---
_id: '1270'
abstract:
- lang: eng
text: A crucial step in the early development of multicellular organisms involves
the establishment of spatial patterns of gene expression which later direct proliferating
cells to take on different cell fates. These patterns enable the cells to infer
their global position within a tissue or an organism by reading out local gene
expression levels. The patterning system is thus said to encode positional information,
a concept that was formalized recently in the framework of information theory.
Here we introduce a toy model of patterning in one spatial dimension, which can
be seen as an extension of Wolpert's paradigmatic "French Flag" model,
to patterning by several interacting, spatially coupled genes subject to intrinsic
and extrinsic noise. Our model, a variant of an Ising spin system, allows us to
systematically explore expression patterns that optimally encode positional information.
We find that optimal patterning systems use positional cues, as in the French
Flag model, together with gene-gene interactions to generate combinatorial codes
for position which we call "Counter" patterns. Counter patterns can
also be stabilized against noise and variations in system size or morphogen dosage
by longer-range spatial interactions of the type invoked in the Turing model.
The simple setup proposed here qualitatively captures many of the experimentally
observed properties of biological patterning systems and allows them to be studied
in a single, theoretically consistent framework.
acknowledgement: The authors would like to thank Thomas Sokolowski and Filipe Tostevin
for helpful discussions. PH and UG were funded by the German Excellence Initiative
via the program "Nanosystems Initiative Munich" (https://www.nano-initiative-munich.de)
and the German Research Foundation via the SFB 1032 "Nanoagents for Spatiotemporal
Control of Molecular and Cellular Reactions" (http://www.sfb1032.physik.uni-muenchen.de).
GT was funded by the Austrian Science Fund (FWF P 28844) (http://www.fwf.ac.at).
article_number: e0163628
author:
- first_name: Patrick
full_name: Hillenbrand, Patrick
last_name: Hillenbrand
- first_name: Ulrich
full_name: Gerland, Ulrich
last_name: Gerland
- first_name: Gasper
full_name: Tkacik, Gasper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkacik
orcid: 0000-0002-6699-1455
citation:
ama: 'Hillenbrand P, Gerland U, Tkačik G. Beyond the French flag model: Exploiting
spatial and gene regulatory interactions for positional information. PLoS One.
2016;11(9). doi:10.1371/journal.pone.0163628'
apa: 'Hillenbrand, P., Gerland, U., & Tkačik, G. (2016). Beyond the French flag
model: Exploiting spatial and gene regulatory interactions for positional information.
PLoS One. Public Library of Science. https://doi.org/10.1371/journal.pone.0163628'
chicago: 'Hillenbrand, Patrick, Ulrich Gerland, and Gašper Tkačik. “Beyond the French
Flag Model: Exploiting Spatial and Gene Regulatory Interactions for Positional
Information.” PLoS One. Public Library of Science, 2016. https://doi.org/10.1371/journal.pone.0163628.'
ieee: 'P. Hillenbrand, U. Gerland, and G. Tkačik, “Beyond the French flag model:
Exploiting spatial and gene regulatory interactions for positional information,”
PLoS One, vol. 11, no. 9. Public Library of Science, 2016.'
ista: 'Hillenbrand P, Gerland U, Tkačik G. 2016. Beyond the French flag model: Exploiting
spatial and gene regulatory interactions for positional information. PLoS One.
11(9), e0163628.'
mla: 'Hillenbrand, Patrick, et al. “Beyond the French Flag Model: Exploiting Spatial
and Gene Regulatory Interactions for Positional Information.” PLoS One,
vol. 11, no. 9, e0163628, Public Library of Science, 2016, doi:10.1371/journal.pone.0163628.'
short: P. Hillenbrand, U. Gerland, G. Tkačik, PLoS One 11 (2016).
date_created: 2018-12-11T11:51:03Z
date_published: 2016-09-27T00:00:00Z
date_updated: 2023-02-23T14:11:37Z
day: '27'
ddc:
- '571'
department:
- _id: GaTk
doi: 10.1371/journal.pone.0163628
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month: '09'
oa: 1
oa_version: Published Version
project:
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call_identifier: FWF
grant_number: P28844-B27
name: Biophysics of information processing in gene regulation
publication: PLoS One
publication_status: published
publisher: Public Library of Science
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scopus_import: 1
status: public
title: 'Beyond the French flag model: Exploiting spatial and gene regulatory interactions
for positional information'
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: 11
year: '2016'
...
---
_id: '9870'
abstract:
- lang: eng
text: The effect of noise in the input field on an Ising model is approximated.
