--- _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 file: - access_level: open_access checksum: 3d0d55d373096a033bd9cf79288c8586 content_type: application/pdf creator: system date_created: 2018-12-12T10:10:47Z date_updated: 2020-07-14T12:44:42Z file_id: '4837' file_name: IST-2016-696-v1+1_journal.pone.0163628.PDF file_size: 4950415 relation: main_file file_date_updated: 2020-07-14T12:44:42Z has_accepted_license: '1' intvolume: ' 11' issue: '9' language: - iso: eng license: https://creativecommons.org/licenses/by/4.0/ month: '09' oa: 1 oa_version: Published Version project: - _id: 254E9036-B435-11E9-9278-68D0E5697425 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 publist_id: '6050' pubrep_id: '696' quality_controlled: '1' related_material: record: - id: '9869' relation: research_data status: public - id: '9870' relation: research_data status: public - id: '9871' relation: research_data status: public 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: record: - id: '1270' relation: used_in_publication status: public status: public title: Computation of positional information in an Ising model type: research_data_reference user_id: 6785fbc1-c503-11eb-8a32-93094b40e1cf 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: record: - id: '1270' relation: used_in_publication status: public 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: - '570' degree_awarded: PhD department: - _id: GaTk file: - access_level: closed checksum: ec453918c3bf8e6f460fd1156ef7b493 content_type: application/pdf creator: dernst date_created: 2019-08-13T11:46:25Z date_updated: 2019-08-13T11:46:25Z file_id: '6815' file_name: Thesis_Georg_Rieckh_w_signature_page.pdf file_size: 2614660 relation: main_file - access_level: open_access checksum: 51ae398166370d18fd22478b6365c4da content_type: application/pdf creator: dernst date_created: 2020-09-21T11:30:40Z date_updated: 2020-09-21T11:30:40Z file_id: '8542' file_name: Thesis_Georg_Rieckh.pdf file_size: 6096178 relation: main_file success: 1 file_date_updated: 2020-09-21T11:30:40Z has_accepted_license: '1' language: - iso: eng 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' ...