Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics
In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary...
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| Published in: | Bulletin of mathematical biology Vol. 78; no. 12; pp. 2390 - 2407 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
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New York
Springer US
01.12.2016
Springer Nature B.V |
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| ISSN: | 0092-8240, 1522-9602 |
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| Abstract | In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary distributions can be computed explicitly. In particular, we study continuous-time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint. Analogous with previous related results, the distributions can be written in product form. |
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| AbstractList | In many applications, for example when computing statistics of fast subsystems in a multiscale setting, we wish to find the stationary distributions of systems of continuous-time Markov chains. Here we present a class of models that appears naturally in certain averaging approaches whose stationary distributions can be computed explicitly. In particular, we study continuous-time Markov chain models for biochemical interaction systems with non-mass action kinetics whose network satisfies a certain constraint. Analogous with previous related results, the distributions can be written in product form. |
| Author | Cotter, Simon L. Anderson, David F. |
| Author_xml | – sequence: 1 givenname: David F. surname: Anderson fullname: Anderson, David F. organization: Department of Mathematics, University of Wisconsin – sequence: 2 givenname: Simon L. orcidid: 0000-0001-5974-7393 surname: Cotter fullname: Cotter, Simon L. email: simon.cotter@manchester.ac.uk organization: Department of Mathematics, University of Manchester |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/27796722$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1007_s11538_018_0473_8 crossref_primary_10_1088_1751_8121_aa89d0 crossref_primary_10_1007_s00285_020_01512_y crossref_primary_10_1007_s10910_021_01278_8 crossref_primary_10_24072_pcjournal_614 crossref_primary_10_1038_s42003_021_02117_x crossref_primary_10_1137_23M1549316 crossref_primary_10_1017_jpr_2020_28 crossref_primary_10_1137_22M150469X crossref_primary_10_1007_s00285_020_01485_y crossref_primary_10_1088_1751_8121_aa91de crossref_primary_10_1137_24M1665933 crossref_primary_10_1017_jpr_2021_65 crossref_primary_10_1007_s10910_020_01148_9 crossref_primary_10_1017_S0956792522000146 crossref_primary_10_1109_TMBMC_2020_3035360 crossref_primary_10_1007_s00285_019_01394_9 crossref_primary_10_1109_TCBB_2019_2938502 crossref_primary_10_1137_17M1134299 crossref_primary_10_1017_S0956792523000335 crossref_primary_10_1088_1751_8121_aab968 |
| Cites_doi | 10.1007/s11538-015-0102-8 10.1016/0021-9991(76)90041-3 10.1016/j.jcp.2006.06.019 10.1137/070698282 10.1021/jp993732q 10.1137/11082631X 10.1137/14100052X 10.1016/0009-2509(87)80099-4 10.1186/1752-0509-6-39 10.1007/978-1-4419-6766-4_1 10.1007/s11538-010-9517-4 10.1007/BF00255665 10.1137/15M1029916 10.1063/1.1889434 10.1063/1.3624333 10.1063/1.2109987 10.1016/j.jcp.2016.07.035 10.1063/1.2799998 10.1063/1.481811 10.1016/0375-9601(76)90398-4 10.1007/BF01023640 10.1063/1.1824902 10.1007/978-3-319-16895-1_6 10.1007/BF00255664 |
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| DOI | 10.1007/s11538-016-0220-y |
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| Keywords | Constrained averaging Product-form stationary distributions Stochastically modeled reaction network Deficiency zero |
| Language | English |
| License | Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
