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Quasi-steady-state approximations derived from the stochastic model of enzyme kinetics

Kang, H.-W. and Khuda Bukhsh, W.R. and Koeppl, H. and Rempala, G.A. (2019):
Quasi-steady-state approximations derived from the stochastic model of enzyme kinetics.
In: Bulletin of Mathematical Biology, Springer US, pp. 1-34, ISSN 0092-8240, DOI: 10.1007/s11538-019-00574-4, [Online-Edition: https://link.springer.com/article/10.1007/s11538-019-00574-4...],
[Article]

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.

Item Type: Article
Erschienen: 2019
Creators: Kang, H.-W. and Khuda Bukhsh, W.R. and Koeppl, H. and Rempala, G.A.
Title: Quasi-steady-state approximations derived from the stochastic model of enzyme kinetics
Language: English
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.

Journal or Publication Title: Bulletin of Mathematical Biology
Publisher: Springer US
Divisions: 18 Department of Electrical Engineering and Information Technology
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications > Bioinspired Communication Systems
18 Department of Electrical Engineering and Information Technology > Institute for Telecommunications
Date Deposited: 26 Feb 2019 09:25
DOI: 10.1007/s11538-019-00574-4
Official URL: https://link.springer.com/article/10.1007/s11538-019-00574-4...
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