title: Accuracy of the Michaelis-Menten approximation when analysing effects of molecular noise.
abstract: Quantitative biology relies on the construction of accurate mathematical models, yet the effectiveness of these models is often predicated on making simplifying approximations that allow for direct comparisons with available experimental data. The Michaelis-Menten (MM) approximation is widely used in both deterministic and discrete stochastic models of intracellular reaction networks, owing to the ubiquity of enzymatic activity in cellular processes and the clear biochemical interpretation of its parameters. However, it is not well understood how the approximation applies to the discrete stochastic case or how it extends to spatially inhomogeneous systems. We study the behaviour of the discrete stochastic MM approximation as a function of system size and show that significant errors can occur for small volumes, in comparison with a corresponding mass-action system. We then explore some consequences of these results for quantitative modelling. One consequence is that fluctuation-induced sensitivity, or stochastic focusing, can become highly exaggerated in models that make use of MM kinetics even if the approximations are excellent in a deterministic model. Another consequence is that spatial stochastic simulations based on the reaction-diffusion master equation can become highly inaccurate if the model contains MM terms.
authors.affiliation: Department of Cell and Molecular Biology, Uppsala University, Box 337, Uppsala 75105, Sweden.
authors.forename: Michael J
authors.initials: MJ
authors.lastname: Lawson
authors.affiliation: Department of Computer Science, University of California Santa Barbara, Santa Barbara, CA 93106-5070, USA.
authors.forename: Linda
authors.initials: L
authors.lastname: Petzold
authors.affiliation: Department of Information Technology, Uppsala University, Box 337, Uppsala 75105, Sweden andreas.hellander@it.uu.se.
authors.forename: Andreas
authors.initials: A
authors.lastname: Hellander
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004789:Enzyme Activation; D004798:Enzymes / Q000737:chemistry*; D007700:Kinetics; D008956:Models, Chemical; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D059629:Signal-To-Noise Ratio; D013269:Stochastic Processes; D013379:Substrate Specificity
chemical_list: D004798:Enzymes
keywords: Michaelis–Menten; reaction–diffusion master equation; stochastic models
references.citation: J Chem Phys. 2013 May 7;138(17):170901
references.pmid: 23656106
references.citation: Proc Natl Acad Sci U S A. 2000 Jun 20;97(13):7148-53
references.pmid: 10852944
references.citation: Biophys J. 2014 Aug 5;107(3):783-93
references.pmid: 25099817
references.citation: J Chem Phys. 2007 Sep 7;127(9):094106
references.pmid: 17824731
references.citation: Phys Rev Lett. 2009 May 29;102(21):218103
references.pmid: 19519139
references.citation: Proc Natl Acad Sci U S A. 2010 Feb 9;107(6):2473-8
references.pmid: 20133748
references.citation: Proc Natl Acad Sci U S A. 1996 Sep 17;93(19):10078-83
references.pmid: 8816754
references.citation: IET Syst Biol. 2011 Jan;5(1):58
references.pmid: 21261403
references.citation: J Chem Phys. 2011 Apr 7;134(13):134112
references.pmid: 21476748
references.citation: J Chem Phys. 2011 Nov 14;135(18):181103
references.pmid: 22088045
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Apr;85(4 Pt 1):042901
references.pmid: 22680526
references.citation: Nat Methods. 2012 Dec;9(12):1163-6
references.pmid: 23223170
references.citation: J R Soc Interface. 2013 Mar 6;10(80):20120988
references.pmid: 23325756
references.citation: Nature. 2010 Jul 1;466(7302):77-81
references.pmid: 20562858