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| References | Weinan, Vanden-Eijnden (CR29) 2007; 221 Anderson (CR4) 2011; 71 Anderson, Kurtz, Koeppl, Densmore, Setti, di Bernardo (CR6) 2011 Gibson, Bruck (CR17) 2000; 105 Van Kampen (CR27) 2007 CR15 Cotter (CR11) 2016; 323 CR13 Cotter, Zygalakis, Kevrekidis, Erban (CR10) 2011; 135 Weinan, Liu, Vanden-Eijnden (CR28) 2005; 123 Anderson, Craciun, Gopalkrishnan, Wiuf (CR5) 2015; 77 Feinberg (CR14) 1972; 49 Janssen (CR23) 1989; 57 Gillespie (CR19) 2000; 113 Kelly (CR24) 1979 Cappelletti, Wiuf (CR9) 2016; 76 Van Kampen (CR26) 1976; 59 Gillespie (CR18) 1976; 22 CR7 Feinberg (CR16) 1987; 42 Anderson (CR1) 2007; 127 CR22 Cao, Gillespie, Petzold (CR8) 2005; 122 CR21 Cotter, Erban (CR12) 2016; 38 Anderson (CR2) 2008; 68 Goutsias (CR20) 2005; 122 Anderson, Craciun, Kurtz (CR3) 2010; 72 Thomas, Straube, Grima (CR25) 2012; 6 P Thomas (220_CR25) 2012; 6 M Feinberg (220_CR14) 1972; 49 220_CR7 D Cappelletti (220_CR9) 2016; 76 DF Anderson (220_CR6) 2011 DF Anderson (220_CR5) 2015; 77 DF Anderson (220_CR2) 2008; 68 DF Anderson (220_CR1) 2007; 127 DF Anderson (220_CR3) 2010; 72 NG Van Kampen (220_CR27) 2007 SL Cotter (220_CR12) 2016; 38 J Goutsias (220_CR20) 2005; 122 MA Gibson (220_CR17) 2000; 105 DT Gillespie (220_CR18) 1976; 22 DT Gillespie (220_CR19) 2000; 113 M Feinberg (220_CR16) 1987; 42 DF Anderson (220_CR4) 2011; 71 FP Kelly (220_CR24) 1979 E Weinan (220_CR29) 2007; 221 220_CR21 NG Van Kampen (220_CR26) 1976; 59 220_CR22 JAM Janssen (220_CR23) 1989; 57 SL Cotter (220_CR11) 2016; 323 220_CR13 SL Cotter (220_CR10) 2011; 135 220_CR15 Y Cao (220_CR8) 2005; 122 E Weinan (220_CR28) 2005; 123 20306147 - Bull Math Biol. 2010 Nov;72(8):1947-70 15638651 - J Chem Phys. 2005 Jan 1;122(1):14116 26376889 - Bull Math Biol. 2015 Sep;77(9):1744-67 15918689 - J Chem Phys. 2005 May 8;122(18):184102 18067349 - J Chem Phys. 2007 Dec 7;127(21):214107 22583770 - BMC Syst Biol. 2012 May 14;6:39 21913748 - J Chem Phys. 2011 Sep 7;135(9):094102 16321076 - J Chem Phys. 2005 Nov 15;123(19):194107 |
| References_xml | – ident: CR22 – volume: 77 start-page: 1744 issue: 9 year: 2015 end-page: 1767 ident: CR5 article-title: Lyapunov functions, stationary distributions, and non-equilibrium potential for reaction networks publication-title: Bull Math Bio doi: 10.1007/s11538-015-0102-8 – volume: 22 start-page: 403 year: 1976 end-page: 434 ident: CR18 article-title: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions publication-title: J Comput Phys doi: 10.1016/0021-9991(76)90041-3 – volume: 221 start-page: 158 issue: 1 year: 2007 end-page: 180 ident: CR29 article-title: Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales publication-title: J Comput Phys doi: 10.1016/j.jcp.2006.06.019 – volume: 68 start-page: 1464 issue: 5 year: 2008 end-page: 1476 ident: CR2 article-title: Global asymptotic stability for a class of nonlinear chemical equations publication-title: SIAM J Appl Math doi: 10.1137/070698282 – volume: 105 start-page: 1876 year: 2000 end-page: 1889 ident: CR17 article-title: Efficient exact stochastic simulation of chemical systems with many species and many channels publication-title: J Phys Chem A doi: 10.1021/jp993732q – volume: 71 start-page: 1487 issue: 4 year: 2011 end-page: 1508 ident: CR4 article-title: A proof of the global attractor conjecture in the single linkage class case publication-title: Siam J Appl Math doi: 10.1137/11082631X – volume: 38 start-page: 144 issue: 1 year: 2016 end-page: 163 ident: CR12 article-title: Error analysis of diffusion approximation methods for multiscale systems in reaction kinetics publication-title: SIAM J Sci Comput doi: 10.1137/14100052X – volume: 42 start-page: 2229 year: 1987 end-page: 2268 ident: CR16 article-title: Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems, review article 25 publication-title: Chem Eng Sci doi: 