Stochastic simulations of the Schnakenberg model with spatial inhomogeneities using reactive multiparticle collision dynamics
A numerically efficient globally averaged number density approach is used to simulate a reaction-diffusion system using a particle-based stochastic simulation algorithm called reactive multiparticle collision (RMPC) dynamics. Constant diffusivity of the particles is achieved through a time-varying r...
Uloženo v:
| Vydáno v: | AIMS mathematics Ročník 4; číslo 6; s. 1805 - 1823 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
AIMS Press
01.01.2019
|
| Témata: | |
| ISSN: | 2473-6988, 2473-6988 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | A numerically efficient globally averaged number density approach is used to simulate a reaction-diffusion system using a particle-based stochastic simulation algorithm called reactive multiparticle collision (RMPC) dynamics. Constant diffusivity of the particles is achieved through a time-varying rotation angle (also called collision angle). Variation in the diffusion coefficient between two different chemical species is achieved in one of two ways: (i) using a different kBT/m value for one species compared to the other, or (ii) using the same kBT/m value for both species, but using a different probability to free-stream for one species compared to another. For smaller diffusivities and larger spatial inhomogeneities, bath particles were necessary for the model to agree with the PDE solution. The latter approach was further used without a bath, and shown to be capable of producing Turing patterns after long simulation times. The significance of our work is that RMPC can serve as a feasible simulation tool for both short and long-term simulations, can handle spatial inhomogeneities, can model a fairly large range of diffusivities in a reaction-diffusion scenario, and is capable of producing Turing patterns. An advantage of this method includes more detailed system information in feasible simulation times. |
|---|---|
| AbstractList | A numerically efficient globally averaged number density approach is used to simulate a reaction-diffusion system using a particle-based stochastic simulation algorithm called reactive multiparticle collision (RMPC) dynamics. Constant diffusivity of the particles is achieved through a time-varying rotation angle (also called collision angle). Variation in the diffusion coefficient between two different chemical species is achieved in one of two ways: (i) using a different kBT/m value for one species compared to the other, or (ii) using the same kBT/m value for both species, but using a different probability to free-stream for one species compared to another. For smaller diffusivities and larger spatial inhomogeneities, bath particles were necessary for the model to agree with the PDE solution. The latter approach was further used without a bath, and shown to be capable of producing Turing patterns after long simulation times. The significance of our work is that RMPC can serve as a feasible simulation tool for both short and long-term simulations, can handle spatial inhomogeneities, can model a fairly large range of diffusivities in a reaction-diffusion scenario, and is capable of producing Turing patterns. An advantage of this method includes more detailed system information in feasible simulation times. |
| Author | Rohlf, Katrin Sayyidmousavi, Alireza |
| Author_xml | – sequence: 1 givenname: Alireza surname: Sayyidmousavi fullname: Sayyidmousavi, Alireza – sequence: 2 givenname: Katrin surname: Rohlf fullname: Rohlf, Katrin |
| BookMark | eNp1kU1rGzEQhkVJoanje4_6A3b0tVrrGELbBAw9JDkL7WjWK2dXMpLckkP_e9eJKSXQ0wwz8z4zzPuZXMQUkZAvnK2lkep6cnVYC8bNWq_5hjUfyKVQrVxps9lc_JN_IstS9owxwYUSrbokvx9qgsGVGoCWMB1HV0OKhaae1gHpAwzRPWPsMO_olDyO9FeoAy2Hec6NNMQhTWmHEUMNWOixhLijGR3U8BPpzKvh4PJMH5FCGsdQZjz1L9FNAcoV-di7seDyHBfk6dvXx9u71fbH9_vbm-0KpGF1hZ577X2jeqEVIAfT6Y610KBjpjGdMlK2TIueoYCOezCq5d5zZtjc90ouyP0b1ye3t4ccJpdfbHLBvhZS3tnzkZYJIRqp1byuVQ6UcWbTKm4MgpIazMxibyzIqZSM_V8eZ_bkhj25YU9uWG1PbswS_U4Cob4-umYXxv8L_wDKBpUn |
