TY - JOUR
T1 - Enlightening the blind spot of the Michaelis–Menten rate law
T2 - The role of relaxation dynamics in molecular complex formation
AU - Chae, Junghun
AU - Lim, Roktaek
AU - Martin, Thomas L.P.
AU - Ghim, Cheol Min
AU - Kim, Pan Jun
N1 - Funding Information:
This work was supported by the National Research Foundation of Korea, South Korea (RS-2023-00263411) and the UBSI Research Fund of Ulsan National Institute of Science and Technology (No. 1.230070.01) (J.C., R.L., and C.-M.G.). We also acknowledge the support of the Blue Sky Research Fund of Hong Kong Baptist University (RC-BSRF/21-22/09) and the General Research Fund from the Research Grants Council of the Hong Kong Special Administrative Region, China (No. 12202322) (R.L., T.L.P.M., and P.-J.K.). This work was conducted with the resources of the UNIST Supercomputing Center and the HKBU High Performance Cluster Computing Centre.
Publisher Copyright:
© 2024 The Authors. Published by Elsevier Ltd.
PY - 2025/1/21
Y1 - 2025/1/21
N2 - The century-long Michaelis–Menten rate law and its modifications in the modeling of biochemical rate processes stand on the assumption that the concentration of the complex of interacting molecules, at each moment, rapidly approaches an equilibrium (quasi-steady state) compared to the pace of molecular concentration changes. Yet, in the case of actively time-varying molecular concentrations with transient or oscillatory dynamics, the deviation of the complex profile from the quasi-steady state becomes relevant. A recent theoretical approach, known as the effective time-delay scheme (ETS), suggests that the delay from the relaxation time of molecular complex formation contributes to the substantial breakdown of the quasi-steady state assumption. Here, we systematically expand this ETS and inquire into the comprehensive roles of relaxation dynamics in complex formation. Through the modeling of rhythmic protein–protein and protein–DNA interactions and the mammalian circadian clock, our analysis reveals the effect of the relaxation dynamics beyond the time delay, which extends to the dampening of changes in the complex concentration with a reduction in the oscillation amplitude compared to the quasi-steady state. Interestingly, the combined effect of the time delay and amplitude reduction shapes both qualitative and quantitative oscillatory patterns such as the emergence and variability of the mammalian circadian rhythms. These findings highlight the downside of the routine assumption of quasi-steady states and enhance the mechanistic understanding of rich time-varying biomolecular processes.
AB - The century-long Michaelis–Menten rate law and its modifications in the modeling of biochemical rate processes stand on the assumption that the concentration of the complex of interacting molecules, at each moment, rapidly approaches an equilibrium (quasi-steady state) compared to the pace of molecular concentration changes. Yet, in the case of actively time-varying molecular concentrations with transient or oscillatory dynamics, the deviation of the complex profile from the quasi-steady state becomes relevant. A recent theoretical approach, known as the effective time-delay scheme (ETS), suggests that the delay from the relaxation time of molecular complex formation contributes to the substantial breakdown of the quasi-steady state assumption. Here, we systematically expand this ETS and inquire into the comprehensive roles of relaxation dynamics in complex formation. Through the modeling of rhythmic protein–protein and protein–DNA interactions and the mammalian circadian clock, our analysis reveals the effect of the relaxation dynamics beyond the time delay, which extends to the dampening of changes in the complex concentration with a reduction in the oscillation amplitude compared to the quasi-steady state. Interestingly, the combined effect of the time delay and amplitude reduction shapes both qualitative and quantitative oscillatory patterns such as the emergence and variability of the mammalian circadian rhythms. These findings highlight the downside of the routine assumption of quasi-steady states and enhance the mechanistic understanding of rich time-varying biomolecular processes.
KW - Circadian rhythm
KW - Gene expression regulation
KW - Kinetic modeling
KW - Protein-protein interaction
UR - http://www.scopus.com/inward/record.url?scp=85209657107&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2024.111989
DO - 10.1016/j.jtbi.2024.111989
M3 - Journal article
C2 - 39557361
AN - SCOPUS:85209657107
SN - 0022-5193
VL - 597
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
M1 - 111989
ER -