---
_id: '10939'
abstract:
- lang: eng
text: Understanding and characterising biochemical processes inside single cells
requires experimental platforms that allow one to perturb and observe the dynamics
of such processes as well as computational methods to build and parameterise models
from the collected data. Recent progress with experimental platforms and optogenetics
has made it possible to expose each cell in an experiment to an individualised
input and automatically record cellular responses over days with fine time resolution.
However, methods to infer parameters of stochastic kinetic models from single-cell
longitudinal data have generally been developed under the assumption that experimental
data is sparse and that responses of cells to at most a few different input perturbations
can be observed. Here, we investigate and compare different approaches for calculating
parameter likelihoods of single-cell longitudinal data based on approximations
of the chemical master equation (CME) with a particular focus on coupling the
linear noise approximation (LNA) or moment closure methods to a Kalman filter.
We show that, as long as cells are measured sufficiently frequently, coupling
the LNA to a Kalman filter allows one to accurately approximate likelihoods and
to infer model parameters from data even in cases where the LNA provides poor
approximations of the CME. Furthermore, the computational cost of filtering-based
iterative likelihood evaluation scales advantageously in the number of measurement
times and different input perturbations and is thus ideally suited for data obtained
from modern experimental platforms. To demonstrate the practical usefulness of
these results, we perform an experiment in which single cells, equipped with an
optogenetic gene expression system, are exposed to various different light-input
sequences and measured at several hundred time points and use parameter inference
based on iterative likelihood evaluation to parameterise a stochastic model of
the system.
acknowledgement: We thank Virgile Andreani for useful discussions about the model
and parameter inference. We thank Johan Paulsson and Jeffrey J Tabor for kind gifts
of plasmids. R was supported by the ANR grant CyberCircuits (ANR-18-CE91-0002).
The funders had no role in study design, data collection and analysis, decision
to publish, or preparation of the manuscript.
article_number: e1009950
article_processing_charge: No
article_type: original
author:
- first_name: Anđela
full_name: Davidović, Anđela
last_name: Davidović
- first_name: Remy P
full_name: Chait, Remy P
id: 3464AE84-F248-11E8-B48F-1D18A9856A87
last_name: Chait
orcid: 0000-0003-0876-3187
- first_name: Gregory
full_name: Batt, Gregory
last_name: Batt
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
citation:
ama: Davidović A, Chait RP, Batt G, Ruess J. Parameter inference for stochastic
biochemical models from perturbation experiments parallelised at the single cell
level. PLoS Computational Biology. 2022;18(3). doi:10.1371/journal.pcbi.1009950
apa: Davidović, A., Chait, R. P., Batt, G., & Ruess, J. (2022). Parameter inference
for stochastic biochemical models from perturbation experiments parallelised at
the single cell level. PLoS Computational Biology. Public Library of Science.
https://doi.org/10.1371/journal.pcbi.1009950
chicago: Davidović, Anđela, Remy P Chait, Gregory Batt, and Jakob Ruess. “Parameter
Inference for Stochastic Biochemical Models from Perturbation Experiments Parallelised
at the Single Cell Level.” PLoS Computational Biology. Public Library of
Science, 2022. https://doi.org/10.1371/journal.pcbi.1009950.
ieee: A. Davidović, R. P. Chait, G. Batt, and J. Ruess, “Parameter inference for
stochastic biochemical models from perturbation experiments parallelised at the
single cell level,” PLoS Computational Biology, vol. 18, no. 3. Public
Library of Science, 2022.
ista: Davidović A, Chait RP, Batt G, Ruess J. 2022. Parameter inference for stochastic
biochemical models from perturbation experiments parallelised at the single cell
level. PLoS Computational Biology. 18(3), e1009950.
mla: Davidović, Anđela, et al. “Parameter Inference for Stochastic Biochemical Models
from Perturbation Experiments Parallelised at the Single Cell Level.” PLoS
Computational Biology, vol. 18, no. 3, e1009950, Public Library of Science,
2022, doi:10.1371/journal.pcbi.1009950.
short: A. Davidović, R.P. Chait, G. Batt, J. Ruess, PLoS Computational Biology 18
(2022).
date_created: 2022-04-03T22:01:42Z
date_published: 2022-03-18T00:00:00Z
date_updated: 2022-04-04T10:21:53Z
day: '18'
ddc:
- '570'
- '000'
department:
- _id: CaGu
doi: 10.1371/journal.pcbi.1009950
file:
- access_level: open_access
checksum: 458ef542761fb714ced214f240daf6b2
content_type: application/pdf
creator: dernst
date_created: 2022-04-04T10:14:39Z
date_updated: 2022-04-04T10:14:39Z
file_id: '10947'
file_name: 2022_PLoSCompBio_Davidovic.pdf
file_size: 2958642
relation: main_file
success: 1
file_date_updated: 2022-04-04T10:14:39Z
has_accepted_license: '1'
intvolume: ' 18'
issue: '3'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
publication: PLoS Computational Biology
publication_identifier:
eissn:
- 1553-7358
issn:
- 1553-734X
publication_status: published
publisher: Public Library of Science
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://gitlab.pasteur.fr/adavidov/inferencelnakf
scopus_import: '1'
status: public
title: Parameter inference for stochastic biochemical models from perturbation experiments
parallelised at the single cell level
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 18
year: '2022'
...
