Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations
An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient...
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| Veröffentlicht in: | Journal of computational electronics 2023-10, Vol.22 (5), p.1396-1408 |
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| container_title | Journal of computational electronics |
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| creator | Chao, Zhen Geng, Weihua Krasny, Robert |
| description | An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K
+
ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results. |
| doi_str_mv | 10.1007/s10825-023-02092-y |
| format | Article |
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+
ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.</description><identifier>ISSN: 1569-8025</identifier><identifier>EISSN: 1572-8137</identifier><identifier>DOI: 10.1007/s10825-023-02092-y</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Boundary conditions ; Boundary layers ; Charge density ; Differential equations ; Electrical Engineering ; Engineering ; Integral equations ; Integrals ; Ion channels ; Ion transport ; Iterative methods ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical models ; Mechanical Engineering ; One dimensional models ; Optical and Electronic Materials ; Potential gradient ; Simulation ; Steady state ; Theoretical</subject><ispartof>Journal of computational electronics, 2023-10, Vol.22 (5), p.1396-1408</ispartof><rights>The Author(s) 2023</rights><rights>The Author(s) 2023. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-d668de45d04b225ab6419a262094c9b3deec68c9b375fd3bfb0a95628159970d3</cites><orcidid>0000-0003-1821-6929</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10825-023-02092-y$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918277575?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21367,27901,27902,33721,41464,42533,43781,51294</link.rule.ids></links><search><creatorcontrib>Chao, Zhen</creatorcontrib><creatorcontrib>Geng, Weihua</creatorcontrib><creatorcontrib>Krasny, Robert</creatorcontrib><title>Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations</title><title>Journal of computational electronics</title><addtitle>J Comput Electron</addtitle><description>An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. The differential equations are recast as integral equations using Green’s 3rd identity yielding a fixed-point problem for the electric potential gradient and ion concentrations. The integrals are discretized by a combination of midpoint and trapezoid rules, and the resulting algebraic equations are solved by Gummel iteration. Numerical tests for electroneutral and non-electroneutral systems demonstrate the method’s 2nd order accuracy and ability to resolve sharp boundary layers. The method is applied to a 1D model of the K
+
ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.</description><subject>Boundary conditions</subject><subject>Boundary layers</subject><subject>Charge density</subject><subject>Differential equations</subject><subject>Electrical Engineering</subject><subject>Engineering</subject><subject>Integral equations</subject><subject>Integrals</subject><subject>Ion channels</subject><subject>Ion transport</subject><subject>Iterative methods</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical models</subject><subject>Mechanical Engineering</subject><subject>One dimensional models</subject><subject>Optical and Electronic Materials</subject><subject>Potential gradient</subject><subject>Simulation</subject><subject>Steady state</subject><subject>Theoretical</subject><issn>1569-8025</issn><issn>1572-8137</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>BENPR</sourceid><recordid>eNp9kEtPAyEUhYnRxFr9A65IXKM8BhiWpr6aNNqFrgkzMH3YQgt0Mf9e6hjdubi5Z_Gdc28OANcE3xKM5V0iuKYcYcrKYEVRfwJGhEuKasLk6VELhWpM-Tm4SGmNC0UrMgLzqc9uEc0Guv3B5FXwcOvyMljYhQjz0kHyAFN2xvYoZZMdnIdVSsGjVxd9ymi-Mb79_HWnS3DWmU1yVz97DD6eHt8nL2j29jyd3M9Qy0iVkRWitq7iFlcNpdw0oiLKUFGer1rVMOtcK-qjkryzrOkabBQXtCZcKYktG4ObIXcXw_7gUtbrcIi-nNRUkZpKySUvFB2oNoaUouv0Lq62JvaaYH1sTg_N6dKc_m5O98XEBlMqsF-4-Bf9j-sLOghxbA</recordid><startdate>20231001</startdate><enddate>20231001</enddate><creator>Chao, Zhen</creator><creator>Geng, Weihua</creator><creator>Krasny, Robert</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0003-1821-6929</orcidid></search><sort><creationdate>20231001</creationdate><title>Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations</title><author>Chao, Zhen ; Geng, Weihua ; Krasny, Robert</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-d668de45d04b225ab6419a262094c9b3deec68c9b375fd3bfb0a95628159970d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Boundary conditions</topic><topic>Boundary layers</topic><topic>Charge density</topic><topic>Differential equations</topic><topic>Electrical Engineering</topic><topic>Engineering</topic><topic>Integral equations</topic><topic>Integrals</topic><topic>Ion channels</topic><topic>Ion transport</topic><topic>Iterative methods</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical models</topic><topic>Mechanical Engineering</topic><topic>One dimensional models</topic><topic>Optical and Electronic Materials</topic><topic>Potential gradient</topic><topic>Simulation</topic><topic>Steady state</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chao, Zhen</creatorcontrib><creatorcontrib>Geng, Weihua</creatorcontrib><creatorcontrib>Krasny, Robert</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Journal of computational electronics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Chao, Zhen</au><au>Geng, Weihua</au><au>Krasny, Robert</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations</atitle><jtitle>Journal of computational electronics</jtitle><stitle>J Comput Electron</stitle><date>2023-10-01</date><risdate>2023</risdate><volume>22</volume><issue>5</issue><spage>1396</spage><epage>1408</epage><pages>1396-1408</pages><issn>1569-8025</issn><eissn>1572-8137</eissn><abstract>An integral equation method is presented for the 1D steady-state Poisson-Nernst-Planck equations modeling ion transport through membrane channels. 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+
ion channel with a fixed charge density that ensures cation selectivity. In these tests, the proposed integral equation method yields potential and concentration profiles in good agreement with published results.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10825-023-02092-y</doi><tpages>13</tpages><orcidid>https://orcid.org/0000-0003-1821-6929</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Boundary conditions Boundary layers Charge density Differential equations Electrical Engineering Engineering Integral equations Integrals Ion channels Ion transport Iterative methods Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical models Mechanical Engineering One dimensional models Optical and Electronic Materials Potential gradient Simulation Steady state Theoretical |
| title | Integral equation method for the 1D steady-state Poisson-Nernst-Planck equations |
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