Furthermore, methods to compute positional information in an Ising model by transfer
matrices and Monte Carlo sampling are outlined.
article_processing_charge: No
author:
- first_name: Patrick
full_name: Hillenbrand, Patrick
last_name: Hillenbrand
- first_name: Ulrich
full_name: Gerland, Ulrich
last_name: Gerland
- first_name: Gašper
full_name: Tkačik, Gašper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkačik
orcid: 0000-0002-6699-1455
citation:
ama: Hillenbrand P, Gerland U, Tkačik G. Computation of positional information in
an Ising model. 2016. doi:10.1371/journal.pone.0163628.s002
apa: Hillenbrand, P., Gerland, U., & Tkačik, G. (2016). Computation of positional
information in an Ising model. Public Library of Science. https://doi.org/10.1371/journal.pone.0163628.s002
chicago: Hillenbrand, Patrick, Ulrich Gerland, and Gašper Tkačik. “Computation of
Positional Information in an Ising Model.” Public Library of Science, 2016. https://doi.org/10.1371/journal.pone.0163628.s002.
ieee: P. Hillenbrand, U. Gerland, and G. Tkačik, “Computation of positional information
in an Ising model.” Public Library of Science, 2016.
ista: Hillenbrand P, Gerland U, Tkačik G. 2016. Computation of positional information
in an Ising model, Public Library of Science, 10.1371/journal.pone.0163628.s002.
mla: Hillenbrand, Patrick, et al. Computation of Positional Information in an
Ising Model. Public Library of Science, 2016, doi:10.1371/journal.pone.0163628.s002.
short: P. Hillenbrand, U. Gerland, G. Tkačik, (2016).
date_created: 2021-08-10T09:23:45Z
date_published: 2016-09-27T00:00:00Z
date_updated: 2023-02-21T16:56:40Z
day: '27'
department:
- _id: GaTk
doi: 10.1371/journal.pone.0163628.s002
month: '09'
oa_version: Published Version
publisher: Public Library of Science
related_material:
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- id: '1270'
relation: used_in_publication
status: public
status: public
title: Computation of positional information in an Ising model
type: research_data_reference
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year: '2016'
...
---
_id: '9869'
abstract:
- lang: eng
text: A lower bound on the error of a positional estimator with limited positional
information is derived.
article_processing_charge: No
author:
- first_name: Patrick
full_name: Hillenbrand, Patrick
last_name: Hillenbrand
- first_name: Ulrich
full_name: Gerland, Ulrich
last_name: Gerland
- first_name: Gašper
full_name: Tkačik, Gašper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkačik
orcid: 0000-0002-6699-1455
citation:
ama: Hillenbrand P, Gerland U, Tkačik G. Error bound on an estimator of position.
2016. doi:10.1371/journal.pone.0163628.s001
apa: Hillenbrand, P., Gerland, U., & Tkačik, G. (2016). Error bound on an estimator
of position. Public Library of Science. https://doi.org/10.1371/journal.pone.0163628.s001
chicago: Hillenbrand, Patrick, Ulrich Gerland, and Gašper Tkačik. “Error Bound on
an Estimator of Position.” Public Library of Science, 2016. https://doi.org/10.1371/journal.pone.0163628.s001.
ieee: P. Hillenbrand, U. Gerland, and G. Tkačik, “Error bound on an estimator of
position.” Public Library of Science, 2016.
ista: Hillenbrand P, Gerland U, Tkačik G. 2016. Error bound on an estimator of position,
Public Library of Science, 10.1371/journal.pone.0163628.s001.
mla: Hillenbrand, Patrick, et al. Error Bound on an Estimator of Position.
Public Library of Science, 2016, doi:10.1371/journal.pone.0163628.s001.
short: P. Hillenbrand, U. Gerland, G. Tkačik, (2016).
date_created: 2021-08-10T08:53:48Z
date_published: 2016-09-27T00:00:00Z
date_updated: 2023-02-21T16:56:40Z
day: '27'
department:
- _id: GaTk
doi: 10.1371/journal.pone.0163628.s001
month: '09'
oa_version: Published Version
publisher: Public Library of Science
related_material:
record:
- id: '1270'
relation: used_in_publication
status: public
status: public
title: Error bound on an estimator of position
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2016'
...