---
_id: '6784'
abstract:
- lang: eng
text: Mathematical models have been used successfully at diverse scales of biological
organization, ranging from ecology and population dynamics to stochastic reaction
events occurring between individual molecules in single cells. Generally, many
biological processes unfold across multiple scales, with mutations being the best
studied example of how stochasticity at the molecular scale can influence outcomes
at the population scale. In many other contexts, however, an analogous link between
micro- and macro-scale remains elusive, primarily due to the challenges involved
in setting up and analyzing multi-scale models. Here, we employ such a model to
investigate how stochasticity propagates from individual biochemical reaction
events in the bacterial innate immune system to the ecology of bacteria and bacterial
viruses. We show analytically how the dynamics of bacterial populations are shaped
by the activities of immunity-conferring enzymes in single cells and how the ecological
consequences imply optimal bacterial defense strategies against viruses. Our results
suggest that bacterial populations in the presence of viruses can either optimize
their initial growth rate or their population size, with the first strategy favoring
simple immunity featuring a single restriction modification system and the second
strategy favoring complex bacterial innate immunity featuring several simultaneously
active restriction modification systems.
article_number: e1007168
article_processing_charge: No
article_type: original
author:
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
- first_name: Maros
full_name: Pleska, Maros
id: 4569785E-F248-11E8-B48F-1D18A9856A87
last_name: Pleska
orcid: 0000-0001-7460-7479
- first_name: Calin C
full_name: Guet, Calin C
id: 47F8433E-F248-11E8-B48F-1D18A9856A87
last_name: Guet
orcid: 0000-0001-6220-2052
- first_name: Gašper
full_name: Tkačik, Gašper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkačik
orcid: 0000-0002-6699-1455
citation:
ama: Ruess J, Pleska M, Guet CC, Tkačik G. Molecular noise of innate immunity shapes
bacteria-phage ecologies. PLoS Computational Biology. 2019;15(7). doi:10.1371/journal.pcbi.1007168
apa: Ruess, J., Pleska, M., Guet, C. C., & Tkačik, G. (2019). Molecular noise
of innate immunity shapes bacteria-phage ecologies. PLoS Computational Biology.
Public Library of Science. https://doi.org/10.1371/journal.pcbi.1007168
chicago: Ruess, Jakob, Maros Pleska, Calin C Guet, and Gašper Tkačik. “Molecular
Noise of Innate Immunity Shapes Bacteria-Phage Ecologies.” PLoS Computational
Biology. Public Library of Science, 2019. https://doi.org/10.1371/journal.pcbi.1007168.
ieee: J. Ruess, M. Pleska, C. C. Guet, and G. Tkačik, “Molecular noise of innate
immunity shapes bacteria-phage ecologies,” PLoS Computational Biology,
vol. 15, no. 7. Public Library of Science, 2019.
ista: Ruess J, Pleska M, Guet CC, Tkačik G. 2019. Molecular noise of innate immunity
shapes bacteria-phage ecologies. PLoS Computational Biology. 15(7), e1007168.
mla: Ruess, Jakob, et al. “Molecular Noise of Innate Immunity Shapes Bacteria-Phage
Ecologies.” PLoS Computational Biology, vol. 15, no. 7, e1007168, Public
Library of Science, 2019, doi:10.1371/journal.pcbi.1007168.
short: J. Ruess, M. Pleska, C.C. Guet, G. Tkačik, PLoS Computational Biology 15
(2019).
date_created: 2019-08-11T21:59:19Z
date_published: 2019-07-02T00:00:00Z
date_updated: 2023-08-29T07:10:06Z
day: '02'
ddc:
- '570'
department:
- _id: CaGu
- _id: GaTk
doi: 10.1371/journal.pcbi.1007168
external_id:
isi:
- '000481577700032'
file:
- access_level: open_access
checksum: 7ded4721b41c2a0fc66a1c634540416a
content_type: application/pdf
creator: dernst
date_created: 2019-08-12T12:27:26Z
date_updated: 2020-07-14T12:47:40Z
file_id: '6803'
file_name: 2019_PlosComputBiology_Ruess.pdf
file_size: 2200003
relation: main_file
file_date_updated: 2020-07-14T12:47:40Z
has_accepted_license: '1'
intvolume: ' 15'
isi: 1
issue: '7'
language:
- iso: eng
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 251D65D8-B435-11E9-9278-68D0E5697425
grant_number: '24210'
name: Effects of Stochasticity on the Function of Restriction-Modi cation Systems
at the Single-Cell Level
- _id: 251BCBEC-B435-11E9-9278-68D0E5697425
grant_number: RGY0079/2011
name: Multi-Level Conflicts in Evolutionary Dynamics of Restriction-Modification
Systems
publication: PLoS Computational Biology
publication_identifier:
eissn:
- 1553-7358
publication_status: published
publisher: Public Library of Science
quality_controlled: '1'
related_material:
record:
- id: '9786'
relation: research_data
status: public
scopus_import: '1'
status: public
title: Molecular noise of innate immunity shapes bacteria-phage ecologies
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 15
year: '2019'
...
