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

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

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


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, systems 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 (quasi-steady state) 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 generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated 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), which goes beyond the quasi-steady state assumption.

Original languageEnglish
Article numbere1011711
Number of pages18
JournalPLoS Computational Biology
Issue number12
Publication statusPublished - 11 Dec 2023

Scopus Subject Areas

  • Ecology, Evolution, Behavior and Systematics
  • Modelling and Simulation
  • Ecology
  • Molecular Biology
  • Genetics
  • Cellular and Molecular Neuroscience
  • Computational Theory and Mathematics


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