Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems
Oscillation is one of the most important phenomena in the chemical reaction systems inliving cells. The general purpose simulation algorithms fail to take into account this specialcharacter and produce unsatisfying results. In order to enhance the accuracy of the integrator,the second-order derivati...
Gespeichert in:
| Veröffentlicht in: | Computational and mathematical methods in medicine 2015-01, Vol.2015 (2015), p.1-14 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 14 |
|---|---|
| container_issue | 2015 |
| container_start_page | 1 |
| container_title | Computational and mathematical methods in medicine |
| container_volume | 2015 |
| creator | You, Xiong Zhang, Ruqiang Li, Juan Chen, Zhaoxia |
| description | Oscillation is one of the most important phenomena in the chemical reaction systems inliving cells. The general purpose simulation algorithms fail to take into account this specialcharacter and produce unsatisfying results. In order to enhance the accuracy of the integrator,the second-order derivative is incorporated in the scheme. The oscillatory feature of the solutionis captured by the integrators with an exponential fitting property. Three practical exponentiallyfitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRKmethods, the two-gene system with cross-regulation and the circadian oscillation of the periodprotein in Drosophila are simulated. Each EFTDRK method has the best fitting frequencywhich minimizes the global error. The numerical results show that the new EFTDRK methodsare more accurate and more efficient than their prototype TDRK methods or RK methods ofthe same order and the traditional exponentially fitted RK method in the literature. |
| doi_str_mv | 10.1155/2015/689137 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_pubme</sourceid><recordid>TN_cdi_pubmedcentral_primary_oai_pubmedcentral_nih_gov_4645493</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1744660937</sourcerecordid><originalsourceid>FETCH-LOGICAL-c439t-fe87714dbcb998f6c25d86090c29b4168775fed6f85488e62f40034b63e872703</originalsourceid><addsrcrecordid>eNqNkUtv1DAUhSMEog9YsUdeIlCoHb83SKi0BVFUqS0SO8tJrmeMknhqO9POv8fVDKOyY-XH_e65j1NVbwj-SAjnJw0m_EQoTah8Vh0SyVQtJFHP93f866A6Suk3xpxITl5WB40QlGpNDqvV2cMqTDBlb4dhg859ztCj2_tQf4Ho1zb7NaDreVpA_X3O2aIfkJehT8iFiG78OA8FCRMKDl2lzg_lGeIGXcAE2XfoGhbz7utmkzKM6VX1wtkhwevdeVz9PD-7Pf1aX15dfDv9fFl3jOpcO1BSEta3Xau1cqJreK8E1rhrdMuIKFHuoBdOcaYUiMYxjClrBS2JjcT0uPq01V3N7Qh9V0aMdjCr6EcbNyZYb_6NTH5pFmFtmGCcaVoE3u0EYribIWUz-tRBmXCCMCdTlstE6YjKgn7Yol0MKUVw-zIEm0ePzKNHZutRod8-7WzP_jWlAO-3wNJPvb33_6cGBQFnn8BcasnoH7fYpWo</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1744660937</pqid></control><display><type>article</type><title>Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems</title><source>MEDLINE</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>PubMed Central Open Access</source><source>Wiley Online Library Open Access</source><source>PubMed Central</source><source>Alma/SFX Local Collection</source><creator>You, Xiong ; Zhang, Ruqiang ; Li, Juan ; Chen, Zhaoxia</creator><contributor>Tiuryn, Jerzy</contributor><creatorcontrib>You, Xiong ; Zhang, Ruqiang ; Li, Juan ; Chen, Zhaoxia ; Tiuryn, Jerzy</creatorcontrib><description>Oscillation is one of the most important phenomena in the chemical reaction systems inliving cells. The general purpose simulation algorithms fail to take into account this specialcharacter and produce unsatisfying results. In order to enhance the accuracy of the integrator,the second-order derivative is incorporated in the scheme. The oscillatory feature of the solutionis captured by the integrators with an exponential fitting property. Three practical exponentiallyfitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRKmethods, the two-gene system with cross-regulation and the circadian oscillation of the periodprotein in Drosophila are simulated. Each EFTDRK method has the best fitting frequencywhich minimizes the global error. The numerical results show that the new EFTDRK methodsare more accurate and more efficient than their prototype TDRK methods or RK methods ofthe same order and the traditional exponentially fitted RK method in the literature.