---
_id: '9786'
article_processing_charge: No
author:
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
- first_name: Maros
full_name: Pleska, Maros
id: 4569785E-F248-11E8-B48F-1D18A9856A87
last_name: Pleska
orcid: 0000-0001-7460-7479
- first_name: Calin C
full_name: Guet, Calin C
id: 47F8433E-F248-11E8-B48F-1D18A9856A87
last_name: Guet
orcid: 0000-0001-6220-2052
- first_name: Gašper
full_name: Tkačik, Gašper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkačik
orcid: 0000-0002-6699-1455
citation:
ama: Ruess J, Pleska M, Guet CC, Tkačik G. Supporting text and results. 2019. doi:10.1371/journal.pcbi.1007168.s001
apa: Ruess, J., Pleska, M., Guet, C. C., & Tkačik, G. (2019). Supporting text
and results. Public Library of Science. https://doi.org/10.1371/journal.pcbi.1007168.s001
chicago: Ruess, Jakob, Maros Pleska, Calin C Guet, and Gašper Tkačik. “Supporting
Text and Results.” Public Library of Science, 2019. https://doi.org/10.1371/journal.pcbi.1007168.s001.
ieee: J. Ruess, M. Pleska, C. C. Guet, and G. Tkačik, “Supporting text and results.”
Public Library of Science, 2019.
ista: Ruess J, Pleska M, Guet CC, Tkačik G. 2019. Supporting text and results, Public
Library of Science, 10.1371/journal.pcbi.1007168.s001.
mla: Ruess, Jakob, et al. Supporting Text and Results. Public Library of
Science, 2019, doi:10.1371/journal.pcbi.1007168.s001.
short: J. Ruess, M. Pleska, C.C. Guet, G. Tkačik, (2019).
date_created: 2021-08-06T08:23:43Z
date_published: 2019-07-02T00:00:00Z
date_updated: 2023-08-29T07:10:05Z
day: '02'
department:
- _id: CaGu
- _id: GaTk
doi: 10.1371/journal.pcbi.1007168.s001
month: '07'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '6784'
relation: used_in_publication
status: public
status: public
title: Supporting text and results
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2019'
...
---
_id: '613'
abstract:
- lang: eng
text: 'Bacteria in groups vary individually, and interact with other bacteria and
the environment to produce population-level patterns of gene expression. Investigating
such behavior in detail requires measuring and controlling populations at the
single-cell level alongside precisely specified interactions and environmental
characteristics. Here we present an automated, programmable platform that combines
image-based gene expression and growth measurements with on-line optogenetic expression
control for hundreds of individual Escherichia coli cells over days, in a dynamically
adjustable environment. This integrated platform broadly enables experiments that
bridge individual and population behaviors. We demonstrate: (i) population structuring
by independent closed-loop control of gene expression in many individual cells,
(ii) cell-cell variation control during antibiotic perturbation, (iii) hybrid
bio-digital circuits in single cells, and freely specifiable digital communication
between individual bacteria. These examples showcase the potential for real-time
integration of theoretical models with measurement and control of many individual
cells to investigate and engineer microbial population behavior.'
acknowledgement: We are grateful to M. Lang, H. Janovjak, M. Khammash, A. Milias-Argeitis,
M. Rullan, G. Batt, A. Bosma-Moody, Aryan, S. Leibler, and members of the Guet and
Tkačik groups for helpful discussion, comments, and suggestions. We thank A. Moglich,
T. Mathes, J. Tabor, and S. Schmidl for kind gifts of strains, and R. Hauschild,
B. Knep, M. Lang, T. Asenov, E. Papusheva, T. Menner, T. Adletzberger, and J. Merrin
for technical assistance. The research leading to these results has received funding
from the People Programme (Marie Curie Actions) of the European Union’s Seventh
Framework Programme (FP7/2007–2013) under REA grant agreement no. [291734]. (to
R.C. and J.R.), Austrian Science Fund grant FWF P28844 (to G.T.), and internal IST
Austria Interdisciplinary Project Support. J.R. acknowledges support from the Agence
Nationale de la Recherche (ANR) under Grant Nos. ANR-16-CE33-0018 (MEMIP), ANR-16-CE12-0025
(COGEX) and ANR-10-BINF-06-01 (ICEBERG).
article_number: '1535'
article_processing_charge: Yes (in subscription journal)
author:
- first_name: Remy P
full_name: Chait, Remy P
id: 3464AE84-F248-11E8-B48F-1D18A9856A87
last_name: Chait
orcid: 0000-0003-0876-3187
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
- first_name: Tobias
full_name: Bergmiller, Tobias
id: 2C471CFA-F248-11E8-B48F-1D18A9856A87
last_name: Bergmiller
orcid: 0000-0001-5396-4346
- first_name: Gasper
full_name: Tkacik, Gasper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkacik
orcid: 0000-0002-6699-1455
- first_name: Calin C
full_name: Guet, Calin C
id: 47F8433E-F248-11E8-B48F-1D18A9856A87
last_name: Guet
orcid: 0000-0001-6220-2052
citation:
ama: Chait RP, Ruess J, Bergmiller T, Tkačik G, Guet CC. Shaping bacterial population
behavior through computer interfaced control of individual cells. Nature Communications.