10.1016/0009-2509(87)80099-4 – volume: 6 start-page: 1 issue: 1 year: 2012 ident: CR25 article-title: The slow-scale linear noise approximation: an accurate, reduced stochastic description of biochemical networks under timescale separation conditions publication-title: BMC Syst Biol doi: 10.1186/1752-0509-6-39 – start-page: 3 year: 2011 end-page: 42 ident: CR6 article-title: Continuous time Markov chain models for chemical reaction networks publication-title: Design and analysis of biomolecular circuits: engineering approaches to systems and synthetic biology doi: 10.1007/978-1-4419-6766-4_1 – volume: 72 start-page: 1947 issue: 8 year: 2010 end-page: 1970 ident: CR3 article-title: Product-form stationary distributions for deficiency zero chemical reaction networks publication-title: Bull Math Biol doi: 10.1007/s11538-010-9517-4 – volume: 49 start-page: 187 year: 1972 end-page: 194 ident: CR14 article-title: Complex balancing in general kinetic systems publication-title: Arch Ration Mech Anal doi: 10.1007/BF00255665 – volume: 76 start-page: 411 issue: 1 year: 2016 end-page: 432 ident: CR9 article-title: Product-form poisson-like distributions and complex balanced reaction systems publication-title: Siam J Appl Math doi: 10.1137/15M1029916 – volume: 122 start-page: 184102 issue: 18 year: 2005 ident: CR20 article-title: Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems publication-title: J Chem Phys doi: 10.1063/1.1889434 – ident: CR21 – volume: 135 start-page: 094102 issue: 9 year: 2011 ident: CR10 article-title: A constrained approach to multiscale stochastic simulation of chemically reacting systems publication-title: J Chem Phys doi: 10.1063/1.3624333 – volume: 123 start-page: 194107 issue: 19 year: 2005 ident: CR28 article-title: Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates publication-title: J Chem Phys doi: 10.1063/1.2109987 – ident: CR15 – ident: CR13 – volume: 323 start-page: 265 year: 2016 end-page: 282 ident: CR11 article-title: Constrained approximation of effective generators for multiscale stochastic reaction networks and application to conditioned path sampling publication-title: J Comput Phys doi: 10.1016/j.jcp.2016.07.035 – year: 1979 ident: CR24 publication-title: Reversibility and stochastic networks, Wiley series in probability and mathematical statistics – volume: 127 start-page: 214107 issue: 21 year: 2007 ident: CR1 article-title: A modified next reaction method for simulating chemical systems with time dependent propensities and delays publication-title: J Chem Phys doi: 10.1063/1.2799998 – volume: 113 start-page: 297 issue: 1 year: 2000 end-page: 306 ident: CR19 article-title: The chemical Langevin equation publication-title: J Chem Phys doi: 10.1063/1.481811 – ident: CR7 – volume: 59 start-page: 333 issue: 5 year: 1976 end-page: 334 ident: CR26 article-title: The equilibrium distribution of a chemical mixture publication-title: Phys Lett A doi: 10.1016/0375-9601(76)90398-4 – volume: 57 start-page: 187 issue: 1–2 year: 1989 end-page: 198 ident: CR23 article-title: The elimination of fast variables in complex chemical reactions. iii. mesoscopic level (irreducible case) publication-title: J Stat Phys doi: 10.1007/BF01023640 – year: 2007 ident: CR27 publication-title: Stochastic processes in physics and chemistry – volume: 122 start-page: 014116 issue: 1 year: 2005 ident: CR8 article-title: The slow-scale stochastic simulation algorithm publication-title: J Chem Phys doi: 10.1063/1.1824902 – volume: 76 start-page: 411 issue: 1 year: 2016 ident: 220_CR9 publication-title: Siam J Appl Math doi: 10.1137/15M1029916 – volume: 38 start-page: 144 issue: 1 year: 2016 ident: 220_CR12 publication-title: SIAM J Sci Comput doi: 10.1137/14100052X – ident: 220_CR15 – volume: 122 start-page: 184102 issue: 18 year: 2005 ident: 220_CR20 publication-title: J Chem Phys