Open AccessBifurcation and oscillatory dynamics of delayed CDK1‐APC feedback loop
Author(s) -
Zhou Shenshuang,
Zhang Wei,
Zhang Yuan,
Ni Xuan,
Li Zhouhong
Publication year - 2020
Publication title -
iet systems biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.367
H-Index - 50
eISSN - 1751-8857
pISSN - 1751-8849
DOI - 10.1049/iet-syb.2020.0050
Subject(s) - control theory (sociology) , hopf bifurcation , bifurcation , physics , loop (graph theory) , feedback loop , cyclin dependent kinase 1 , stability (learning theory) , positive feedback , negative feedback , dynamics (music) , mathematics , computer science , chemistry , nonlinear system , cell cycle , engineering , quantum mechanics , cell , combinatorics , computer security , voltage , artificial intelligence , acoustics , biochemistry , control (management) , machine learning , electrical engineering
Extensive experimental evidence has been demonstrated that the dynamics of CDK1‐APC feedback loop play crucial roles in regulating cell cycle processes, but the dynamical mechanisms underlying the regulation of this loop are still not completely understood. Here, the authors systematically investigated the stability and bifurcation criteria for a delayed CDK1‐APC feedback loop. They showed that the maximum reaction rate of CDK1 inactivation by APC can drive sustained oscillations of CDK1 activity ( C D K 1 ∗ ) and APC activity ( A P C ∗ ), and the amplitude of these oscillations is increasing with the increase of the reaction rate over a wide range; a certain range of the self‐activation rate for CDK1 is also significant for generating these oscillations, for too high or too low rates the oscillations cannot be generated. Moreover, they derived the sufficient conditions to determine the stability and Hopf bifurcations, and found that the sum of time delays required for activating CDK1 and APC can induce C D K 1 ∗ and A P C ∗ to be oscillatory, even when the C D K 1 ∗ and A P C ∗ settle in a definite stable steady state. Furthermore, they presented an explicit algorithm for the properties of periodic oscillations. Finally, numerical simulations have been presented to justify the validity of theoretical analysis.