2017;8(1). doi:10.1038/s41467-017-01683-1
apa: Chait, R. P., Ruess, J., Bergmiller, T., Tkačik, G., & Guet, C. C. (2017).
Shaping bacterial population behavior through computer interfaced control of individual
cells. Nature Communications. Nature Publishing Group. https://doi.org/10.1038/s41467-017-01683-1
chicago: Chait, Remy P, Jakob Ruess, Tobias Bergmiller, Gašper Tkačik, and Calin
C Guet. “Shaping Bacterial Population Behavior through Computer Interfaced Control
of Individual Cells.” Nature Communications. Nature Publishing Group, 2017.
https://doi.org/10.1038/s41467-017-01683-1.
ieee: R. P. Chait, J. Ruess, T. Bergmiller, G. Tkačik, and C. C. Guet, “Shaping
bacterial population behavior through computer interfaced control of individual
cells,” Nature Communications, vol. 8, no. 1. Nature Publishing Group,
2017.
ista: Chait RP, Ruess J, Bergmiller T, Tkačik G, Guet CC. 2017. Shaping bacterial
population behavior through computer interfaced control of individual cells. Nature
Communications. 8(1), 1535.
mla: Chait, Remy P., et al. “Shaping Bacterial Population Behavior through Computer
Interfaced Control of Individual Cells.” Nature Communications, vol. 8,
no. 1, 1535, Nature Publishing Group, 2017, doi:10.1038/s41467-017-01683-1.
short: R.P. Chait, J. Ruess, T. Bergmiller, G. Tkačik, C.C. Guet, Nature Communications
8 (2017).
date_created: 2018-12-11T11:47:30Z
date_published: 2017-12-01T00:00:00Z
date_updated: 2021-01-12T08:06:15Z
day: '01'
ddc:
- '576'
- '579'
department:
- _id: CaGu
- _id: GaTk
doi: 10.1038/s41467-017-01683-1
ec_funded: 1
file:
- access_level: open_access
checksum: 44bb5d0229926c23a9955d9fe0f9723f
content_type: application/pdf
creator: system
date_created: 2018-12-12T10:16:05Z
date_updated: 2020-07-14T12:47:20Z
file_id: '5190'
file_name: IST-2017-911-v1+1_s41467-017-01683-1.pdf
file_size: 1951699
relation: main_file
file_date_updated: 2020-07-14T12:47:20Z
has_accepted_license: '1'
intvolume: ' 8'
issue: '1'
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
- _id: 254E9036-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P28844-B27
name: Biophysics of information processing in gene regulation
publication: Nature Communications
publication_identifier:
issn:
- '20411723'
publication_status: published
publisher: Nature Publishing Group
publist_id: '7191'
pubrep_id: '911'
quality_controlled: '1'
scopus_import: 1
status: public
title: Shaping bacterial population behavior through computer interfaced control of
individual cells
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2017'
...
---
_id: '1148'
abstract:
- lang: eng
text: Continuous-time Markov chain (CTMC) models have become a central tool for
understanding the dynamics of complex reaction networks and the importance of
stochasticity in the underlying biochemical processes. When such models are employed
to answer questions in applications, in order to ensure that the model provides
a sufficiently accurate representation of the real system, it is of vital importance
that the model parameters are inferred from real measured data. This, however,
is often a formidable task and all of the existing methods fail in one case or
the other, usually because the underlying CTMC model is high-dimensional and computationally
difficult to analyze. The parameter inference methods that tend to scale best
in the dimension of the CTMC are based on so-called moment closure approximations.
However, there exists a large number of different moment closure approximations
and it is typically hard to say a priori which of the approximations is the most
suitable for the inference procedure. Here, we propose a moment-based parameter
inference method that automatically chooses the most appropriate moment closure
method. Accordingly, contrary to existing methods, the user is not required to
be experienced in moment closure techniques. In addition to that, our method adaptively
changes the approximation during the parameter inference to ensure that always
the best approximation is used, even in cases where different approximations are
best in different regions of the parameter space. © 2016 Elsevier Ireland Ltd
acknowledgement: This work is based on the CMSB 2015 paper “Adaptive moment closure
for parameter inference of biochemical reaction networks” (Bogomolov et al., 2015).
