title: Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation.
abstract: Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.
authors.affiliation: Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.
authors.forename: Otto
authors.initials: O
authors.lastname: Pulkkinen
authors.affiliation: Department of Physics, Tampere University of Technology, FI-33101 Tampere, Finland.|Institute for Physics &Astronomy, University of Potsdam, D-14476 Potsdam-Golm, Germany.
authors.forename: Ralf
authors.initials: R
authors.lastname: Metzler
mesh_terms: D004789:Enzyme Activation; D004926:Escherichia coli / Q000737:chemistry / Q000235:genetics; D029968:Escherichia coli Proteins / Q000737:chemistry* / Q000235:genetics; D015964:Gene Expression Regulation, Bacterial; D007700:Kinetics; D056968:Lac Repressors / Q000737:chemistry* / Q000235:genetics; D008962:Models, Theoretical; D013379:Substrate Specificity; D014158:Transcription, Genetic
chemical_list: D029968:Escherichia coli Proteins; D056968:Lac Repressors; C539064:LacI protein, E coli