--- _id: '1539' abstract: - lang: eng text: 'Many stochastic models of biochemical reaction networks contain some chemical species for which the number of molecules that are present in the system can only be finite (for instance due to conservation laws), but also other species that can be present in arbitrarily large amounts. The prime example of such networks are models of gene expression, which typically contain a small and finite number of possible states for the promoter but an infinite number of possible states for the amount of mRNA and protein. One of the main approaches to analyze such models is through the use of equations for the time evolution of moments of the chemical species. Recently, a new approach based on conditional moments of the species with infinite state space given all the different possible states of the finite species has been proposed. It was argued that this approach allows one to capture more details about the full underlying probability distribution with a smaller number of equations. Here, I show that the result that less moments provide more information can only stem from an unnecessarily complicated description of the system in the classical formulation. The foundation of this argument will be the derivation of moment equations that describe the complete probability distribution over the finite state space but only low-order moments over the infinite state space. I will show that the number of equations that is needed is always less than what was previously claimed and always less than the number of conditional moment equations up to the same order. To support these arguments, a symbolic algorithm is provided that can be used to derive minimal systems of unconditional moment equations for models with partially finite state space. ' article_number: '244103' author: - first_name: Jakob full_name: Ruess, Jakob id: 4A245D00-F248-11E8-B48F-1D18A9856A87 last_name: Ruess orcid: 0000-0003-1615-3282 citation: ama: Ruess J. Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space. Journal of Chemical Physics. 2015;143(24). doi:10.1063/1.4937937 apa: Ruess, J. (2015). Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space. Journal of Chemical Physics. American Institute of Physics. https://doi.org/10.1063/1.4937937 chicago: Ruess, Jakob. “Minimal Moment Equations for Stochastic Models of Biochemical Reaction Networks with Partially Finite State Space.” Journal of Chemical Physics. American Institute of Physics, 2015. https://doi.org/10.1063/1.4937937. ieee: J. Ruess, “Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space,” Journal of Chemical Physics, vol. 143, no. 24. American Institute of Physics, 2015. ista: Ruess J. 2015. Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space. Journal of Chemical Physics. 143(24), 244103. mla: Ruess, Jakob. “Minimal Moment Equations for Stochastic Models of Biochemical Reaction Networks with Partially Finite State Space.” Journal of Chemical Physics, vol. 143, no. 24, 244103, American Institute of Physics, 2015, doi:10.1063/1.4937937. short: J. Ruess, Journal of Chemical Physics 143 (2015). date_created: 2018-12-11T11:52:36Z date_published: 2015-12-22T00:00:00Z date_updated: 2021-01-12T06:51:28Z day: '22' ddc: - '000' department: - _id: ToHe - _id: GaTk doi: 10.1063/1.4937937 ec_funded: 1 file: - access_level: open_access checksum: 838657118ae286463a2b7737319f35ce content_type: application/pdf creator: system date_created: 2018-12-12T10:07:43Z date_updated: 2020-07-14T12:45:01Z file_id: '4641' file_name: IST-2016-593-v1+1_Minimal_moment_equations.pdf file_size: 605355 relation: main_file file_date_updated: 2020-07-14T12:45:01Z has_accepted_license: '1' intvolume: ' 143' issue: '24' language: - iso: eng month: '12' oa: 1 oa_version: Published Version project: - _id: 25EE3708-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '267989' name: Quantitative Reactive Modeling - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 25F42A32-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z211 name: The Wittgenstein Prize - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Journal of Chemical Physics publication_status: published publisher: American Institute of Physics publist_id: '5632' pubrep_id: '593' quality_controlled: '1' scopus_import: 1 status: public title: Minimal moment equations for stochastic models of biochemical reaction networks with partially finite state space type: journal_article user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 volume: 143 year: '2015' ...