---
_id: '9871'
abstract:
- lang: eng
text: The positional information in a discrete morphogen field with Gaussian noise
is computed.
article_processing_charge: No
author:
- first_name: Patrick
full_name: Hillenbrand, Patrick
last_name: Hillenbrand
- first_name: Ulrich
full_name: Gerland, Ulrich
last_name: Gerland
- first_name: Gašper
full_name: Tkačik, Gašper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkačik
orcid: 0000-0002-6699-1455
citation:
ama: Hillenbrand P, Gerland U, Tkačik G. Computation of positional information in
a discrete morphogen field. 2016. doi:10.1371/journal.pone.0163628.s003
apa: Hillenbrand, P., Gerland, U., & Tkačik, G. (2016). Computation of positional
information in a discrete morphogen field. Public Library of Science. https://doi.org/10.1371/journal.pone.0163628.s003
chicago: Hillenbrand, Patrick, Ulrich Gerland, and Gašper Tkačik. “Computation of
Positional Information in a Discrete Morphogen Field.” Public Library of Science,
2016. https://doi.org/10.1371/journal.pone.0163628.s003.
ieee: P. Hillenbrand, U. Gerland, and G. Tkačik, “Computation of positional information
in a discrete morphogen field.” Public Library of Science, 2016.
ista: Hillenbrand P, Gerland U, Tkačik G. 2016. Computation of positional information
in a discrete morphogen field, Public Library of Science, 10.1371/journal.pone.0163628.s003.
mla: Hillenbrand, Patrick, et al. Computation of Positional Information in a
Discrete Morphogen Field. Public Library of Science, 2016, doi:10.1371/journal.pone.0163628.s003.
short: P. Hillenbrand, U. Gerland, G. Tkačik, (2016).
date_created: 2021-08-10T09:27:35Z
date_updated: 2023-02-21T16:56:40Z
day: '27'
department:
- _id: GaTk
doi: 10.1371/journal.pone.0163628.s003
month: '09'
oa_version: Published Version
publisher: Public Library of Science
related_material:
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status: public
title: Computation of positional information in a discrete morphogen field
type: research_data_reference
user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf
year: '2016'
...
---
_id: '1128'
abstract:
- lang: eng
text: "The process of gene expression is central to the modern understanding of
how cellular systems\r\nfunction. In this process, a special kind of regulatory
proteins, called transcription factors,\r\nare important to determine how much
protein is produced from a given gene. As biological\r\ninformation is transmitted
from transcription factor concentration to mRNA levels to amounts of\r\nprotein,
various sources of noise arise and pose limits to the fidelity of intracellular
signaling.\r\nThis thesis concerns itself with several aspects of stochastic gene
expression: (i) the mathematical\r\ndescription of complex promoters responsible
for the stochastic production of biomolecules,\r\n(ii) fundamental limits to information
processing the cell faces due to the interference from multiple\r\nfluctuating
signals, (iii) how the presence of gene expression noise influences the evolution\r\nof
regulatory sequences, (iv) and tools for the experimental study of origins and
consequences\r\nof cell-cell heterogeneity, including an application to bacterial
stress response systems."
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Georg
full_name: Rieckh, Georg
id: 34DA8BD6-F248-11E8-B48F-1D18A9856A87
last_name: Rieckh
citation:
ama: Rieckh G. Studying the complexities of transcriptional regulation. 2016.
apa: Rieckh, G. (2016). Studying the complexities of transcriptional regulation.
Institute of Science and Technology Austria.
chicago: Rieckh, Georg. “Studying the Complexities of Transcriptional Regulation.”
Institute of Science and Technology Austria, 2016.
ieee: G. Rieckh, “Studying the complexities of transcriptional regulation,” Institute
of Science and Technology Austria, 2016.
ista: Rieckh G. 2016. Studying the complexities of transcriptional regulation. Institute
of Science and Technology Austria.
mla: Rieckh, Georg. Studying the Complexities of Transcriptional Regulation.
Institute of Science and Technology Austria, 2016.
short: G. Rieckh, Studying the Complexities of Transcriptional Regulation, Institute
of Science and Technology Austria, 2016.
date_created: 2018-12-11T11:50:18Z
date_published: 2016-08-01T00:00:00Z
date_updated: 2023-09-07T11:44:34Z
day: '01'
ddc:
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degree_awarded: PhD
department:
- _id: GaTk
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creator: dernst
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date_updated: 2019-08-13T11:46:25Z
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language:
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month: '08'
oa: 1
oa_version: Published Version
page: '114'
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
publist_id: '6232'
status: public
supervisor:
- first_name: Gasper
full_name: Tkacik, Gasper
id: 3D494DCA-F248-11E8-B48F-1D18A9856A87
last_name: Tkacik
orcid: 0000-0002-6699-1455
title: Studying the complexities of transcriptional regulation
type: dissertation
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
year: '2016'
...