Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation
The input/output dynamic behavior of a biomolecular system is affected by interconnection to other downstream systems through impedance-like effects called retroactivity. In this paper, we study the effects of retroactivity at the interconnection between two transcriptional modules, focusing on stoc...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2013
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| Online Access: | http://hdl.handle.net/1721.1/78660 https://orcid.org/0000-0001-6472-8576 |
| _version_ | 1811089491721453568 |
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| author | Ghaemi, Reza Del Vecchio, Domitilla |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Ghaemi, Reza Del Vecchio, Domitilla |
| author_sort | Ghaemi, Reza |
| collection | MIT |
| description | The input/output dynamic behavior of a biomolecular system is affected by interconnection to other downstream systems through impedance-like effects called retroactivity. In this paper, we study the effects of retroactivity at the interconnection between two transcriptional modules, focusing on stochastic behavior. In particular, we describe the system through the Master equation and develop a singular perturbation theory to obtain a reduced Master equation. We prove that the solution of the original Master equation converges fast to an e neighbor of the solution of the reduced Master equation, in which e is the singular perturbation parameter. Our analysis shows that the upstream system and the downstream one are statistically independent at the steady state. However, the interconnection slows down the dynamics of both the expectation and the variance of the output of the upstream transcriptional module. |
| first_indexed | 2024-09-23T14:20:02Z |
| format | Article |
| id | mit-1721.1/78660 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:20:02Z |
| publishDate | 2013 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/786602022-09-29T08:46:54Z Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation Ghaemi, Reza Del Vecchio, Domitilla Massachusetts Institute of Technology. Department of Mechanical Engineering Ghaemi, Reza Del Vecchio, Domitilla The input/output dynamic behavior of a biomolecular system is affected by interconnection to other downstream systems through impedance-like effects called retroactivity. In this paper, we study the effects of retroactivity at the interconnection between two transcriptional modules, focusing on stochastic behavior. In particular, we describe the system through the Master equation and develop a singular perturbation theory to obtain a reduced Master equation. We prove that the solution of the original Master equation converges fast to an e neighbor of the solution of the reduced Master equation, in which e is the singular perturbation parameter. Our analysis shows that the upstream system and the downstream one are statistically independent at the steady state. However, the interconnection slows down the dynamics of both the expectation and the variance of the output of the upstream transcriptional module. 2013-05-01T18:51:24Z 2013-05-01T18:51:24Z 2012-06 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-2102-0 978-1-4577-1095-7 0743-1619 INSPEC Accession Number: 13036612 http://hdl.handle.net/1721.1/78660 Ghaemi, Reza and Domitilla Del Vecchio. "Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation." In 2012 American Control Conference Fairmont Queen Elizabeth, Montréal, Canada June 27-June 29, 2012. Proceedings. IEEE. https://orcid.org/0000-0001-6472-8576 en_US http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6315645 Proceedings of the 2012 American Control Conference (ACC) Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Institute of Electrical and Electronics Engineers MIT web domain |
| spellingShingle | Ghaemi, Reza Del Vecchio, Domitilla Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation |
| title | Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation |
| title_full | Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation |
| title_fullStr | Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation |
| title_full_unstemmed | Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation |
| title_short | Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation |
| title_sort | stochastic analysis of retroactivity in transcriptional networks through singular perturbation |
| url | http://hdl.handle.net/1721.1/78660 https://orcid.org/0000-0001-6472-8576 |
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