The work was partly supported by the German Research Foundation (DFG) as part of
the Transregional Collaborative Research Center “Automatic Verification and Analysis
of Complex Systems” (SFB/TR 14 AVACS1), by the European Research Council (ERC) under
grant 267989 (QUAREM) and by the Austrian Science Fund (FWF) under grants S11402-N23
(RiSE) and Z211-N23 (Wittgenstein Award). J.R. acknowledges support from the People
Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme
(FP7/2007-2013) under REA grant agreement no. 291734.
author:
- first_name: Christian
full_name: Schilling, Christian
last_name: Schilling
- first_name: Sergiy
full_name: Bogomolov, Sergiy
id: 369D9A44-F248-11E8-B48F-1D18A9856A87
last_name: Bogomolov
orcid: 0000-0002-0686-0365
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Andreas
full_name: Podelski, Andreas
last_name: Podelski
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
citation:
ama: Schilling C, Bogomolov S, Henzinger TA, Podelski A, Ruess J. Adaptive moment
closure for parameter inference of biochemical reaction networks. Biosystems.
2016;149:15-25. doi:10.1016/j.biosystems.2016.07.005
apa: Schilling, C., Bogomolov, S., Henzinger, T. A., Podelski, A., & Ruess,
J. (2016). Adaptive moment closure for parameter inference of biochemical reaction
networks. Biosystems. Elsevier. https://doi.org/10.1016/j.biosystems.2016.07.005
chicago: Schilling, Christian, Sergiy Bogomolov, Thomas A Henzinger, Andreas Podelski,
and Jakob Ruess. “Adaptive Moment Closure for Parameter Inference of Biochemical
Reaction Networks.” Biosystems. Elsevier, 2016. https://doi.org/10.1016/j.biosystems.2016.07.005.
ieee: C. Schilling, S. Bogomolov, T. A. Henzinger, A. Podelski, and J. Ruess, “Adaptive
moment closure for parameter inference of biochemical reaction networks,” Biosystems,
vol. 149. Elsevier, pp. 15–25, 2016.
ista: Schilling C, Bogomolov S, Henzinger TA, Podelski A, Ruess J. 2016. Adaptive
moment closure for parameter inference of biochemical reaction networks. Biosystems.
149, 15–25.
mla: Schilling, Christian, et al. “Adaptive Moment Closure for Parameter Inference
of Biochemical Reaction Networks.” Biosystems, vol. 149, Elsevier, 2016,
pp. 15–25, doi:10.1016/j.biosystems.2016.07.005.
short: C. Schilling, S. Bogomolov, T.A. Henzinger, A. Podelski, J. Ruess, Biosystems
149 (2016) 15–25.
date_created: 2018-12-11T11:50:24Z
date_published: 2016-11-01T00:00:00Z
date_updated: 2023-02-23T10:08:46Z
day: '01'
department:
- _id: ToHe
- _id: GaTk
doi: 10.1016/j.biosystems.2016.07.005
ec_funded: 1
intvolume: ' 149'
language:
- iso: eng
month: '11'
oa_version: None
page: 15 - 25
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: Biosystems
publication_status: published
publisher: Elsevier
publist_id: '6210'
quality_controlled: '1'
related_material:
record:
- id: '1658'
relation: earlier_version
status: public
scopus_import: 1
status: public
title: Adaptive moment closure for parameter inference of biochemical reaction networks
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 149
year: '2016'
...
---
_id: '10794'
abstract:
- lang: eng
text: Mathematical models are of fundamental importance in the understanding of
complex population dynamics. For instance, they can be used to predict the population
evolution starting from different initial conditions or to test how a system responds
to external perturbations. For this analysis to be meaningful in real applications,
however, it is of paramount importance to choose an appropriate model structure
and to infer the model parameters from measured data. While many parameter inference
methods are available for models based on deterministic ordinary differential
equations, the same does not hold for more detailed individual-based models. Here
we consider, in particular, stochastic models in which the time evolution of the
species abundances is described by a continuous-time Markov chain. These models
are governed by a master equation that is typically difficult to solve. Consequently,
traditional inference methods that rely on iterative evaluation of parameter likelihoods
are computationally intractable. The aim of this paper is to present recent advances
in parameter inference for continuous-time Markov chain models, based on a moment
closure approximation of the parameter likelihood, and to investigate how these
results can help in understanding, and ultimately controlling, complex systems
in ecology. Specifically, we illustrate through an agricultural pest case study
how parameters of a stochastic individual-based model can be identified from measured
data and how the resulting model can be used to solve an optimal control problem
in a stochastic setting. In particular, we show how the matter of determining
the optimal combination of two different pest control methods can be formulated
as a chance constrained optimization problem where the control action is modeled
as a state reset, leading to a hybrid system formulation.
acknowledgement: "The authors would like to acknowledge contributions from Baptiste
Mottet who performed preliminary analysis regarding parameter inference for the
considered case study in a student project (Mottet, 2014/2015).\r\nThe research
leading to these results has received funding from the People Programme (Marie Curie
Actions) of the European Union's Seventh Framework Programme (FP7/2007-2013) under
REA grant agreement No. [291734] and from SystemsX under the project SignalX."
article_number: '42'
article_processing_charge: No
article_type: original
author:
- first_name: Francesca
full_name: Parise, Francesca
last_name: Parise
- first_name: John
full_name: Lygeros, John
last_name: Lygeros
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
citation:
ama: 'Parise F, Lygeros J, Ruess J. Bayesian inference for stochastic individual-based
models of ecological systems: a pest control simulation study. Frontiers in
Environmental Science. 2015;3. doi:10.3389/fenvs.2015.00042'
apa: 'Parise, F., Lygeros, J., & Ruess, J. (2015). Bayesian inference for stochastic
individual-based models of ecological systems: a pest control simulation study.