| CitedBy_id | crossref_primary_10_1063_5_0245376 crossref_primary_10_1063_5_0223361 |
| Cites_doi | 10.1007/s10910-008-9373-8 10.1007/s00285-011-0412-x 10.1093/bioinformatics/bti431 10.1021/j100540a008 10.1137/15M1030509 10.1016/j.apm.2011.12.041 10.1007/s11538-014-0044-6 10.1016/j.jcp.2009.09.030 10.1063/1.481289 10.1006/jcph.1996.0168 10.1098/rsif.2011.0574 10.1063/1.1690244 10.1007/BF00277392 10.3390/e16010418 10.1088/1478-3967/1/3/001 10.1021/la200272x 10.1137/110832148 10.1063/1.478857 10.1137/15M1030662 10.1021/jp052701u 10.1016/j.cpc.2008.01.027 10.1137/040605060 10.1063/1.1378322 10.1007/s10237-012-0454-z |
| ContentType | Journal Article |
| CorporateAuthor | Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, ON, M5B 2K3, Canada |
| CorporateAuthor_xml | – name: Department of Mathematics, Ryerson University, 350 Victoria St., Toronto, ON, M5B 2K3, Canada |
| DBID | AAYXX CITATION DOA |
| DOI | 10.3934/math.2019.6.1805 |
| DatabaseName | CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2473-6988 |
| EndPage | 1823 |
| ExternalDocumentID | oai_doaj_org_article_02225364dd574ac49a9874199ec436c9 10_3934_math_2019_6_1805 |
| GroupedDBID | AAYXX ADBBV ALMA_UNASSIGNED_HOLDINGS AMVHM BCNDV CITATION EBS FRJ GROUPED_DOAJ IAO ITC M~E OK1 RAN |
| ID | FETCH-LOGICAL-c390t-ed1d6dd54f264ce1c9b6b07c5ea0959b49337062f0e2cb1dc9471dd1090095d43 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000680830800003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2473-6988 |
| IngestDate | Fri Oct 03 12:30:28 EDT 2025 Sat Nov 29 06:04:13 EST 2025 Tue Nov 18 22:13:36 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 6 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c390t-ed1d6dd54f264ce1c9b6b07c5ea0959b49337062f0e2cb1dc9471dd1090095d43 |
| OpenAccessLink | https://doaj.org/article/02225364dd574ac49a9874199ec436c9 |
| PageCount | 19 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_02225364dd574ac49a9874199ec436c9 crossref_primary_10_3934_math_2019_6_1805 crossref_citationtrail_10_3934_math_2019_6_1805 |
| PublicationCentury | 2000 |
| PublicationDate | 2019-01-01 |
| PublicationDateYYYYMMDD | 2019-01-01 |
| PublicationDate_xml | – month: 01 year: 2019 text: 2019-01-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationTitle | AIMS mathematics |
| PublicationYear | 2019 |
| Publisher | AIMS Press |
| Publisher_xml | – name: AIMS Press |
| References | K. Rohlf (26) D. T. Gillespie (2) 27 28 S. Bedkihal, J. C. Kumaradas, K. Rohlf (29) D. A. Garzon-Alvarado, C. H. Galeano, J. M. Mantilla (40) M. B. Flegg, S. J. Chapman, R. Erban (10) T. Akhter, K. Rohlf (30) L. Ferm, A. Hellander, P. Lotstedt (6) A. Hellander, S. Hellander, P. Lotstedt (11) A. Malevanets, R. Kapral (22) A. Stundzia, C. Lumsden (3) K. Tucci, R. Kapral (24) 31 K. Rohlf, S. Fraser, R. Kapral (25) 32 Y. Cao, R. Erban (19) 33 12 34 D. T. Gillespie (1) S. Isaacson, C. Peskin (4) 35 V. Mortazavi, M. Nosonovsky (39) J. Wei, M. Winter (41) 36 15 37 16 38 A. Malevanets, R. Kapral (21) S. S. Andrews, D. Bray (14) M. B. Flegg (20) H. G. Othmer, S. R. Dunbar, W. Alt (18) J. Hattne, D. Fange, J. Elf (13) K. Tucci, R. Kapral (23) 5 7 8 S. J. Chapman, R. Erban, S. A. Isaacson (17) 9 |
