{"id":"https://openalex.org/W7207752149","doi":"https://doi.org/10.3389/fnins.2026.1896585","title":"Symmetry-based derivation of neuronal membrane dynamics: a Lie group approach to action potential generation","display_name":"Symmetry-based derivation of neuronal membrane dynamics: a Lie group approach to action potential generation","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7207752149","doi":"https://doi.org/10.3389/fnins.2026.1896585","pmid":"https://pubmed.ncbi.nlm.nih.gov/42757185","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/13584316"},"language":"en","primary_location":{"id":"doi:10.3389/fnins.2026.1896585","doi":"https://doi.org/10.3389/fnins.2026.1896585","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fnins.2026.1896585","pdf_url":"https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2026.1896585/pdf","source":{"id":"https://openalex.org/S115201632","display_name":"Frontiers in Neuroscience","issn_l":"1662-453X","issn":["1662-453X","1662-4548"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Neuroscience","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2026.1896585/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051522449","display_name":"Robert F. Melendy","orcid":"https://orcid.org/0000-0002-0380-0826","observed_orcids":["https://orcid.org/0000-0002-0380-0826"]},"institutions":[{"id":"https://openalex.org/I179651463","display_name":"George Fox University","ror":"https://ror.org/00w641b14","country_code":"US","type":"education","lineage":["https://openalex.org/I179651463"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert F. Melendy","raw_affiliation_strings":["George Fox University, Department of Electrical Engineering and Computer Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"George Fox University, Department of Electrical Engineering and Computer Science","institution_ids":["https://openalex.org/I179651463"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5123549693","display_name":"Daniel H. Blue","orcid":"https://orcid.org/0009-0002-8473-9285","observed_orcids":["https://orcid.org/0009-0002-8473-9285"]},"institutions":[{"id":"https://openalex.org/I179651463","display_name":"George Fox University","ror":"https://ror.org/00w641b14","country_code":"US","type":"education","lineage":["https://openalex.org/I179651463"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel H. Blue","raw_affiliation_strings":["George Fox University, Department of Electrical Engineering and Computer Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"George Fox University, Department of Electrical Engineering and Computer Science","institution_ids":["https://openalex.org/I179651463"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051522449"],"corresponding_institution_ids":["https://openalex.org/I179651463"],"apc_list":{"value":3150,"currency":"CHF","value_usd":3801},"apc_paid":{"value":3150,"currency":"CHF","value_usd":3801},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":null,"first_page":"1896585","last_page":"1896585"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.4758000075817108,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.4758000075817108,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T10493","display_name":"Ion channel regulation and function","score":0.22419999539852142,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.10119999945163727,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/action-potential-generation","display_name":"action potential generation","score":0.9800000190734863},{"id":"https://openalex.org/keywords/lie-group-theory","display_name":"Lie group theory","score":0.8859999775886536},{"id":"https://openalex.org/keywords/physical-symmetries","display_name":"physical symmetries","score":0.8019999861717224},{"id":"https://openalex.org/keywords/semidirect-products","display_name":"semidirect products","score":0.7979999780654907},{"id":"https://openalex.org/keywords/scale-invariance","display_name":"scale invariance","score":0.878000020980835},{"id":"https://openalex.org/keywords/time-translation-symmetry","display_name":"time-translation symmetry","score":0.9279999732971191},{"id":"https://openalex.org/keywords/hodgkin-huxley-model","display_name":"Hodgkin-Huxley model","score":0.8320000171661377},{"id":"https://openalex.org/keywords/neuronal-excitability","display_name":"neuronal excitability","score":0.6039999723434448},{"id":"https://openalex.org/keywords/faraday-s-law","display_name":"Faraday's law","score":0.6790000200271606}],"concepts":[{"id":"https://openalex.org/C75066664","wikidata":"https://www.wikidata.org/wiki/Q291126","display_name":"Semidirect product","level":3,"score":0.7190999984741211},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.6545000076293945},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5864999890327454},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.5102999806404114},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5094000101089478},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4837000072002411},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.4724000096321106},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4648999869823456},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4284000098705292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42649999260902405},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C44306375","wikidata":"https://www.wikidata.org/wiki/Q902019","display_name":"Symmetry