Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation
- 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 notMany 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.…
Verfasserangaben: | Otto Pulkkinen, Ralf MetzlerORCiDGND |
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DOI: | https://doi.org/10.1038/srep17820 |
ISSN: | 2045-2322 |
Titel des übergeordneten Werks (Englisch): | Scientific reports |
Verlag: | Nature Publishing Group |
Verlagsort: | London |
Publikationstyp: | Wissenschaftlicher Artikel |
Sprache: | Englisch |
Datum der Erstveröffentlichung: | 04.12.2015 |
Erscheinungsjahr: | 2015 |
Veröffentlichende Institution: | Universität Potsdam |
Datum der Freischaltung: | 19.01.2016 |
Ausgabe: | 5 |
Fördernde Institution: | Universität Potsdam, Publikationsfonds |
Fördernummer: | PA 2015_35 |
Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC-Klassifikation: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
Peer Review: | Referiert |
Fördermittelquelle: | Publikationsfonds der Universität Potsdam |
Publikationsweg: | Open Access |
Lizenz (Deutsch): | CC-BY - Namensnennung 4.0 International |
Externe Anmerkung: | Zweitveröffentlichung in der Schriftenreihe Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 210 |