Communications in Theoretical Physics ›› 2021, Vol. 73 ›› Issue (3): 035601. doi: 10.1088/1572-9494/abd84c
• Statistical Physics, Soft Matter and Biophysics • Previous Articles Next Articles
Nan Liu(刘楠)(),Hongli Yang(杨红丽)(),Liangui Yang(杨联贵)
Received:
2020-10-09
Revised:
2020-12-03
Accepted:
2020-12-24
Published:
2021-03-01
Contact:
Nan Liu(刘楠)
E-mail:IMULiuNan@163.com;imuyhl@imu.edu.cn
Funding Information:
Nan Liu(刘楠),Hongli Yang(杨红丽),Liangui Yang(杨联贵), Commun. Theor. Phys. 73 (2021) 035601.
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Table 1.
Simulation parameters."
Parameter | Description | Values (units) |
---|---|---|
vatm | ATM activation rate | 1.2 (C min−1) |
datm | ATM maximum inactivation rate | 0.53 ($/\min $) |
vp53 | P53 maximum production rate | 0.95 (C min−1) |
dp53 | P53 maximum degradation rate | 1.2 ($/\min $) |
vmdm2 | Mdm2 maximum production rate | 0.153 (C min−1) |
kp | Mdm2 maximum phosphorylation rate | 0.65 ($/\min $) |
kq | Mdm2 dephosphorylation rate | 0.24 ($/\min $) |
kin | The rate of Mdm2 transfer from the cytoplasm to the nucleus | 0.14 ($/\min $) |
kout | The rate of Mdm2 transfer from the nucleus to the cytoplasm | 0.01 ($/\min $) |
dmdm2 | Mdm2c degradation rate | 0.034 ($/\min $) |
vmir | miR-34 maximum production rate | 0.035 (C min−1) |
dmir | miR-34 degradation rate | 0.05 ($/\min $) |
ρ0 | P53-dependent ATM inactivation proportional constant | 0.9 (\) |
ρ1 | ATM-dependent p53 activation proportional constant | 0.9 (\) |
ρ2 | Mdm2p-dependent p53 production proportional constant | 0.98 (\) |
ρ3 | Mdm2n-dependent p53 degradation proportional constant | 0.97 (\) |
ρ4 | P53-dependent Mdm2 production proportional constant | 0.98 (\) |
ρ5 | ATM-dependent Mdm2 phosphorylation proportional constant | 0.9 (\) |
ρ6 | P53-dependent miR-34 production proportional constant | 0.99 (\) |
k0 | Half-saturated concentration of p53-dependent ATM inactivation | 1 (C) |
k1 | Half-saturated concentration of ATM-dependent p53 activation | 0.3 (C) |
k2 | Half-saturated concentration of Mdm2p-dependent p53 production | 0.057 (C) |
k3 | The maximum half-saturated concentration of Mdm2n-dependent p53 degradation | 0.5 (C) |
k4 | Half-saturated concentration of p53-dependent Mdm2 production | 4.43 (C) |
k5 | Half-saturated concentration of ATM-dependent Mdm2 phosphorylation | 1 (C) |
k6 | Half-saturated concentration of p53-dependent miR-34 production | 0.8 (C) |
α | Proportional constant of miR-34-regulated half-saturated | |
concentration of Mdm2n for p53 degradation | 0.9 (\) | |
κ | Half-saturated concentration of miR-34-regulated half-saturated | |
concentration of Mdm2n for p53 degradation | 1 (C) | |
r0 | Mdm2n and Mdm2c degradation rate ratio | 1.7 (\) |
g0 | Mdm2p and Mdm2c degradation rate ratio | 3.58 (\) |
Figure 5.
(a) Codimension-one bifurcation diagram of [p53] versus the parameter vmir. The red solid and the black solid lines represent stable and unstable equilibria, respectively. The green solid lines and the blue dotted lines are the maxima and minima of stable and unstable limit cycles, respectively. (b) The oscillation period as a function of vmir. The green solid lines and the blue dotted lines are the period of stable and unstable limit cycles, respectively."
Figure 9.
Codimension-one bifurcation diagram of [p53] versus the parameter vatm when vmir = 0.2. Here HC is the homoclinic bifurcation point. The red solid and the black solid lines represent stable and unstable steady-state, respectively. Blue dotted lines are the maxima and minima of unstable limit cycles."
Figure 10.
The scenario of another miR-34 pathway is introduced into the model. Codimension-one bifurcation diagram of [p53] versus the parameter vmir at the given j. Only steady-state branches are presented here. The red solid and the black solid lines represent stable and unstable steady-state, respectively."
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