| References_xml | – ident: 8 article-title: i>An adaptive tau-leaping method for stochastic systems with slow and fast dynamics</i – ident: 26 article-title: i>Stochastic phase-space description for reactions that change particle numbers</i publication-title: J. Math. Chem. doi: 10.1007/s10910-008-9373-8 – ident: 41 article-title: i>Flow-distributed spikes for Schnakenberg kinetics</i publication-title: J. Math. Biol. doi: 10.1007/s00285-011-0412-x – ident: 9 article-title: i>Spatially extended hybrid methods: A review</i – ident: 13 article-title: i>Stochastic reaction-diffusion simulation with MesoRD</i publication-title: Bioinformatics doi: 10.1093/bioinformatics/bti431 – ident: 1 article-title: i>Exact stochastic simulation of coupled chemical reactions</i publication-title: J. Phys. Chem. doi: 10.1021/j100540a008 – ident: 20 article-title: i>Smoluchowski reaction kinetics for reactions of any order</i publication-title: SIAM J. Appl. Math. doi: 10.1137/15M1030509 – ident: 5 article-title: i>Noise-induced min phenotypes in E. coli</i – ident: 40 article-title: i>Computational examples of reaction-convection-diffusion equations solution under the influence of fluid flow: A first example</i publication-title: Appl. Math. Model. doi: 10.1016/j.apm.2011.12.041 – ident: 19 article-title: i>Stochastic Turing patterns: Analysis of compartment-based approaches</i publication-title: B. Math. Biol. doi: 10.1007/s11538-014-0044-6 – ident: 6 article-title: i>An adaptive algorithm for simulation of stochastic reaction-diffusion processes</i publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.09.030 – ident: 34 article-title: i>Stochastic rotation dynamics: II. Transport coefficients, numerics, and long-time tails</i – ident: 35 article-title: i>Transport coefficients of off-lattice mesoscale-hydrodynamics simulation techniques</i – ident: 22 article-title: i>Solute molecular dynamics in a mesoscale solvent</i publication-title: J. Chem. Phys. doi: 10.1063/1.481289 – ident: 3 article-title: i>Stochastic simulation of coupled reaction-diffusion processes</i publication-title: J. Comput. Phys. doi: 10.1006/jcph.1996.0168 – ident: 10 article-title: i>The two regime method for optimizing stochastic reaction-diffusion simulations</i publication-title: J. R. Soc. Interface doi: 10.1098/rsif.2011.0574 – ident: 23 article-title: i>Mesoscopic model for diffusion influenced reaction dynamics</i publication-title: J. Chem. Phys. doi: 10.1063/1.1690244 – ident: 12 article-title: i>Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations</i – ident: 33 article-title: i>Stochastic rotation dynamics: I. Formalis – ident: 18 article-title: i>Models of dispersal in biological systems</i publication-title: J. Math. Biol. doi: 10.1007/BF00277392 – ident: 16 article-title: i>Simulating biochemical networks at the particle level and in time and space: Green's function reaction dynamics</i – ident: 30 article-title: i>Quantifying compressibility and slip in multiparticle collision (MPC) flow through a local constriction</i publication-title: Entropy doi: 10.3390/e16010418 – ident: 14 article-title: i>Stochastic simulation of chemical reactions with spatial resolution and single molecule detail</i publication-title: Phys. Biol. doi: 10.1088/1478-3967/1/3/001 – ident: 37 article-title: i>Multiparticle collision dynamics for diffusion-influenced signaling pathways</i – ident: 28 article-title: i>Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics</i – ident: 39 article-title: i>Friction-induced pattern formation and Turing systems</i publication-title: Langmuir doi: 10.1021/la200272x – ident: 36 article-title: i>Dynamic correlations in stochastic rotation dynamics</i – ident: 32 article-title: i>Stochastic rotation dynamics: A Galilean-invariant mesoscopic model for fluid flow</i – ident: 11 article-title: i>Coupled mesoscopic and microscopic simulation of stochastic reaction-diffusion processes in mixed dimensions</i publication-title: Multiscale Model. Sim. doi: 10.1137/110832148 – ident: 21 article-title: i>Mesoscopic model for solvent dynamics</i publication-title: J. Chem. Phys. doi: 10.1063/1.478857 – ident: 17 article-title: i>Reactive boundary conditions as limits of interaction potentials for Brownian and Langevin dynamics</i publication-title: SIAM J. Appl. Math. doi: 