Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺
Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we conside...
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| Format: | Article |
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American Institute of Physics (AIP)
2018
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| Online Access: | http://hdl.handle.net/1721.1/118988 https://orcid.org/0000-0003-2194-3051 https://orcid.org/0000-0001-6472-8576 |
| _version_ | 1826214524445786112 |
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| author | Herath, Narmada K Del Vecchio, Domitilla |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Herath, Narmada K Del Vecchio, Domitilla |
| author_sort | Herath, Narmada K |
| collection | MIT |
| description | Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA⁺". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks. |
| first_indexed | 2024-09-23T16:07:07Z |
| format | Article |
| id | mit-1721.1/118988 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T16:07:07Z |
| publishDate | 2018 |
| publisher | American Institute of Physics (AIP) |
| record_format | dspace |
| spelling | mit-1721.1/1189882022-10-02T06:27:26Z Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺ Herath, Narmada K Del Vecchio, Domitilla Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mechanical Engineering Herath, Narmada K Del Vecchio, Domitilla Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA⁺". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks. United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0060) 2018-11-13T16:55:00Z 2018-11-13T16:55:00Z 2018-03 2017-11 2018-11-09T16:04:52Z Article http://purl.org/eprint/type/JournalArticle 0021-9606 1089-7690 http://hdl.handle.net/1721.1/118988 Herath, Narmada and Domitilla Del Vecchio. “Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺.” The Journal of Chemical Physics 148, 9 (March 2018): 094108 © 2018 Author(s) https://orcid.org/0000-0003-2194-3051 https://orcid.org/0000-0001-6472-8576 http://dx.doi.org/10.1063/1.5012752 The Journal of Chemical Physics Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/4.0/ application/pdf American Institute of Physics (AIP) AIP |
| spellingShingle | Herath, Narmada K Del Vecchio, Domitilla Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺ |
| title | Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺ |
| title_full | Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺ |
| title_fullStr | Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺ |
| title_full_unstemmed | Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺ |
| title_short | Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺ |
| title_sort | reduced linear noise approximation for biochemical reaction networks with time scale separation the stochastic tqssa⁺ |
| url | http://hdl.handle.net/1721.1/118988 https://orcid.org/0000-0003-2194-3051 https://orcid.org/0000-0001-6472-8576 |
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