group","level":2,"score":0.3961000144481659},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3894999921321869},{"id":"https://openalex.org/C2779569378","wikidata":"https://www.wikidata.org/wiki/Q25303768","display_name":"Phenomenological model","level":2,"score":0.328000009059906},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.3255999982357025},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2962000072002411},{"id":"https://openalex.org/C22365015","wikidata":"https://www.wikidata.org/wiki/Q1003162","display_name":"Simple Lie group","level":3,"score":0.2732999920845032},{"id":"https://openalex.org/C135593079","wikidata":"https://www.wikidata.org/wiki/Q1750766","display_name":"Scale invariance","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.25949999690055847},{"id":"https://openalex.org/C207570611","wikidata":"https://www.wikidata.org/wiki/Q1256500","display_name":"Rotation group SO","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.2556999921798706},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.25360000133514404},{"id":"https://openalex.org/C121932024","wikidata":"https://www.wikidata.org/wiki/Q5159376","display_name":"Conductance","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2500999867916107}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3389/fnins.2026.1896585","doi":"https://doi.org/10.3389/fnins.2026.1896585","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fnins.2026.1896585","pdf_url":"https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2026.1896585/pdf","source":{"id":"https://openalex.org/S115201632","display_name":"Frontiers in Neuroscience","issn_l":"1662-453X","issn":["1662-453X","1662-4548"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Neuroscience","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13584316","doi":null,"is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13584316/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13584316/pdf/fnins-20-1896585.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Front Neurosci","raw_type":"Text"},{"id":"pmid:42757185","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42757185","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in neuroscience","raw_type":"Journal Article"},{"id":"pmh:oai:doaj.org/article:297e11c24baf4622a94ede0ce9b55d99","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/297e11c24baf4622a94ede0ce9b55d99","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frontiers in Neuroscience, Vol 20 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3389/fnins.2026.1896585","doi":"https://doi.org/10.3389/fnins.2026.1896585","is_oa":true,"landing_page_url":"https://doi.org/10.3389/fnins.2026.1896585","pdf_url":"https://www.frontiersin.org/journals/neuroscience/articles/10.3389/fnins.2026.1896585/pdf","source":{"id":"https://openalex.org/S115201632","display_name":"Frontiers in Neuroscience","issn_l":"1662-453X","issn":["1662-453X","1662-4548"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","jufo-1","ki-jl-1","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320527","host_organization_name":"Frontiers Media","host_organization_lineage":["https://openalex.org/P4310320527"],"host_organization_lineage_names":["Frontiers Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Frontiers in Neuroscience","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207752149.pdf","grobid_xml":"https://content.openalex.org/works/W7207752149.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W972589330","https://openalex.org/W1631114555","https://openalex.org/W1847162973","https://openalex.org/W1985940938","https://openalex.org/W1993811771","https://openalex.org/W2008697074","https://openalex.org/W2081517547","https://openalex.org/W2097400197","https://openalex.org/W2126293191","https://openalex.org/W2126479355","https://openalex.org/W2150285506","https://openalex.org/W2164653071","https://openalex.org/W2218275280","https://openalex.org/W2418849590","https://openalex.org/W2502880094","https://openalex.org/W2524429653","https://openalex.org/W2911212358","https://openalex.org/W4238614602","https://openalex.org/W4242705658","https://openalex.org/W4243055393","https://openalex.org/W4292170110","https://openalex.org/W4401529654"],"related_works":["https://openalex.org/W7133838840","https://openalex.org/W2489543702","https://openalex.org/W1998695235","https://openalex.org/W2006152036","https://openalex.org/W7211910142","https://openalex.org/W2889692698","https://openalex.org/W4287922322","https://openalex.org/W2001103948","https://openalex.org/W2911212358","https://openalex.org/W4405930863"],"abstract_inverted_index":{"We":[0,325],"derive":[1,95,169],"the":[2,60,109,122,154,159,243,254,259,281,288,297,306,317,363,384,394,408,480],"nonlinear":[3],"dynamics":[4,391],"of":[5,25,40,124,347,454],"neuronal":[6,263,455],"membrane":[7,41,174],"potential":[8,119,403],"from":[9,18,96,141,277,371,383],"fundamental