Generalized Michaelis–Menten rate law with time-varying molecular concentrations

Roktaek Lim, Thomas L. P. Martin, Junghun Chae, WooJoong Kim, Cheol-Min Ghim*, Pan-Jun Kim*

*Corresponding author for this work

Research output: Working paperPreprint


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.
Original languageEnglish
PublisherCold Spring Harbor Laboratory Press
Number of pages22
Publication statusPublished - 7 Jan 2022

Publication series



Dive into the research topics of 'Generalized Michaelis–Menten rate law with time-varying molecular concentrations'. Together they form a unique fingerprint.

Cite this