Mathematical description of the interactions of CycE/Cdk2, Cdc25A, and P27Kip1 in a core cancer subnetwork

Recent studies have shown that the initiation of human cancer is due to the malfunction of some genes (such as E2F, CycE, CycD, Cdc25A, P27Kip1, and Rb) at the R‐checkpoint during the G1‐to‐S transition of the cell cycle. Identifying and modeling the dynamics of these genes provide new insight into...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-05, Vol.40 (8), p.2961-2979
Main Authors: Bayleyegn, Y. N., Govinder, K. S.
Format: Article
Language:English
Subjects:
Activation
Bifurcations
Cancer
cancer network
Cell cycle
cyclin E
cyclin‐dependent kinases
dynamical system
Genes
limit cycle
Mathematical models
Oscillators
P27Kip1
phosphatase Cdc25A
Robustness (mathematics)
saddle–node
simulations
steady states
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Summary:Recent studies have shown that the initiation of human cancer is due to the malfunction of some genes (such as E2F, CycE, CycD, Cdc25A, P27Kip1, and Rb) at the R‐checkpoint during the G1‐to‐S transition of the cell cycle. Identifying and modeling the dynamics of these genes provide new insight into the initiation and progression of many types of cancers. In this study, a cancer subnetwork that has a mutual activation between phosphatase Cdc25A and the CycE/Cdk2 complex and a mutual inhibition between the Cdk inhibitor P27Kip1 and the CycE/Cdk2 complex is identified. A new mathematical model for the dynamics of this cancer subnetwork is developed. Positive steady states are determined and rigorously analyzed. We have found a condition for the existence of positive steady states from the activation, inhibition, and degradation parameter values of the dynamical system. We also found a robust condition that needs to be satisfied for the steady states to be asymptotically stable. We determine the parameter value(s) under which the system exhibits a saddle–node bifurcation. We also identify the condition for which the system exhibits damped oscillation solutions. We further explore the possibility of Hopf and homoclinic bifurcations from the saddle–focus steady state of the system. Our analytic and numerical results confirm experimental results in the literature, thus validating our model. Copyright © 2016 John Wiley & Sons, Ltd.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4213