":[10,260,462],"physical":[11,56,126,279,345,361,476],"symmetries":[12,22,274],"using":[13],"Lie":[14,111,255,335,396],"group":[15,63,160,256,282,348,397],"theory.":[16],"Starting":[17],"three":[19,170],"experimentally":[20],"verified":[21],"[rotational":[23],"invariance":[24,39,184],"paramagnetic":[26],"ion":[27],"(Ca":[28],"2":[29,69,85,166],"+":[30,33],",":[31,70,90,167,428],"Na":[32],")":[34],"orientation":[35],"producing":[36,44,49],"SO(2),":[37],"scale":[38,183],"conductance":[42],"ratios":[43],"\u211d,":[45],"and":[46,105,192,287,350,380,445,451],"time-translation":[47],"symmetry":[48,194,323,463],"\u211d],":[50],"we":[51,168],"prove":[52],"that":[53,136,152,253,305,393],"these":[54,125],"independent":[55,97,278],"observations":[57],"uniquely":[58],"determine":[59],"semidirect":[61],"product":[62],"structure":[64,77,161,283,337],"G":[65,162,219],"=":[66,81,86,93,163],"SO(2)":[67,164,176],"\u22c9\u211d":[68,165],"as":[71,344,354],"established":[72],"in":[73,99,461],"Theorem":[74],"1.4.":[75],"The":[76,273,301,357],"constants":[78],"(\u03b3":[79],"1":[80],"1.58":[82],"V/s,":[83],"\u03b3":[84,91],"0.025":[87],"V":[88],"\u22121":[89],"3":[92],"0.003)":[94],"measurements":[98],"cable":[100],"theory,":[101],"Hodgkin\u2013Huxley":[102,390],"voltage":[103],"gating,":[104],"Faraday":[106],"induction,":[107],"establishing":[108],"complete":[110],"algebra":[112,336],"without":[113,294],"reference":[114,295],"to":[115,296,339,447],"any":[116],"phenomenological":[117,233,312,467],"action":[118,402],"model.":[120],"Despite":[121],"presence":[123],"symmetries,":[127],"existing":[128],"neuromorphic":[129,331,439,459],"models":[130,453],"lack":[131],"a":[132,206,327,435],"rigorous":[133],"mathematical":[134,171,414,430,443],"framework":[135,358,433],"systematically":[137],"predicts":[138],"functional":[139,208,289,409],"forms":[140],"first":[142],"principles,":[143,280],"relying":[144],"instead":[145],"on":[146,173],"empirical":[147,239,299],"fitting":[148,240,313],"or":[149],"stochastic":[150],"approximations":[151],"obscure":[153],"underlying":[155,322],"deterministic":[156,328],"structure.":[157,386,415,482],"From":[158],"constraints":[172,204],"voltage:":[175],"compactness":[177],"requires":[178,195],"bounded":[179],"functions":[180,418],"(tanh,":[181],"1/cosh),":[182],"mandates":[185],"power-law":[186,364],"terms":[187],"(":[188,226],"x":[189,199,212,215,221,227],"\u03be":[190,213],"),":[191],"temporal":[193],"oscillatory":[196],"behavior":[197],"[sin(\u03c0":[198],"/\u03c4":[200,216,222],"0":[201,217,223,427],")].":[202,228],"These":[203],"predict":[205],"unique":[207,318],"form":[209,290,319,410],"V(x)":[210],"\u223c":[211],"\u22c5sin(\u03c0":[214],")/[":[218],"(x)\u22c5cosh(\u03c0":[220],")\u22c5":[224],"f":[225],"Remarkably,":[229],"our":[230],"previously":[231],"published":[232],"equation":[234,308,398],"(Melendy,":[235],"2018)":[236],"(discovered":[237],"through":[238,423],"before":[241],"developing":[242],"present":[244,326],"theoretical":[245],"framework)":[246],"exhibits":[247],"exactly":[248],"this":[249,469],"predicted":[250],"structure,":[251],"validating":[252],"approach":[257,470],"captures":[258,399],"physics":[261,444],"governing":[262],"excitability.":[264,456],"This":[265,432],"represents":[266],"theory":[267],"predicting":[268],"phenomenology,":[269],"not":[270,310],"post-hoc":[271],"rationalization.":[272],"were":[275],"identified":[276],"was":[284,291,309],"mathematically":[285],"derived,":[286],"predicted:":[292],"all":[293],"2018":[298,307],"equation.":[300],"subsequent":[302],"agreement":[303],"demonstrates":[304,392],"arbitrary":[311],"but":[314],"rather":[315,465],"discovered":[316],"required":[320],"by":[321,479],"principles.":[324],"algorithm":[329],"for":[330,438],"circuit":[332,340,440,473],"synthesis":[333,474],"wherein":[334],"maps":[338],"topology,":[341],"with":[342,388,475],"components":[343],"realizations":[346],"exponentials":[349],"Kirchhoff\u2019s":[351],"laws":[352],"emerging":[353],"Casimir":[355],"constraints.":[356],"determines":[359],"concrete":[360],"predictions:":[362],"exponent":[365],"\u03be\u2248":[366],"e/2":[367],"\u2248":[368],"1.359,":[369],"obtained":[370],"Lyapunov":[372],"trajectory":[373],"separation":[374],"analysis,":[375],"characterizes":[376],"depolarization":[377],"growth":[378],"rate":[379],"emerges":[381],"naturally":[382],"algebraic":[385,481],"Comparison":[387],"classical":[389],"simplified":[395],"physiologically":[400],"realistic":[401],"waveforms":[404],"while":[405],"revealing":[406],"why":[407],"takes":[411],"its":[412],"specific":[413],"All":[416],"transcendental":[417],"employ":[419],"proper":[420],"dimensional":[421],"scaling":[422],"characteristic":[424],"time":[425],"\u03c4":[426],"ensuring":[429],"rigor.":[431],"offers":[434],"principled":[436],"foundation":[437],"design,":[441],"bridging":[442],"engineering":[446],"enable":[448],"reproducible,":[449],"scalable,":[450],"symmetry-preserving":[452],"By":[457],"grounding":[458],"systems":[460],"principles":[464],"than":[466],"approximations,":[468],"enables":[471],"systematic":[472],"consistency":[477],"guaranteed":[478]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-09-04T00:00:00"}