10.1137/15M1030662 – ident: 24 article-title: i>Mesoscopic multiparticle collision dynamics of reaction-diffusion fronts</i publication-title: J. Chem. Phys. B doi: 10.1021/jp052701u – ident: 25 article-title: i>Reactive multiparticle collision dynamics</i publication-title: Comput. Phys. Commun. doi: 10.1016/j.cpc.2008.01.027 – ident: 38 article-title: i>Reactive multi-particle collision dynamics with reactive boundary conditions</i – ident: 15 article-title: i>Greens-function reaction dynamics: A particle-based approach for simulating biochemical networks in time and space</i – ident: 27 article-title: i>Mesoscale simulations: Lattice Boltzmann and particle algorithms</i – ident: 31 article-title: i>Compressible slip flow through constricted cylinders with density-dependent viscosity</i – ident: 4 article-title: i>Incorporating diffusion in complex geometries into stochastic chemical kinetics simulations</i publication-title: SIAM J. Sci. Comput. doi: 10.1137/040605060 – ident: 2 article-title: i>Approximate accelerated stochastic simulation of reacting systems</i publication-title: J. Phys. Chem. doi: 10.1063/1.1378322 – ident: 7 article-title: i>An adaptive tau-leaping method for stochastic simulations of reaction-diffusion systems</i – ident: 29 article-title: i>Steady flow through a constricted cylinder by multiparticle collision dynamics</i publication-title: Biomech. Model. Mechan. doi: 10.1007/s10237-012-0454-z |
| SSID | ssj0002124274 |
| Score | 2.0667984 |
| Snippet | A numerically efficient globally averaged number density approach is used to simulate a reaction-diffusion system using a particle-based stochastic simulation... |
| SourceID | doaj crossref |
| SourceType | Open Website Enrichment Source Index Database |
| StartPage | 1805 |
| SubjectTerms | reaction-diffusion reactive multiparticle collision dynamics schnakenberg model stochastic simulations |
| Title | Stochastic simulations of the Schnakenberg model with spatial inhomogeneities using reactive multiparticle collision dynamics |
| URI | https://doaj.org/article/02225364dd574ac49a9874199ec436c9 |
| Volume | 4 |
| WOSCitedRecordID | wos000680830800003&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2473-6988 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002124274 issn: 2473-6988 databaseCode: DOA dateStart: 20160101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 2473-6988 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002124274 issn: 2473-6988 databaseCode: M~E dateStart: 20160101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV09T8MwELUQYoAB8Sm-5YGFIW1SO048AqJioBVSAXWLkrNDKyBBpLDBb-fODlUnWFgyJI5lPZ_su_P5PcZOTZQmBVDSPUlUINMiDnQclkEkDOgQIFXuIu3DTTIcpuOxvl2Q-qKaME8P7IHruoBEKGlMnMgcpM4xSpaR1hakUOCu7oWJXgimaA3GBVlivOXPJYUWsov-H509RLqjOlFKanUL-9ACXb_bV_obbL11CPm5H8gmW7LVFlsbzNlUm232OZrVMMmJUZk305dWcKvhdcmxFR_BpMqffKUWd8o2nLKrvKFiaex6Wk3qlxoNxTr2VE6l7o8cnUW31HFfUtgCwcku3HVzbrxWfbPD7vtXd5fXQSubEIDQ4SywJjIK4ZIlOjtgI9CFKsIEYptT0q-QWogkVL0ytD0oIpwT3KCMoQpN_G6k2GXLVV3ZPcYxmumVYCWEJpUytkT2J4zpKTrcK4TZZ90fEDNoOcVJ2uI5w9iCYM8I9oxgz1RGsO-zs_kfr55P45e2FzQv83bEhO1eoH1kLSzZX_Zx8B-dHLJVGpdPvRyx5dnbuz1mK_AxmzZvJ8708Dn4uvoGUSvgOw |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Stochastic+simulations+of+the+Schnakenberg+model+with+spatial+inhomogeneities+using+reactive+multiparticle+collision+dynamics&rft.jtitle=AIMS+mathematics&rft.au=Alireza+Sayyidmousavi&rft.au=Katrin+Rohlf&rft.date=2019-01-01&rft.pub=AIMS+Press&rft.eissn=2473-6988&rft.volume=4&rft.issue=6&rft.spage=1805&rft.epage=1823&rft_id=info:doi/10.3934%2Fmath.2019.6.1805&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_02225364dd574ac49a9874199ec436c9 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2473-6988&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2473-6988&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2473-6988&client=summon |