{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,17]],"date-time":"2026-10-17T15:04:17Z","timestamp":1792249457324,"version":"4.4.0"},"reference-count":30,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T00:00:00Z","timestamp":1644364800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"publisher","award":["17H06386"],"award-info":[{"award-number":["17H06386"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS ONE"],"abstract":"<jats:p>Many skin diseases show circular red lesions on the skin, called erythema. Erythema is characterized by the expansion of its circular area solely from local stimulation. A pathological inflammatory response caused by the stimulation persistently increases inflammatory mediators in the dermis, whereas a normal inflammatory response transiently increases mediators, resulting in the shrinkage of the erythema. Although the diffusion of mediators theoretically reproduces the expansion, how the inflammatory response expands or shrinks the erythema remains unknown. A possibility is positive feedback, which affects mediator production and can generate two distinct stable states (i.e., inflamed and noninflamed), referred to as bistability. Bistability causes a state transition either from the noninflamed to inflamed state or the reverse direction by suprathreshold stimulation. Additionally, the diffusion selectively causes state transition in either direction, resulting in spatial spread of the transited state, known as the traveling wave. Therefore, we hypothesize that the traveling wave of the inflammatory response can account for both the expansion and shrinkage. Using a reaction-diffusion model with bistability, we theoretically show a possible mechanism in which the circular inflamed area expands via the traveling wave from the noninflamed to the inflamed state. During the expansion, the boundary between the inflamed and noninflamed areas moves at a constant velocity while maintaining its concentration gradient. Moreover, when the positive feedback is weak, the traveling wave selectively occurs from the inflamed to noninflamed state, shrinking the inflamed area. Whether the inflamed area expands or shrinks is mainly controlled by the balance of mediator concentration between the noninflamed and inflamed states, relative to the threshold. The traveling wave of the inflammatory response provides an experimentally testable framework for erythema expansion and shrinkage, thereby contributing to the development of effective treatments, including probiotics.<\/jats:p>","DOI":"10.1371\/journal.pone.0263049","type":"journal-article","created":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T18:30:57Z","timestamp":1644431457000},"page":"e0263049","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":13,"title":["Traveling wave of inflammatory response to regulate the expansion or shrinkage of skin erythema"],"prefix":"10.1371","volume":"17","author":[{"given":"Maki","family":"Sudo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6473-7990","authenticated-orcid":true,"given":"Koichi","family":"Fujimoto","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2022,2,9]]},"reference":[{"key":"pone.0263049.ref001","volume-title":"Shimizu\u2019s textbook of dermatology","author":"H. Shimizu","year":"2007","edition":"1"},{"key":"pone.0263049.ref002","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1007\/978-3-642-76977-1_22","article-title":"Rash theory","author":"LA Segel","year":"1992","journal-title":"Theoretical and Experimental Insights into Immunology"},{"issue":"2","key":"pone.0263049.ref003","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1097\/AIA.0b013e318034194e","article-title":"Cytokines, inflammation, and pain","volume":"45","author":"J-M Zhang","year":"2007","journal-title":"International Anesthesiology Clinics"},{"issue":"3","key":"pone.0263049.ref004","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1097\/QCO.0b013e3283298e62","article-title":"Molecular mechanisms of maculopapular exanthema","volume":"22","author":"TD Fern\u00e1ndez","year":"2009","journal-title":"Current Opinion in Infectious Diseases"},{"issue":"10","key":"pone.0263049.ref005","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1038\/nri2622","article-title":"Skin immune sentinels in health and disease","volume":"9","author":"FO Nestle","year":"2009","journal-title":"Nat Rev Immunol"},{"key":"pone.0263049.ref006","doi-asserted-by":"crossref","first-page":"924","DOI":"10.1201\/9781315533247","volume-title":"Janeway\u2019s immunobiology","author":"K Murphy","year":"2016","edition":"9"},{"issue":"1","key":"pone.0263049.ref007","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1038\/s41577-018-0084-5","article-title":"The immunological anatomy of the skin","volume":"19","author":"K Kabashima","year":"2019","journal-title":"Nat Rev Immunol"},{"key":"pone.0263049.ref008","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.jocn.2018.06.056","article-title":"Post-infectious sensory neuropathy with anti-GT1a and GQ1b antibodies associated with cold urticaria","volume":"56","author":"E Zucchi","year":"2018","journal-title":"Journal of Clinical Neuroscience"},{"issue":"6","key":"pone.0263049.ref009","doi-asserted-by":"crossref","first-page":"1351","DOI":"10.1111\/bjd.14419","article-title":"The 2016 International League of Dermatological Societies\u2019 revised glossary for the description of cutaneous lesions","volume":"174","author":"A Nast","year":"2016","journal-title":"Br J Dermatol"},{"issue":"2","key":"pone.0263049.ref010","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.jdermsci.2014.08.010","article-title":"Classification of inflammatory skin diseases: A proposal based on the disorders of the three-layered defense systems, barrier, innate immunity and acquired immunity","volume":"76","author":"T Dainichi","year":"2014","journal-title":"Journal of Dermatological Science"},{"issue":"1","key":"pone.0263049.ref011","doi-asserted-by":"crossref","first-page":"3016","DOI":"10.1038\/s41467-018-05274-6","article-title":"A positive feedback loop bi-stably activates fibroblasts","volume":"9","author":"S-Y Yeo","year":"2018","journal-title":"Nat