NHS Foundation Trust, Manchester M20 4BX, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8422-5255","authenticated-orcid":false,"given":"Michael J.","family":"Merchant","sequence":"additional","affiliation":[{"name":"Division of Cancer Sciences, Faculty of Biology, Medicine and Health, The University of Manchester, Manchester M13 9PL, UK"},{"name":"The Christie NHS Foundation Trust, Manchester M20 4BX, UK"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Walter, P. (2007). Molecular Biology of the Cell, Garland Sci.. [5th ed.].","DOI":"10.1201\/9780203833445"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2595","DOI":"10.15252\/embj.201695842","article-title":"Chromatin stiffening underlies enhanced locus mobility after DNA damage in budding yeast","volume":"36","author":"Herbert","year":"2017","journal-title":"Embo J."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1038\/nsmb.3347","article-title":"Histone degradation in response to DNA damage enhances chromatin dynamics and recombination rates","volume":"24","author":"Hauer","year":"2017","journal-title":"Nat. Struct. Mol. Biol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1091\/mbc.e16-12-0846","article-title":"Microtubule dynamics drive enhanced chromatin motion and mobilize telomeres in response to DNA damage","volume":"28","author":"Lawrimore","year":"2017","journal-title":"Mol. Biol. Cell"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3323","DOI":"10.1091\/mbc.e17-05-0317","article-title":"Multi-scale tracking reveals scale-dependent chromatin dynamics after DNA damage","volume":"28","author":"Recamier","year":"2017","journal-title":"Mol. Biol. Cell"},{"key":"ref_6","first-page":"545679","article-title":"Complex chromatin motions for DNA repair","volume":"11","author":"Chiolo","year":"2020","journal-title":"Front. Genet."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1016\/j.molcel.2016.02.010","article-title":"Two-stage synapsis of DNA ends during non-homologous end joining","volume":"61","author":"Graham","year":"2016","journal-title":"Mol. Cell"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"018102","DOI":"10.1103\/PhysRevLett.103.018102","article-title":"Transient anomalous diffusion of telomeres in the nucleus of mammalian cells","volume":"103","author":"Bronstein","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"238102","DOI":"10.1103\/PhysRevLett.104.238102","article-title":"Bacterial chromosomal loci move subdiffusively through a viscoelastic cytoplasm","volume":"104","author":"Weber","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1839","DOI":"10.1016\/j.bpj.2012.09.040","article-title":"Universal algorithm for identification of fractional Brownian motion. A case of telomere subdiffusion","volume":"103","author":"Burnecki","year":"2012","journal-title":"Biophys. J."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1101\/gr.157008.113","article-title":"High-throughput chromatin motion tracking in living yeast reveals the flexibility of the fiber throughout the genome","volume":"23","author":"Hajjoul","year":"2013","journal-title":"Genome Res."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1479","DOI":"10.1016\/j.cell.2013.12.001","article-title":"Dynamic imaging of genomic loci in living human cells by an optimized CRISPR\/Cas system","volume":"155","author":"Chen","year":"2013","journal-title":"Cell"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.cell.2014.05.036","article-title":"3D trajectories adopted by coding and regulatory DNA elements: First-passage times for genomic interactions","volume":"158","author":"Lucas","year":"2014","journal-title":"Cell"},{"key":"ref_14","first-page":"062716","article-title":"Chromosomal locus tracking with proper accounting of static and dynamic errors","volume":"91","author":"Backlund","year":"2015","journal-title":"Phys. Rev."},{"key":"ref_15","unstructured":"De Gennes, P.G. (1979). Scaling Concepts in Polymer Physics, Cornell University Press."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2511","DOI":"10.1038\/srep02511","article-title":"Subdiffusion Supports Joining Of Correct Ends During Repair Of DNA Double-Strand Breaks","volume":"3","author":"Girst","year":"2013","journal-title":"Sci. Rep."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7753","DOI":"10.1073\/pnas.1806297115","article-title":"Anomalous diffusion, spatial coherence, and viscoelasticity from the energy landscape of human chromosomes","volume":"115","author":"Potoyan","year":"2018","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"126601","DOI":"10.1088\/1361-6633\/ad058f","article-title":"Heterogeneous anomalous transport in cellular and molecular biology","volume":"86","author":"Waigh","year":"2023","journal-title":"Rep. Prog. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1200","DOI":"10.1016\/j.celrep.2017.01.018","article-title":"Visualization of chromatin decompaction and break site extrusion as predicted by statistical polymer modeling of single-locus trajectories","volume":"18","author":"Amitai","year":"2017","journal-title":"Cell Rep."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1038\/s41556-019-0379-1","article-title":"Nuclear actin filaments in DNA repair dynamics","volume":"21","author":"Caridi","year":"2019","journal-title":"Nat. Cell Biol."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shinkai, S., Nozaki, T., Maeshima, K., and Togashi, Y. (2016). Dynamic nucleosome movement provides structural information of topological chromatin domains in living human cells. Plos Comput. Biol., 12.","DOI":"10.1101\/059147"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1645","DOI":"10.1016\/j.celrep.2012.11.008","article-title":"Local nucleosome dynamics facilitate chromatin accessibility in living mammalian cells","volume":"2","author":"Hihara","year":"2012","journal-title":"Cell Rep."