Frontiers in Environmental Science. Frontiers. https://doi.org/10.3389/fenvs.2015.00042'
chicago: 'Parise, Francesca, John Lygeros, and Jakob Ruess. “Bayesian Inference
for Stochastic Individual-Based Models of Ecological Systems: A Pest Control Simulation
Study.” Frontiers in Environmental Science. Frontiers, 2015. https://doi.org/10.3389/fenvs.2015.00042.'
ieee: 'F. Parise, J. Lygeros, and J. Ruess, “Bayesian inference for stochastic individual-based
models of ecological systems: a pest control simulation study,” Frontiers in
Environmental Science, vol. 3. Frontiers, 2015.'
ista: 'Parise F, Lygeros J, Ruess J. 2015. Bayesian inference for stochastic individual-based
models of ecological systems: a pest control simulation study. Frontiers in Environmental
Science. 3, 42.'
mla: 'Parise, Francesca, et al. “Bayesian Inference for Stochastic Individual-Based
Models of Ecological Systems: A Pest Control Simulation Study.” Frontiers in
Environmental Science, vol. 3, 42, Frontiers, 2015, doi:10.3389/fenvs.2015.00042.'
short: F. Parise, J. Lygeros, J. Ruess, Frontiers in Environmental Science 3 (2015).
date_created: 2022-02-25T11:42:25Z
date_published: 2015-06-10T00:00:00Z
date_updated: 2022-02-25T11:59:23Z
day: '10'
ddc:
- '000'
- '570'
department:
- _id: ToHe
- _id: GaTk
doi: 10.3389/fenvs.2015.00042
ec_funded: 1
file:
- access_level: open_access
checksum: 26c222487564e1be02a11d688d6f769d
content_type: application/pdf
creator: dernst
date_created: 2022-02-25T11:55:26Z
date_updated: 2022-02-25T11:55:26Z
file_id: '10795'
file_name: 2015_FrontiersEnvironmScience_Parise.pdf
file_size: 1371201
relation: main_file
success: 1
file_date_updated: 2022-02-25T11:55:26Z
has_accepted_license: '1'
intvolume: ' 3'
keyword:
- General Environmental Science
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: Frontiers in Environmental Science
publication_identifier:
issn:
- 2296-665X
publication_status: published
publisher: Frontiers
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Bayesian inference for stochastic individual-based models of ecological systems:
a pest control simulation study'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 3
year: '2015'
...
---
_id: '1658'
abstract:
- lang: eng
text: Continuous-time Markov chain (CTMC) models have become a central tool for
understanding the dynamics of complex reaction networks and the importance of
stochasticity in the underlying biochemical processes. When such models are employed
to answer questions in applications, in order to ensure that the model provides
a sufficiently accurate representation of the real system, it is of vital importance
that the model parameters are inferred from real measured data. This, however,
is often a formidable task and all of the existing methods fail in one case or
the other, usually because the underlying CTMC model is high-dimensional and computationally
difficult to analyze. The parameter inference methods that tend to scale best
in the dimension of the CTMC are based on so-called moment closure approximations.
However, there exists a large number of different moment closure approximations
and it is typically hard to say a priori which of the approximations is the most
suitable for the inference procedure. Here, we propose a moment-based parameter
inference method that automatically chooses the most appropriate moment closure
method. Accordingly, contrary to existing methods, the user is not required to
be experienced in moment closure techniques. In addition to that, our method adaptively
changes the approximation during the parameter inference to ensure that always
the best approximation is used, even in cases where different approximations are
best in different regions of the parameter space.
alternative_title:
- LNCS
author:
- first_name: Sergiy
full_name: Bogomolov, Sergiy
id: 369D9A44-F248-11E8-B48F-1D18A9856A87
last_name: Bogomolov
orcid: 0000-0002-0686-0365
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Andreas
full_name: Podelski, Andreas
last_name: Podelski
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
- first_name: Christian
full_name: Schilling, Christian
last_name: Schilling
citation:
ama: Bogomolov S, Henzinger TA, Podelski A, Ruess J, Schilling C. Adaptive moment
closure for parameter inference of biochemical reaction networks. 2015;9308:77-89.
doi:10.1007/978-3-319-23401-4_8
apa: 'Bogomolov, S., Henzinger, T. A., Podelski, A., Ruess, J., & Schilling,
C. (2015). Adaptive moment closure for parameter inference of biochemical reaction
networks. Presented at the CMSB: Computational Methods in Systems Biology, Nantes,
France: Springer. https://doi.org/10.1007/978-3-319-23401-4_8'
chicago: Bogomolov, Sergiy, Thomas A Henzinger, Andreas Podelski, Jakob Ruess, and
Christian Schilling. “Adaptive Moment Closure for Parameter Inference of Biochemical
Reaction Networks.” Lecture Notes in Computer Science. Springer, 2015. https://doi.org/10.1007/978-3-319-23401-4_8.
ieee: S. Bogomolov, T. A. Henzinger, A. Podelski, J. Ruess, and C. Schilling, “Adaptive
moment closure for parameter inference of biochemical reaction networks,” vol.