</description><identifier>ISSN: 1748-670X</identifier><identifier>EISSN: 1748-6718</identifier><identifier>DOI: 10.1155/2015/689137</identifier><identifier>PMID: 26633991</identifier><language>eng</language><publisher>Cairo, Egypt: Hindawi Publishing Corporation</publisher><subject>Algorithms ; Animals ; Computational Biology - methods ; Computer Simulation ; Drosophila - genetics ; Drosophila Proteins - genetics ; Gene Regulatory Networks ; Models, Genetic ; Period Circadian Proteins - genetics</subject><ispartof>Computational and mathematical methods in medicine, 2015-01, Vol.2015 (2015), p.1-14</ispartof><rights>Copyright © 2015 Zhaoxia Chen et al.</rights><rights>Copyright © 2015 Zhaoxia Chen et al. 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c439t-fe87714dbcb998f6c25d86090c29b4168775fed6f85488e62f40034b63e872703</citedby><cites>FETCH-LOGICAL-c439t-fe87714dbcb998f6c25d86090c29b4168775fed6f85488e62f40034b63e872703</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4645493/pdf/$$EPDF$$P50$$Gpubmedcentral$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4645493/$$EHTML$$P50$$Gpubmedcentral$$Hfree_for_read</linktohtml><link.rule.ids>230,314,724,777,781,882,27905,27906,53772,53774</link.rule.ids><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/26633991$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><contributor>Tiuryn, Jerzy</contributor><creatorcontrib>You, Xiong</creatorcontrib><creatorcontrib>Zhang, Ruqiang</creatorcontrib><creatorcontrib>Li, Juan</creatorcontrib><creatorcontrib>Chen, Zhaoxia</creatorcontrib><title>Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems</title><title>Computational and mathematical methods in medicine</title><addtitle>Comput Math Methods Med</addtitle><description>Oscillation is one of the most important phenomena in the chemical reaction systems inliving cells. The general purpose simulation algorithms fail to take into account this specialcharacter and produce unsatisfying results. In order to enhance the accuracy of the integrator,the second-order derivative is incorporated in the scheme. The oscillatory feature of the solutionis captured by the integrators with an exponential fitting property. Three practical exponentiallyfitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRKmethods, the two-gene system with cross-regulation and the circadian oscillation of the periodprotein in Drosophila are simulated. Each EFTDRK method has the best fitting frequencywhich minimizes the global error. The numerical results show that the new EFTDRK methodsare more accurate and more efficient than their prototype TDRK methods or RK methods ofthe same order and the traditional exponentially fitted RK method in the literature.</description><subject>Algorithms</subject><subject>Animals</subject><subject>Computational Biology - methods</subject><subject>Computer Simulation</subject><subject>Drosophila - genetics</subject><subject>Drosophila Proteins - genetics</subject><subject>Gene Regulatory Networks</subject><subject>Models, Genetic</subject><subject>Period Circadian Proteins - genetics</subject><issn>1748-670X</issn><issn>1748-6718</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>RHX</sourceid><sourceid>EIF</sourceid><recordid>eNqNkUtv1DAUhSMEog9YsUdeIlCoHb83SKi0BVFUqS0SO8tJrmeMknhqO9POv8fVDKOyY-XH_e65j1NVbwj-SAjnJw0m_EQoTah8Vh0SyVQtJFHP93f866A6Suk3xpxITl5WB40QlGpNDqvV2cMqTDBlb4dhg859ztCj2_tQf4Ho1zb7NaDreVpA_X3O2aIfkJehT8iFiG78OA8FCRMKDl2lzg_lGeIGXcAE2XfoGhbz7utmkzKM6VX1wtkhwevdeVz9PD-7Pf1aX15dfDv9fFl3jOpcO1BSEta3Xau1cqJreK8E1rhrdMuIKFHuoBdOcaYUiMYxjClrBS2JjcT0uPq01V3N7Qh9V0aMdjCr6EcbNyZYb_6NTH5pFmFtmGCcaVoE3u0EYribIWUz-tRBmXCCMCdTlstE6YjKgn7Yol0MKUVw-zIEm0ePzKNHZutRod8-7WzP_jWlAO-3wNJPvb33_6cGBQFnn8BcasnoH7fYpWo</recordid><startdate>20150101</startdate><enddate>20150101</enddate><creator>You, Xiong</creator><creator>Zhang, Ruqiang</creator><creator>Li, Juan</creator><creator>Chen, Zhaoxia</creator><general>Hindawi Publishing Corporation</general><scope>ADJCN</scope><scope>AHFXO</scope><scope>RHU</scope><scope>RHW</scope><scope>RHX</scope><scope>CGR</scope><scope>CUY</scope><scope>CVF</scope><scope>ECM</scope><scope>EIF</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>5PM</scope></search><sort><creationdate>20150101</creationdate><title>Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems</title><author>You, Xiong ; Zhang, Ruqiang ; Li, Juan ; Chen, Zhaoxia</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c439t-fe87714dbcb998f6c25d86090c29b4168775fed6f85488e62f40034b63e872703</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algorithms</topic><topic>Animals</topic><topic>Computational Biology - methods</topic><topic>Computer Simulation</topic><topic>Drosophila - genetics</topic><topic>Drosophila Proteins - genetics</topic><topic>Gene Regulatory Networks</topic><topic>Models, Genetic</topic><topic>Period Circadian Proteins - genetics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>You, Xiong</creatorcontrib><creatorcontrib>Zhang, Ruqiang</creatorcontrib><creatorcontrib>Li, Juan</creatorcontrib><creatorcontrib>Chen, Zhaoxia</creatorcontrib><collection>الدوريات العلمية والإحصائية - e-Marefa Academic and Statistical Periodicals</collection><collection>معرفة - المحتوى العربي الأكاديمي المتكامل - e-Marefa Academic Complete</collection><collection>Hindawi Publishing Complete</collection><collection>Hindawi Publishing Subscription Journals</collection><collection>Hindawi Publishing Open Access</collection><collection>Medline</collection><collection>MEDLINE</collection><collection>MEDLINE (Ovid)</collection><collection>MEDLINE</collection><collection>MEDLINE</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Computational and mathematical methods in medicine</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>You, Xiong</au><au>Zhang, Ruqiang</au><au>Li, Juan</au><au>Chen, Zhaoxia</au><au>Tiuryn, Jerzy</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems</atitle><jtitle>Computational and mathematical methods in medicine</jtitle><addtitle>Comput Math Methods Med</addtitle><date>2015-01-01</date><risdate>2015</risdate><volume>2015</volume><issue>2015</issue><spage>1</spage><epage>14</epage><pages>1-14</pages><issn>1748-670X</issn><eissn>1748-6718</eissn><abstract>Oscillation is one of the most important phenomena in the chemical reaction systems inliving cells. The general purpose simulation algorithms fail to take into account this specialcharacter and produce unsatisfying results. In order to enhance the accuracy of the integrator,the second-order derivative is incorporated in the scheme. The oscillatory feature of the solutionis captured by the integrators with an exponential fitting property. Three practical exponentiallyfitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRKmethods, the two-gene system with cross-regulation and the circadian oscillation of the periodprotein in Drosophila are simulated. Each EFTDRK method has the best fitting frequencywhich minimizes the global error. The numerical results show that the new EFTDRK methodsare more accurate and more efficient than their prototype TDRK methods or RK methods ofthe same order and the traditional exponentially fitted RK method in the literature.</abstract><cop>Cairo, Egypt</cop><pub>Hindawi Publishing Corporation</pub><pmid>26633991</pmid><doi>10.1155/2015/689137</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1748-670X |
| ispartof | Computational and mathematical methods in medicine, 2015-01, Vol.2015 (2015), p.1-14 |
| issn | 1748-670X 1748-6718 |
| language | eng |
| recordid | cdi_pubmedcentral_primary_oai_pubmedcentral_nih_gov_4645493 |
| source | MEDLINE; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; PubMed Central Open Access; Wiley Online Library Open Access; PubMed Central; Alma/SFX Local Collection |
| subjects | Algorithms Animals Computational Biology - methods Computer Simulation Drosophila - genetics Drosophila Proteins - genetics Gene Regulatory Networks Models, Genetic Period Circadian Proteins - genetics |
| title | Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-19T21%3A29%3A41IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pubme&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Exponentially%20Fitted%20Two-Derivative%20Runge-Kutta%20Methods%20for%20Simulation%20of%20Oscillatory%20Genetic%20Regulatory%20Systems&rft.jtitle=Computational%20and%20mathematical%20methods%20in%20medicine&rft.au=You,%20Xiong&rft.date=2015-01-01&rft.volume=2015&rft.issue=2015&rft.spage=1&rft.epage=14&rft.pages=1-14&rft.issn=1748-670X&rft.eissn=1748-6718&rft_id=info:doi/10.1155/2015/689137&rft_dat=%3Cproquest_pubme%3E1744660937%3C/proquest_pubme%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1744660937&rft_id=info:pmid/26633991&rfr_iscdi=true |