Commun"},{"issue":"6","key":"pone.0263049.ref012","doi-asserted-by":"crossref","first-page":"1861","DOI":"10.1016\/j.jaci.2016.10.026","article-title":"Mathematical modeling of atopic dermatitis reveals \u201cdouble-switch\u201d mechanisms underlying 4 common disease phenotypes","volume":"139","author":"E Dom\u00ednguez-H\u00fcttinger","year":"2017","journal-title":"Journal of Allergy and Clinical Immunology"},{"issue":"12","key":"pone.0263049.ref013","doi-asserted-by":"crossref","first-page":"e1001024","DOI":"10.1371\/journal.pcbi.1001024","article-title":"A systems model for immune cell interactions unravels the mechanism of inflammation in human skin","volume":"6","author":"NV Valeyev","year":"2010","journal-title":"PLoS Comput Biol"},{"key":"pone.0263049.ref014","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/j.isci.2019.10.008","article-title":"Skin patterning in psoriasis by spatial interactions between pathogenic cytokines","volume":"20","author":"L Ringham","year":"2019","journal-title":"iScience"},{"issue":"1","key":"pone.0263049.ref015","doi-asserted-by":"crossref","first-page":"e1007590","DOI":"10.1371\/journal.pcbi.1007590","article-title":"A single reaction-diffusion equation for the multifarious eruptions of urticaria","volume":"16","author":"S Seirin-Lee","year":"2020","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"pone.0263049.ref016","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1080\/10273660500066618","article-title":"Is the skin an excitable medium? pattern formation in erythema gyratum repens","volume":"6","author":"S Gilmore","year":"2005","journal-title":"Journal of Theoretical Medicine"},{"issue":"2","key":"pone.0263049.ref017","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1111\/exd.12302","article-title":"Frontiers in epidermal barrier homeostasis\u2014an approach to mathematical modelling of epidermal calcium dynamics","volume":"23","author":"M Denda","year":"2014","journal-title":"Exp Dermatol"},{"issue":"9","key":"pone.0263049.ref018","doi-asserted-by":"crossref","first-page":"252","DOI":"10.3390\/app6090252","article-title":"Chronic inflammation in the epidermis: a mathematical model","volume":"6","author":"S Nakaoka","year":"2016","journal-title":"Applied Sciences"},{"issue":"3","key":"pone.0263049.ref019","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1016\/j.bpj.2013.12.017","article-title":"Spatiotemporal evolution of erythema migrans, the hallmark rash of lyme disease","volume":"106","author":"DK Vig","year":"2014","journal-title":"Biophysical Journal"},{"key":"pone.0263049.ref020","first-page":"2","volume-title":"Interdisciplinary applied mathematics","author":"JD Murray","year":"2002","edition":"3"},{"issue":"5999","key":"pone.0263049.ref021","doi-asserted-by":"crossref","first-page":"1616","DOI":"10.1126\/science.1179047","article-title":"Reaction-diffusion model as a framework for understanding biological pattern formation","volume":"329","author":"S Kondo","year":"2010","journal-title":"Science"},{"issue":"6","key":"pone.0263049.ref022","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.it.2004.03.008","article-title":"The two NF-\u03baB activation pathways and their role in innate and adaptive immunity","volume":"25","author":"G Bonizzi","year":"2004","journal-title":"Trends in Immunology"},{"issue":"4","key":"pone.0263049.ref023","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1016\/j.plrev.2009.10.002","article-title":"Reaction\u2013diffusion waves in biology","volume":"6","author":"V Volpert","year":"2009","journal-title":"Physics of Life Reviews"},{"issue":"10","key":"pone.0263049.ref024","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1097\/DAD.0000000000000786","article-title":"The Histopathology of Urticaria Revisited\u2014Clinical Pathological Study","volume":"39","author":"A Barzilai","year":"2017","journal-title":"The American Journal of Dermatopathology"},{"issue":"1","key":"pone.0263049.ref025","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s00424-016-1903-9","article-title":"Tight junctions in skin inflammation","volume":"469","author":"K B\u00e4sler","year":"2017","journal-title":"Pflugers Arch\u2014Eur J Physiol"},{"issue":"4","key":"pone.0263049.ref026","doi-asserted-by":"crossref","first-page":"2635","DOI":"10.4049\/jimmunol.175.4.2635","article-title":"Cytokine production by skin-derived mast cells: endogenous proteases are responsible for degradation of cytokines","volume":"175","author":"W Zhao","year":"2005","journal-title":"J Immunol"},{"issue":"1","key":"pone.0263049.ref027","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1186\/s40168-018-0404-9","article-title":"Commensal microbiota modulate gene expression in the skin","volume":"6","author":"JS Meisel","year":"2018","journal-title":"Microbiome"},{"issue":"5","key":"pone.0263049.ref028","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1007\/s10439-009-9652-y","article-title":"The Transport Profile of Cytokines in Epidermal Equivalents Subjected to Mechanical Loading","volume":"37","author":"LH Cornelissen","year":"2009","journal-title":"Ann Biomed Eng"},{"key":"pone.0263049.ref029","unstructured":"Iryojohokagaku-kenkyusho. Medical Disease: An illustrated reference guide vol.14 -Dermatology. (in Japanese). 2020. (Medic Media, Tokyo) ISBN978-4-89632-818-9"},{"key":"pone.0263049.ref030","doi-asserted-by":"crossref","first-page":"589726","DOI":"10.3389\/fmicb.2020.589726","article-title":"Skin and Gut Microbiome in Psoriasis: Gaining Insight Into the Pathophysiology of It and Finding Novel Therapeutic Strategies","volume":"11","author":"L Chen","year":"2020","journal-title":"Front Microbiol"}],"container-title":["PLOS ONE"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0263049","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,9]],"date-time":"2022-02-09T18:31:40Z","timestamp":1644431500000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0263049"}},"subtitle":[],"editor":[{"given":"Daniele","family":"Avitabile","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2022,2,9]]},"references-count":30,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,2,9]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0263049","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,9]]}}}