9308. Springer, pp. 77–89, 2015.
ista: Bogomolov S, Henzinger TA, Podelski A, Ruess J, Schilling C. 2015. Adaptive
moment closure for parameter inference of biochemical reaction networks. 9308,
77–89.
mla: Bogomolov, Sergiy, et al. Adaptive Moment Closure for Parameter Inference
of Biochemical Reaction Networks. Vol. 9308, Springer, 2015, pp. 77–89, doi:10.1007/978-3-319-23401-4_8.
short: S. Bogomolov, T.A. Henzinger, A. Podelski, J. Ruess, C. Schilling, 9308 (2015)
77–89.
conference:
end_date: 2015-09-18
location: Nantes, France
name: 'CMSB: Computational Methods in Systems Biology'
start_date: 2015-09-16
date_created: 2018-12-11T11:53:18Z
date_published: 2015-09-01T00:00:00Z
date_updated: 2023-02-21T16:17:24Z
day: '01'
department:
- _id: ToHe
- _id: GaTk
doi: 10.1007/978-3-319-23401-4_8
ec_funded: 1
intvolume: ' 9308'
language:
- iso: eng
month: '09'
oa_version: None
page: 77 - 89
project:
- _id: 25EE3708-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '267989'
name: Quantitative Reactive Modeling
- _id: 25F42A32-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: Z211
name: The Wittgenstein Prize
- _id: 25832EC2-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: S 11407_N23
name: Rigorous Systems Engineering
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication_status: published
publisher: Springer
publist_id: '5492'
quality_controlled: '1'
related_material:
record:
- id: '1148'
relation: later_version
status: public
scopus_import: 1
series_title: Lecture Notes in Computer Science
status: public
title: Adaptive moment closure for parameter inference of biochemical reaction networks
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 9308
year: '2015'
...
---
_id: '1861'
abstract:
- lang: eng
text: Continuous-time Markov chains are commonly used in practice for modeling biochemical
reaction networks in which the inherent randomness of themolecular interactions
cannot be ignored. This has motivated recent research effort into methods for
parameter inference and experiment design for such models. The major difficulty
is that such methods usually require one to iteratively solve the chemical master
equation that governs the time evolution of the probability distribution of the
system. This, however, is rarely possible, and even approximation techniques remain
limited to relatively small and simple systems. An alternative explored in this
article is to base methods on only some low-order moments of the entire probability
distribution. We summarize the theory behind such moment-based methods for parameter
inference and experiment design and provide new case studies where we investigate
their performance.
acknowledgement: "HYCON2; EC; European Commission\r\n"
article_number: '8'
author:
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
- first_name: John
full_name: Lygeros, John
last_name: Lygeros
citation:
ama: Ruess J, Lygeros J. Moment-based methods for parameter inference and experiment
design for stochastic biochemical reaction networks. ACM Transactions on Modeling
and Computer Simulation. 2015;25(2). doi:10.1145/2688906
apa: Ruess, J., & Lygeros, J. (2015). Moment-based methods for parameter inference
and experiment design for stochastic biochemical reaction networks. ACM Transactions
on Modeling and Computer Simulation. ACM. https://doi.org/10.1145/2688906
chicago: Ruess, Jakob, and John Lygeros. “Moment-Based Methods for Parameter Inference
and Experiment Design for Stochastic Biochemical Reaction Networks.” ACM Transactions
on Modeling and Computer Simulation. ACM, 2015. https://doi.org/10.1145/2688906.
ieee: J. Ruess and J. Lygeros, “Moment-based methods for parameter inference and
experiment design for stochastic biochemical reaction networks,” ACM Transactions
on Modeling and Computer Simulation, vol. 25, no. 2. ACM, 2015.
ista: Ruess J, Lygeros J. 2015. Moment-based methods for parameter inference and
experiment design for stochastic biochemical reaction networks. ACM Transactions
on Modeling and Computer Simulation. 25(2), 8.
mla: Ruess, Jakob, and John Lygeros. “Moment-Based Methods for Parameter Inference
and Experiment Design for Stochastic Biochemical Reaction Networks.” ACM Transactions
on Modeling and Computer Simulation, vol. 25, no. 2, 8, ACM, 2015, doi:10.1145/2688906.
short: J. Ruess, J. Lygeros, ACM Transactions on Modeling and Computer Simulation
25 (2015).
date_created: 2018-12-11T11:54:25Z
date_published: 2015-02-01T00:00:00Z
date_updated: 2021-01-12T06:53:41Z
day: '01'
department:
- _id: ToHe
- _id: GaTk
doi: 10.1145/2688906
intvolume: ' 25'
issue: '2'
language:
- iso: eng
month: '02'
oa_version: None
publication: ACM Transactions on Modeling and Computer Simulation
publication_status: published
publisher: ACM
publist_id: '5238'
quality_controlled: '1'
scopus_import: 1
status: public
title: Moment-based methods for parameter inference and experiment design for stochastic
biochemical reaction networks
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2015'
...
