Mathematical analysis of the limiting behaviors of a chromatin modification circuit
Abstract In the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we de...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer London
2023
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| Online Access: | https://hdl.handle.net/1721.1/148029 |
| _version_ | 1826202669072515072 |
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| author | Bruno, Simone Williams, Ruth J. Del Vecchio, Domitilla |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Bruno, Simone Williams, Ruth J. Del Vecchio, Domitilla |
| author_sort | Bruno, Simone |
| collection | MIT |
| description | Abstract
In the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we determine how the positive feedback loops generated by the auto- and cross-catalysis among repressive modifications affect the temporal duration of the cell identity. To this end, we conduct a stochastic analysis of a recently published chromatin modification circuit considering two limiting behaviors: fast erasure rate of repressive histone modifications or fast erasure rate of DNA methylation. In order to perform this mathematical analysis, we first show that the deterministic model of the system is a singular singularly perturbed (SSP) system and use a model reduction approach for SSP systems to obtain a reduced one-dimensional model. We thus analytically evaluate the reduced system’s stationary probability distribution and the mean switching time between active and repressed chromatin states. We then add a computational study of the original reaction model to validate and extend the analytical findings. Our results show that the absence of DNA methylation reduces the bias of the system’s stationary probability distribution toward the repressed chromatin state and the temporal duration of this state’s memory. In the absence of repressive histone modifications, we also observe that the time needed to reactivate a repressed gene with an activating input is less stochastic, suggesting that repressive histone modifications specifically contribute to the highly variable latency of state reactivation. |
| first_indexed | 2024-09-23T12:13:23Z |
| format | Article |
| id | mit-1721.1/148029 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:13:23Z |
| publishDate | 2023 |
| publisher | Springer London |
| record_format | dspace |
| spelling | mit-1721.1/1480292024-01-19T20:41:13Z Mathematical analysis of the limiting behaviors of a chromatin modification circuit Bruno, Simone Williams, Ruth J. Del Vecchio, Domitilla Massachusetts Institute of Technology. Department of Mechanical Engineering Abstract In the last decade, the interactions among histone modifications and DNA methylation and their effect on the DNA structure, i.e., chromatin state, have been identified as key mediators for the maintenance of cell identity, defined as epigenetic cell memory. In this paper, we determine how the positive feedback loops generated by the auto- and cross-catalysis among repressive modifications affect the temporal duration of the cell identity. To this end, we conduct a stochastic analysis of a recently published chromatin modification circuit considering two limiting behaviors: fast erasure rate of repressive histone modifications or fast erasure rate of DNA methylation. In order to perform this mathematical analysis, we first show that the deterministic model of the system is a singular singularly perturbed (SSP) system and use a model reduction approach for SSP systems to obtain a reduced one-dimensional model. We thus analytically evaluate the reduced system’s stationary probability distribution and the mean switching time between active and repressed chromatin states. We then add a computational study of the original reaction model to validate and extend the analytical findings. Our results show that the absence of DNA methylation reduces the bias of the system’s stationary probability distribution toward the repressed chromatin state and the temporal duration of this state’s memory. In the absence of repressive histone modifications, we also observe that the time needed to reactivate a repressed gene with an activating input is less stochastic, suggesting that repressive histone modifications specifically contribute to the highly variable latency of state reactivation. 2023-02-14T13:10:08Z 2023-02-14T13:10:08Z 2023-02-06 2023-02-12T04:19:39Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/148029 Bruno, Simone, Williams, Ruth J. and Del Vecchio, Domitilla. 2023. "Mathematical analysis of the limiting behaviors of a chromatin modification circuit." PUBLISHER_CC en https://doi.org/10.1007/s00498-023-00343-8 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer London Springer London |
| spellingShingle | Bruno, Simone Williams, Ruth J. Del Vecchio, Domitilla Mathematical analysis of the limiting behaviors of a chromatin modification circuit |
| title | Mathematical analysis of the limiting behaviors of a chromatin modification circuit |
| title_full | Mathematical analysis of the limiting behaviors of a chromatin modification circuit |
| title_fullStr | Mathematical analysis of the limiting behaviors of a chromatin modification circuit |
| title_full_unstemmed | Mathematical analysis of the limiting behaviors of a chromatin modification circuit |
| title_short | Mathematical analysis of the limiting behaviors of a chromatin modification circuit |
| title_sort | mathematical analysis of the limiting behaviors of a chromatin modification circuit |
| url | https://hdl.handle.net/1721.1/148029 |
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