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

Abstract

The Michaelis–Menten (MM) rate law has been the dominant paradigm of modeling23 biochemical rate processes for over a century with applications in biochemistry, biophysics,24 cell biology, and chemical engineering. The MM rate law and its remedied form stand on the25 assumption that the concentration of the complex of interacting molecules, at each moment,26 approaches an equilibrium much faster than the molecular concentrations change. Yet, this27 assumption is not always justified. Here, we relax this quasi‐steady state requirement and28 propose the generalized MM rate law for the interactions of molecules with active29 concentration changes over time. Our approach for time‐varying molecular concentrations,30 termed the effective time‐delay scheme (ETS), is based on rigorously estimated time‐delay31 effects in molecular complex formation. With particularly marked improvements in protein–32 protein and protein–DNA interaction modeling, the ETS provides an analytical framework to33 interpret and predict rich transient or rhythmic dynamics (such as autogenously‐regulated34 cellular adaptation and circadian protein turnover), which goes beyond the quasi‐steady35 state assumption.