Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics

Kang, Hye-Won; KhudaBukhsh, Wasiur R.; Koeppl, Heinz; Rempa?a, Grzegorz A.

Abstract

The paper outlines a general approach to deriving quasi-steady-state approximations (QSSAs) of the stochastic reaction networks describing the Michaelis–Menten enzyme kinetics. In particular, it explains how different sets of assumptions about chemical species abundance and reaction rates lead to the standard QSSA, the total QSSA, and the reverse QSSA. These three QSSAs have been widely studied in the literature in deterministic ordinary differential equation settings, and several sets of conditions for their validity have been proposed. With the help of the multiscaling techniques introduced in Ball et al. (Ann Appl Probab 16(4):1925–1961, 2006), Kang and Kurtz (Ann Appl Probab 23(2):529–583, 2013), it is seen that the conditions for deterministic QSSAs largely agree (with some exceptions) with the ones for stochastic QSSAs in the large-volume limits. The paper also illustrates how the stochastic QSSA approach may be extended to more complex stochastic kinetic networks like, for instance, the enzyme–substrate–inhibitor system.

Citation

Kang, H., KhudaBukhsh, W. R., Koeppl, H., & Rempała, G. A. (2019). Quasi-Steady-State Approximations Derived from the Stochastic Model of Enzyme Kinetics. Bulletin of Mathematical Biology, 81(5), 1303-1336. https://doi.org/10.1007/s11538-019-00574-4

• Journal Article Type: Article
• Acceptance Date: Jan 29, 2019
• Online Publication Date: Feb 12, 2019
• Publication Date: May 15, 2019
• Deposit Date: Apr 9, 2022
• Journal: Bulletin of Mathematical Biology
• Print ISSN: 0092-8240
• Electronic ISSN: 1522-9602
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 81
• Issue: 5
• Pages: 1303-1336
• DOI: https://doi.org/10.1007/s11538-019-00574-4
• Keywords: Computational Theory and Mathematics; General Agricultural and Biological Sciences; Pharmacology; General Environmental Science; General Biochemistry, Genetics and Molecular Biology; General Mathematics; Immunology; General Neuroscience
• Public URL: https://nottingham-repository.worktribe.com/output/7715614
• Publisher URL: https://link.springer.com/article/10.1007/s11538-019-00574-4