---
res:
bibo_abstract:
- 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. @eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Jakob
foaf_name: Ruess, Jakob
foaf_surname: Ruess
foaf_workInfoHomepage: http://www.librecat.org/personId=4A245D00-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-1615-3282
bibo_doi: 10.1063/1.4937937
bibo_issue: '24'
bibo_volume: 143
dct_date: 2015^xs_gYear
dct_language: eng
dct_publisher: American Institute of Physics@
dct_title: Minimal moment equations for stochastic models of biochemical reaction
networks with partially finite state space@
...