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


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Article Info

DATE

2019-05

AUTHORS

Hye-Won Kang, Wasiur R. KhudaBukhsh, Heinz Koeppl, Grzegorz A. Rempała

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. More... »

PAGES

1-34

References to SciGraph publications

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  • 2015-12. The relationship between stochastic and deterministic quasi-steady state approximations in BMC SYSTEMS BIOLOGY
  • 2018-10. Non-explosivity of Stochastically Modeled Reaction Networks that are Complex Balanced in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2017-12. Beyond the Michaelis-Menten equation: Accurate and efficient estimation of enzyme kinetic parameters in SCIENTIFIC REPORTS
  • 2014-11. A constructive approach to quasi-steady state reductions in JOURNAL OF MATHEMATICAL CHEMISTRY
  • 1992. Averaging for martingale problems and stochastic approximation in APPLIED STOCHASTIC ANALYSIS
  • 2011-04-03. Continuous Time Markov Chain Models for Chemical Reaction Networks in DESIGN AND ANALYSIS OF BIOMOLECULAR CIRCUITS
  • 1998-07. Quasi-steady-state approximation for chemical reaction networks in JOURNAL OF MATHEMATICAL BIOLOGY
  • 2003-11. Michaelis-Menten kinetics at high enzyme concentrations in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2007-01. The Total Quasi-Steady-State Approximation for Fully Competitive Enzyme Reactions in BULLETIN OF MATHEMATICAL BIOLOGY
  • 1988-11. On the validity of the steady state assumption of enzyme kinetics in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2000-05. Enzyme kinetics at high enzyme concentration in BULLETIN OF MATHEMATICAL BIOLOGY
  • 2012-05. A perturbation solution of Michaelis–Menten kinetics in a “total” framework in JOURNAL OF MATHEMATICAL CHEMISTRY
  • 2000-05. Model reduction by extended quasi-steady-state approximation in JOURNAL OF MATHEMATICAL BIOLOGY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11538-019-00574-4

    DOI

    http://dx.doi.org/10.1007/s11538-019-00574-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112093062

    PUBMED

    https://www.ncbi.nlm.nih.gov/pubmed/30756234


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