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3854","DOI":"10.1038\/ncomms4854","article-title":"Persistent super-diffusive motion of Escherichia coli chromosomal loci","volume":"5","author":"Javer","year":"2014","journal-title":"Nat. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2181","DOI":"10.1126\/science.1065366","article-title":"Chromosome dynamics in the yeast interphase nucleus","volume":"294","author":"Heun","year":"2001","journal-title":"Science"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2919","DOI":"10.1529\/biophysj.104.044230","article-title":"3-D particle tracking in a two-photon microscope: Application to the study of molecular dynamics in cells","volume":"88","author":"Levi","year":"2005","journal-title":"Biophys. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"15555","DOI":"10.1073\/pnas.1220313110","article-title":"Micron-scale coherence in interphase chromatin dynamics","volume":"110","author":"Zidovska","year":"2013","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3161","DOI":"10.1038\/s41467-018-05606-6","article-title":"Interphase human chromosome exhibits out of equilibrium glassy dynamics","volume":"9","author":"Shi","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.cell.2014.08.030","article-title":"Interchromosomal homology searches drive directional ALT telomere movement and synapsis","volume":"159","author":"Cho","year":"2014","journal-title":"Cell"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2567","DOI":"10.1038\/s41467-018-05009-7","article-title":"Nuclear microtubule filaments mediate non-linear directional motion of chromatin and promote DNA repair","volume":"9","author":"Oshidari","year":"2018","journal-title":"Nat. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1146\/annurev-genet-120417-031334","article-title":"Chromosome dynamics in response to DNA damage","volume":"52","author":"Seeber","year":"2018","journal-title":"Annu. Rev. Genet."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1016\/j.gde.2007.08.004","article-title":"Mobility and immobility of chromatin in transcription and genome stability","volume":"17","author":"Soutoglou","year":"2007","journal-title":"Curr. Opin. Genet. Dev."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1126\/science.1088845","article-title":"Dynamics of DNA double-strand breaks revealed by clustering of damaged chromosome domains","volume":"303","author":"Aten","year":"2004","journal-title":"Science"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1038\/nsmb.3387","article-title":"Genome-wide mapping of long-range contacts unveils clustering of DNA double-strand breaks at damaged active genes","volume":"24","author":"Aymard","year":"2017","journal-title":"Nat. Struct. Mol. Biol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"542","DOI":"10.1093\/rpd\/ncq383","article-title":"Mechanistic simulation of radiation damage to DNA and its repair: On the track towards systems radiation biology modelling","volume":"143","author":"Friedland","year":"2011","journal-title":"Radiat. Prot. Dosim."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"102743","DOI":"10.1016\/j.dnarep.2019.102743","article-title":"Insights into the non-homologous end joining pathway and double strand break end mobility provided by mechanistic in silico modelling","volume":"85","author":"Warmenhoven","year":"2020","journal-title":"Dna Repair"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Kroese, D.P., and Botev, Z.I. (2014). Spatial process simulation. Stochastic Geometry, Spatial Statistics and Random Fields: Models and Algorithms, Springer.","DOI":"10.1007\/978-3-319-10064-7_12"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"6845","DOI":"10.1039\/C8RA10168J","article-title":"Clinically relevant nanodosimetric simulation of DNA damage complexity from photons and protons","volume":"9","author":"Henthorn","year":"2019","journal-title":"Rsc Adv."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2642","DOI":"10.1063\/1.445022","article-title":"Particle\u2013antiparticle annihilation in diffusive motion","volume":"78","author":"Toussaint","year":"1983","journal-title":"J. Chem. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0301-0104(02)00546-3","article-title":"Subdiffusion-limited reactions","volume":"284","author":"Yuste","year":"2002","journal-title":"Chem. Phys."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.ijrobp.2015.07.2279","article-title":"Variations in the processing of DNA double-strand breaks along 60-MeV therapeutic proton beams","volume":"95","author":"Chaudhary","year":"2016","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"776","DOI":"10.1016\/j.ijrobp.2017.11.012","article-title":"Complex DNA damage induced by high linear energy transfer alpha-particles and protons triggers a specific cellular DNA damage response","volume":"100","author":"Carter","year":"2018","journal-title":"Int. J. Radiat. Oncol. Biol. Phys."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF01324225","article-title":"Chromosome aberrations induced by protons up to 31 MeV in cultured human cells","volume":"19","author":"Bettega","year":"1981","journal-title":"Radiat. Environ. Biophys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1080\/095530097142816","article-title":"Chromosome aberration frequencies in human lymphocytes irradiated in a multi-layer array by protons with different LET","volume":"72","author":"Schmid","year":"1997","journal-title":"Int. J. Radiat. Biol."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/6\/502\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:55:46Z","timestamp":1760108146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/26\/6\/502"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,8]]},"references-count":43,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["e26060502"],"URL":"https:\/\/doi.org\/10.3390\/e26060502","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2024,6,8]]}}}