---
_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'
...