{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T13:46:27Z","timestamp":1792158387239,"version":"4.4.0"},"reference-count":31,"publisher":"Wiley","issue":"20","license":[{"start":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T00:00:00Z","timestamp":1790208000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T00:00:00Z","timestamp":1790208000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100000057","name":"National Institute of General Medical Sciences","doi-asserted-by":"publisher","award":["1R16GM153647"],"award-info":[{"award-number":["1R16GM153647"]}],"id":[{"id":"10.13039\/100000057","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2320846"],"award-info":[{"award-number":["2320846"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014074","name":"Integrative and Collaborative Education and Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100014074","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["physoc.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["The Journal of Physiology"],"published-print":{"date-parts":[[2026,10]]},"abstract":"<jats:sec>\n                    <jats:title>Abstract<\/jats:title>\n                    <jats:p>\n                      While the Hodgkin\u2013Huxley formalism successfully describes sodium channel gating, the molecular origin of its nonlinear voltage dependence remains unclear. We developed a structure\u2010based model of Na\n                      <jats:sub>v<\/jats:sub>\n                      1.4 representing the four voltage\u2010sensing domains, the isoleucine\u2010phenylalanine\u2010methionine (IFM) motif and the S6 gate as interacting binary variables, with activation parameters constrained by domain\u2010specific fluorescence measurements. The fitted model reveals strongly heterogeneous voltage sensors whose interactions produce cooperative activation, suppressing channel opening at subthreshold voltages. Using timescale separation, we coarse\u2010grain the 64\u2010microstate system to obtain the Hodgkin\u2013Huxley\u2010like factorization\n                      <jats:italic>P<\/jats:italic>\n                      <jats:sub>o<\/jats:sub>\n                      \u00a0=\u00a0\n                      <jats:italic>m<\/jats:italic>\n                      \u00a0\u00d7\u00a0\n                      <jats:italic>h<\/jats:italic>\n                      , where  represents cooperative activation and  represents availability. The reduced theory shows that the voltage dependence of  is inherited from the domain\u2010IV voltage sensor. Because domain IV activates at more hyperpolarized voltages than the collective activation of domains I\u2013III required for opening, availability declines before the channel reaches its main activation range. Coupling of domain IV to IFM engagement and S6 gate closure further controls the magnitude of this shift. Thus, the model identifies the molecular origin of the separation between activation and availability curves.\n                      <jats:boxed-text content-type=\"graphic\" position=\"anchor\">\n                        <jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mimetype=\"image\/png\" position=\"anchor\" specific-use=\"enlarged-web-image\" xlink:href=\"graphic\/tjp70842-gra-0001-m.png\">\n                          <jats:alt-text>image<\/jats:alt-text>\n                        <\/jats:graphic>\n                      <\/jats:boxed-text>\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Key points<\/jats:title>\n                    <jats:p>\n                      <jats:list list-type=\"bullet\">\n                        <jats:list-item>\n                          <jats:p>Sodium channels are proteins in nerve and muscle cells that open briefly to trigger electrical signals, then close. The 1952 Hodgkin\u2013Huxley model captures this behaviour by treating the channel's four voltage sensors as independent.<\/jats:p>\n                        <\/jats:list-item>\n                        <jats:list-item>\n                          <jats:p>However, experiments show the sensors are not independent: moving one changes how the others respond to voltage.<\/jats:p>\n                        <\/jats:list-item>\n                        <jats:list-item>\n                          <jats:p>We built a structure\u2010based mathematical model of the muscle sodium channel in which all four sensors and the inactivation gate interact and fitted it to measurements of each sensor's movement.<\/jats:p>\n                        <\/jats:list-item>\n                        <jats:list-item>\n                          <jats:p>The model reproduces classic channel behaviour but shows it arises from strong cooperation between sensors and explains why the channel stops being able to open at more negative voltages than those that open it \u2013 an effect traced to a single sensor.<\/jats:p>\n                        <\/jats:list-item>\n                        <jats:list-item>\n                          <jats:p>This voltage gap helps set the range over which muscle sodium channels carry current. Analogous shifts in related sodium\u2010channel isoforms also underlie inherited heart\u2010rhythm disorders, linking structure to disease.<\/jats:p>\n                        <\/jats:list-item>\n                      <\/jats:list>\n                    <\/jats:p>\n                  <\/jats:sec>","DOI":"10.1113\/jp291836","type":"journal-article","created":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T05:37:10Z","timestamp":1790314630000},"page":"8450-8466","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A structure\u2010based model that describes activation and inactivation of a sodium channel"],"prefix":"10.1113","volume":"604","author":[{"given":"D'Artagnan","family":"Greene","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy California State University  Northridge California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sofia","family":"Perez","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy California State University  Northridge California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-4686-5912","authenticated-orcid":false,"given":"Yohannes","family":"Shiferaw","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy California State University  Northridge California USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2026,9,24]]},"reference":[{"key":"e_1_2_5_2_1","doi-asserted-by":"publisher","DOI":"10.1523\/JNEUROSCI.2283-05.2006"},{"key":"e_1_2_5_3_1","doi-asserted-by":"publisher","DOI":"10.1085\/jgp.202112921"},{"issue":"1","key":"e_1_2_5_4_1","first-page":"1","article-title":"A subspace, interior, and conjugate gradient method for large\u2010scale bound\u2010constrained minimization problems","volume":"21","author":"Branch M. 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