doi: 10.1063/1.1889434 – volume: 57 start-page: 187 issue: 1–2 year: 1989 ident: 220_CR23 publication-title: J Stat Phys doi: 10.1007/BF01023640 – volume: 68 start-page: 1464 issue: 5 year: 2008 ident: 220_CR2 publication-title: SIAM J Appl Math doi: 10.1137/070698282 – ident: 220_CR13 – ident: 220_CR21 – volume: 42 start-page: 2229 year: 1987 ident: 220_CR16 publication-title: Chem Eng Sci doi: 10.1016/0009-2509(87)80099-4 – volume: 6 start-page: 1 issue: 1 year: 2012 ident: 220_CR25 publication-title: BMC Syst Biol doi: 10.1186/1752-0509-6-39 – volume: 72 start-page: 1947 issue: 8 year: 2010 ident: 220_CR3 publication-title: Bull Math Biol doi: 10.1007/s11538-010-9517-4 – volume: 135 start-page: 094102 issue: 9 year: 2011 ident: 220_CR10 publication-title: J Chem Phys doi: 10.1063/1.3624333 – volume: 59 start-page: 333 issue: 5 year: 1976 ident: 220_CR26 publication-title: Phys Lett A doi: 10.1016/0375-9601(76)90398-4 – volume: 127 start-page: 214107 issue: 21 year: 2007 ident: 220_CR1 publication-title: J Chem Phys doi: 10.1063/1.2799998 – ident: 220_CR7 doi: 10.1007/978-3-319-16895-1_6 – volume: 77 start-page: 1744 issue: 9 year: 2015 ident: 220_CR5 publication-title: Bull Math Bio doi: 10.1007/s11538-015-0102-8 – volume: 323 start-page: 265 year: 2016 ident: 220_CR11 publication-title: J Comput Phys doi: 10.1016/j.jcp.2016.07.035 – volume: 221 start-page: 158 issue: 1 year: 2007 ident: 220_CR29 publication-title: J Comput Phys doi: 10.1016/j.jcp.2006.06.019 – start-page: 3 volume-title: Design and analysis of biomolecular circuits: engineering approaches to systems and synthetic biology year: 2011 ident: 220_CR6 doi: 10.1007/978-1-4419-6766-4_1 – volume: 105 start-page: 1876 year: 2000 ident: 220_CR17 publication-title: J Phys Chem A doi: 10.1021/jp993732q – volume: 49 start-page: 187 year: 1972 ident: 220_CR14 publication-title: Arch Ration Mech Anal doi: 10.1007/BF00255665 – ident: 220_CR22 doi: 10.1007/BF00255664 – volume: 113 start-page: 297 issue: 1 year: 2000 ident: 220_CR19 publication-title: J Chem Phys doi: 10.1063/1.481811 – volume: 22 start-page: 403 year: 1976 ident: 220_CR18 publication-title: J Comput Phys doi: 10.1016/0021-9991(76)90041-3 – volume: 123 start-page: 194107 issue: 19 year: 2005 ident: 220_CR28 publication-title: J Chem Phys doi: 10.1063/1.2109987 – volume-title: Reversibility and stochastic networks, Wiley series in probability and mathematical statistics year: 1979 ident: 220_CR24 – volume: 122 start-page: 014116 issue: 1 year: 2005 ident: 220_CR8 publication-title: J Chem Phys doi: 10.1063/1.1824902 – volume-title: Stochastic processes in physics and chemistry year: 2007 ident: 220_CR27 – volume: 71 start-page: 1487 issue: 4 year: 2011 ident: 220_CR4 publication-title: Siam J Appl Math doi: 10.1137/11082631X – reference: 21913748 - J Chem Phys. 2011 Sep 7;135(9):094102 – reference: 16321076 - J Chem Phys. 2005 Nov 15;123(19):194107 – reference: 26376889 - Bull Math Biol. 2015 Sep;77(9):1744-67 – reference: 18067349 - J Chem Phys. 2007 Dec 7;127(21):214107 – reference: 15918689 - J Chem Phys. 2005 May 8;122(18):184102 – reference: 22583770 - BMC Syst Biol. 2012 May 14;6:39 – reference: 20306147 - Bull Math Biol. 2010 Nov;72(8):1947-70 – reference: 15638651 - J Chem Phys. 2005 Jan 1;122(1):14116 |
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| SubjectTerms | Algorithms Biochemical Phenomena Cell Biology Kinetics Life Sciences Markov Chains Mathematical and Computational Biology Mathematical Concepts Mathematics Mathematics and Statistics Models, Biological Original Original Article Protein Multimerization Stochastic Processes |
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| Title | Product-Form Stationary Distributions for Deficiency Zero Networks with Non-mass Action Kinetics |
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