---
_id: '1538'
abstract:
- lang: eng
text: Systems biology rests on the idea that biological complexity can be better
unraveled through the interplay of modeling and experimentation. However, the
success of this approach depends critically on the informativeness of the chosen
experiments, which is usually unknown a priori. Here, we propose a systematic
scheme based on iterations of optimal experiment design, flow cytometry experiments,
and Bayesian parameter inference to guide the discovery process in the case of
stochastic biochemical reaction networks. To illustrate the benefit of our methodology,
we apply it to the characterization of an engineered light-inducible gene expression
circuit in yeast and compare the performance of the resulting model with models
identified from nonoptimal experiments. In particular, we compare the parameter
posterior distributions and the precision to which the outcome of future experiments
can be predicted. Moreover, we illustrate how the identified stochastic model
can be used to determine light induction patterns that make either the average
amount of protein or the variability in a population of cells follow a desired
profile. Our results show that optimal experiment design allows one to derive
models that are accurate enough to precisely predict and regulate the protein
expression in heterogeneous cell populations over extended periods of time.
acknowledgement: 'J.R., F.P., and J.L. acknowledge support from the European Commission
under the Network of Excellence HYCON2 (highly-complex and networked control systems)
and SystemsX.ch under the SignalX Project. J.R. acknowledges support from the People
Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme
FP7/2007-2013 under REA (Research Executive Agency) Grant 291734. M.K. acknowledges
support from Human Frontier Science Program Grant RP0061/2011 (www.hfsp.org). '
author:
- first_name: Jakob
full_name: Ruess, Jakob
id: 4A245D00-F248-11E8-B48F-1D18A9856A87
last_name: Ruess
orcid: 0000-0003-1615-3282
- first_name: Francesca
full_name: Parise, Francesca
last_name: Parise
- first_name: Andreas
full_name: Milias Argeitis, Andreas
last_name: Milias Argeitis
- first_name: Mustafa
full_name: Khammash, Mustafa
last_name: Khammash
- first_name: John
full_name: Lygeros, John
last_name: Lygeros
citation:
ama: Ruess J, Parise F, Milias Argeitis A, Khammash M, Lygeros J. Iterative experiment
design guides the characterization of a light-inducible gene expression circuit.
PNAS. 2015;112(26):8148-8153. doi:10.1073/pnas.1423947112
apa: Ruess, J., Parise, F., Milias Argeitis, A., Khammash, M., & Lygeros, J.
(2015). Iterative experiment design guides the characterization of a light-inducible
gene expression circuit. PNAS. National Academy of Sciences. https://doi.org/10.1073/pnas.1423947112
chicago: Ruess, Jakob, Francesca Parise, Andreas Milias Argeitis, Mustafa Khammash,
and John Lygeros. “Iterative Experiment Design Guides the Characterization of
a Light-Inducible Gene Expression Circuit.” PNAS. National Academy of Sciences,
2015. https://doi.org/10.1073/pnas.1423947112.
ieee: J. Ruess, F. Parise, A. Milias Argeitis, M. Khammash, and J. Lygeros, “Iterative
experiment design guides the characterization of a light-inducible gene expression
circuit,” PNAS, vol. 112, no. 26. National Academy of Sciences, pp. 8148–8153,
2015.
ista: Ruess J, Parise F, Milias Argeitis A, Khammash M, Lygeros J. 2015. Iterative
experiment design guides the characterization of a light-inducible gene expression
circuit. PNAS. 112(26), 8148–8153.
mla: Ruess, Jakob, et al. “Iterative Experiment Design Guides the Characterization
of a Light-Inducible Gene Expression Circuit.” PNAS, vol. 112, no. 26,
National Academy of Sciences, 2015, pp. 8148–53, doi:10.1073/pnas.1423947112.
short: J. Ruess, F. Parise, A. Milias Argeitis, M. Khammash, J. Lygeros, PNAS 112
(2015) 8148–8153.
date_created: 2018-12-11T11:52:36Z
date_published: 2015-06-30T00:00:00Z
date_updated: 2021-01-12T06:51:27Z
day: '30'
department:
- _id: ToHe
- _id: GaTk
doi: 10.1073/pnas.1423947112
ec_funded: 1
external_id:
pmid:
- '26085136'
intvolume: ' 112'
issue: '26'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4491780/
month: '06'
oa: 1
oa_version: Submitted Version
page: 8148 - 8153
pmid: 1
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '291734'
name: International IST Postdoc Fellowship Programme
publication: PNAS
publication_status: published
publisher: National Academy of Sciences
publist_id: '5633'
quality_controlled: '1'
scopus_import: 1
status: public
title: Iterative experiment design guides the characterization of a light-inducible
gene expression circuit
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 112
year: '2015'
...
---
_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'
...