Dynamics of Posttranslational Modifications of p53

Table 1

The meaning and values of parameters in the systems (1)–(8).

Parameter	Biological meaning	Value
𝑏𝑝	Inactive p53 production rate	3
𝑏sp	p53 saturating phosphorylate rate by ATM/ATR	10*/1
𝑏𝑚	p53-dependent Mdm2 production rate	0.9
𝑏mi	p53-independent Mdm2 production rate	0.2*
𝑏𝑖	Inhibitor Wip1 production rate	0.25*
𝑏𝑠	Signal ATM production rate	10*
𝑏pac	Acetylation speed of p53 under DSB/UV damage	0.1/0.02
𝑏Bax	Saturating production rate of Bax	0.04
𝑎mpi	Mdm2-dependent p53 inactive degradation rate	5*
𝑎pi	Inactive p53 degradation rate	2*
𝑎mpa	Mdm2-dependent active p53 degradation rate	0.35
𝑎sm	Signal-dependent Mdm2 inactivation rate	0.5
𝑎wpa	Wip1-dependent dephosphorylation rate of p53	2.8
𝑎𝑚	Mdm2 degradation rate	1*
𝑎𝑖	Inhibitor Wip1 degradation rate	0.7*
𝑎𝑖𝑠	Wip1-dependent Signal degradation rate	50*
𝑎𝑠	ATM degradation rate	7.5*
𝑎pac	acetylation of p53 degradation rate	0.05
𝑎depac	deacetylation rate of p53	0.05
𝑎Bax	Bax degradation rate	0.04
𝜏1	Time delay of Mdm2 transcription by p53	0.7*
𝜏2	Time delay of Wip1 transcription by p53	1.25*
𝑡𝑎	Concentration of Bax for half maximal p53ac production	0.15
𝑡𝑠	Concentration of ATM for half-maximal p53 production	1*
𝑡𝑖	Concentration of wip1 for half-maximal Signal degradation	0.2*
𝜃0	The threshold of DSBs for acetylating p53	0.1
𝑘rep	Repair rate of DSBs	0.1
𝑛1	Hill coefficients for phosphorylation and dephosphorylate of p53	4
𝑛2	Hill coefficients for dephosphorylation of ATM by wip	2
[p53i]0	The initial condition of inactive p53	1
[p53p]0	The initial condition of phosphorylated p53	0
[Mdm2]0	The initial condition of Mdm2	0.2
[wip1]0	The initial condition of wip1	0
[ATM]0	The initial condition of ATM	0
[p53ac]0	The initial condition of acetylated p53	0
[Bax]0	The initial condition of Bax	0
[DSBs]0	The initial conditions of two type of DSBs	3/0.3**

∗denotes parameters from [2, 6], the others are estimated. **denotes serious/slight DSBs.