PT  - JOURNAL ARTICLE
AU  - Roktaek Lim
AU  - Thomas L. P. Martin
AU  - Junghun Chae
AU  - WooJoong Kim
AU  - Cheol-Min Ghim
AU  - Pan-Jun Kim
TI  - Revised Michaelis–Menten rate law with time-varying molecular concentrations
AID  - 10.1101/2022.01.07.475310
DP  - 2022 Jan 01
TA  - bioRxiv
PG  - 2022.01.07.475310
4099  - http://biorxiv.org/content/early/2022/11/26/2022.01.07.475310.short
4100  - http://biorxiv.org/content/early/2022/11/26/2022.01.07.475310.full
AB  - The Michaelis–Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the revised MM rate law for actively time-varying molecular concentrations. Our approach, termed the effective time-delay scheme (ETS), is based on rigorously derived time-delay effects in molecular complex formation. With particularly marked improvements in protein–protein and protein–DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover) beyond the quasi-steady state assumption.Competing Interest StatementThe authors have declared no competing interest.