Robust moment closure method for the chemical master equation
The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in. However, in most cases, the moments equation is not closed; i...
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| Format: | Article |
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Institute of Electrical and Electronics Engineers (IEEE)
2018
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| Online Access: | http://hdl.handle.net/1721.1/119165 https://orcid.org/0000-0001-6472-8576 |
| _version_ | 1811074732783566848 |
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| author | Naghnaeian, Mohammad Del Vecchio, Domitilla |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Naghnaeian, Mohammad Del Vecchio, Domitilla |
| author_sort | Naghnaeian, Mohammad |
| collection | MIT |
| description | The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in. However, in most cases, the moments equation is not closed; in the sense that the first n moments depend on the higher order moments, for any positive integer n. In this paper, we develop a moment closure technique in which the higher order moments are approximated by an affine function of the lower order moments. We refer to such functions as the affine Moment Closure Functions (MCF) and prove that they are optimal in the worst-case context, in which no a priori information on the probability distribution is available. Furthermore, we cast the problem of finding the optimal affine MCF as a linear program, which is tractable. We utilize the affine MCFs to derive a finite dimensional linear system that approximates the low-order moments. We quantify the approximation error in terms of the induced norm of some linear system. Our results can be effectively used to approximate the low-order moments and characterize the noise properties of the biochemical network under study. |
| first_indexed | 2024-09-23T09:54:30Z |
| format | Article |
| id | mit-1721.1/119165 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T09:54:30Z |
| publishDate | 2018 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1191652022-09-30T17:38:42Z Robust moment closure method for the chemical master equation Naghnaeian, Mohammad Del Vecchio, Domitilla Massachusetts Institute of Technology. Department of Mechanical Engineering Naghnaeian, Mohammad Del Vecchio, Domitilla The Chemical Master Equation (CME) is used to stochastically model biochemical reaction networks, under the Markovian assumption. The low-order statistical moments induced by the CME are often the key quantities that one is interested in. However, in most cases, the moments equation is not closed; in the sense that the first n moments depend on the higher order moments, for any positive integer n. In this paper, we develop a moment closure technique in which the higher order moments are approximated by an affine function of the lower order moments. We refer to such functions as the affine Moment Closure Functions (MCF) and prove that they are optimal in the worst-case context, in which no a priori information on the probability distribution is available. Furthermore, we cast the problem of finding the optimal affine MCF as a linear program, which is tractable. We utilize the affine MCFs to derive a finite dimensional linear system that approximates the low-order moments. We quantify the approximation error in terms of the induced norm of some linear system. Our results can be effectively used to approximate the low-order moments and characterize the noise properties of the biochemical network under study. United States. Air Force. Office of Scientific Research (grant FA9550-14-1-0060) 2018-11-16T21:35:41Z 2018-11-16T21:35:41Z 2017-08 2018-11-09T16:43:47Z Article http://purl.org/eprint/type/ConferencePaper 978-1-5090-2182-6 978-1-5090-2181-9 978-1-5090-2183-3 http://hdl.handle.net/1721.1/119165 Naghnaeian, Mohammad, and Domitilla Del Vecchio. “Robust Moment Closure Method for the Chemical Master Equation.” 2017 IEEE Conference on Control Technology and Applications (CCTA) (August 2017), Mauna Lani, HI, USA, Institute of Electrical and Electronics Engineers (IEEE), 2017. https://orcid.org/0000-0001-6472-8576 http://dx.doi.org/10.1109/CCTA.2017.8062585 2017 IEEE Conference on Control Technology and Applications (CCTA) Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) arXiv |
| spellingShingle | Naghnaeian, Mohammad Del Vecchio, Domitilla Robust moment closure method for the chemical master equation |
| title | Robust moment closure method for the chemical master equation |
| title_full | Robust moment closure method for the chemical master equation |
| title_fullStr | Robust moment closure method for the chemical master equation |
| title_full_unstemmed | Robust moment closure method for the chemical master equation |
| title_short | Robust moment closure method for the chemical master equation |
| title_sort | robust moment closure method for the chemical master equation |
| url | http://hdl.handle.net/1721.1/119165 https://orcid.org/0000-0001-6472-8576 |
| work_keys_str_mv | AT naghnaeianmohammad robustmomentclosuremethodforthechemicalmasterequation AT delvecchiodomitilla robustmomentclosuremethodforthechemicalmasterequation |