Cellular responding kinetics based on a model of gene regulatory networks under radiotherapy

doi:10.4236/health.2010.22021

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Vol.2, No.2, 137-146 (2010)

doi:10.4236/health.2010.22021

SciRes

Health

Cellular responding kinetics based on a model of gene

regulatory networks under radiotherapy

Jin-Peng Qi1,3*, Yong-Sheng Ding1,2,3*, Shi-Huang Shao1, Xian-Hui Zeng1, Kuo-Chen Chou1,2

1College of Information Sciences and Technology, Donghua University, Shanghai, China

2Gordon Life Science Institute, San Diego, USA; qipengkai@126.com, ysding@dhu.edu.cn

3Engineering Research Center of Digitized Textile & Fashion Technology, Ministry of Education, Donghua University, Shanghai,

China

Received 16 November 2009; revised 3 December 2009; accepted 8 December 2009.

ABSTRACT

Radiotherapy can cause DNA damage into cells,

triggering the cell cycle arrest and cell apop-

tosis through complicated interactions among

vital genes and their signal pathways. In order to

in-depth study the complicated cellular res-

ponses under such a circumstance, a novel mo-

del for P53 stress response networks is pro-

posed. It can be successfully used to simulate

the dynamic processes of DNA damage trans-

ferring, ATM and ARF activation, regulations of

P53-MDM2 feedback loop, as well as the toxins

degradation. Particularly, it has become feasible

to predict the outcomes of cellular response in

fighting against genome stresses. Consequently,

the new model has provided a reasonable

framework for analyzing the complicated regu-

lations of P53 stress response networks, as well

as investigating the mechanisms of the cellular

self-defense under radiotherapy.

Keywords: P53; MDM2; DNA Damage; IR;

Oscillations; Radiotherapy

1. INTRODUCTION

Like immunotherapy, chemotherapy, and surgery, radio-

therapy is one of the major tools in fighting against cancer.

As acute IR is applied, cell can trigger its self-defensive

mechanisms in response to genome stresses [1]. As one of

the pivotal anticancer genes within the cell, P53 can

control the transcription and translation of series genes,

and trigger cell cycle arrest and apoptosis through inter-

action with downstream genes and their complicated

signal pathways [2]. Under radiotherapy, the outcomes of

cellular response depend on the presence of functional

P53 proteins to induce tumor regression through apop-

totic pathways [3]. Conversely, the P53 tumor suppressor

is the most commonly known specific target of mutation

in tumorigenesis [4]. Abnormalities in the P53 have been

identified in over 60% of human cancers and the status of

P53 within tumor cells has been proposed to be one of the

determinant response to anticancer therapies [3,4]. Con-

trolled radiotherapy studies show the existence of a strong

biologic basis for considering P53 status as a radiation

predictor [3,5]. Therefore, the status of P53 in tumor cell

can be considered as a predictor for long-term bio-

chemical control during and after radiotherapy [6-8].

Recently, several models have been proposed to ex-

plain the damped oscillations of P53 in cell populations

[9-12]. However, the dynamic mechanism of the sin-

gle-cell responses is not completely clear yet, and the

complicated regulations among genes and their signal

pathways need to be further addressed, particularly under

the condition of acute IR.

Many studies have indicated that introducing novel

mathematical and computational approaches can stimu-

late in-depth investigation into various complicated bio-

logical systems (see, e.g., [13-23]). These methods have

provided useful tools for both basic research and drug

development [24-33], helping understanding many mar-

velous action mechanisms in various biomacromolecular

systems (see, e.g., [21, 34-39]).

Based on the existing models [9-12] and inspired by

the aforementioned mathematical and computational

approaches in studying biological systems, here a new

model is proposed for studying the P53 stress response

networks under radiotherapy at the cellular level, along

with the kinetics of DNA double-strand breaks (DSBs)

generation and repair, ATM and ARF activation, as well

as the regulating oscillations of P53-MDM2 feedback

loop (MDM2 is an important negative regulator of the

p53 tumor suppressor). Furthermore, the kinetics of the

oncogenes degradation, as well as the eliminations of the

mutation of P53 (mP53) and the toxins were presented.

Also, the plausible outcomes of cellular response were

J. P. Qi et al. / HEALTH 2 (2010) 137-146

138

Openly accessible at

DSBs generation

and repair

ATM activation

P53-MDM2

feedback loop

Oncogenes

over-expression ARF activation

Depression of abnormal

genes and cellular toxins

Figure 1. Illustration showing the integrated model of P53 stress response networks under ra-

diotherapy. It is composed of three modules, including DNA damage generation and repair, ATM

and ARF activation, as well as P53-MDM2 feedback loop. As acute IR is applied, ARF is acti-

vated by the over-expression of oncogenes, and ATM is activated with the cooperation of DSBCs

and ARF*. ATM* and ARF* corporately trigger the responding mechanism of P53-MDM2

feedback loop.

dc1

dc2

cf2

fw1

fw2

cd1

cd2

DSBs Fixed

DSBCs k

cf1

IR dose

DSBC transferring to

downstream

enes

Figure 2. Illustration showing the module of DNA repair process. It includes both a fast repair

pathway and a slow one. DSB can be in one of four states: intact DSB (DSB), DBSC, Fr and Fw.

Subscripts ‘1’ and ‘2’ refer to the fast kinetics and slow one.

analyzed under different IR dose domains.

It is instructive to mention that using differential

equations and graphic approaches to study various dy-

namical and kinetic processes of biological systems can

provide useful insights, as indicated by many previous

studies on a series of important biological topics, such as

enzyme-catalyzed reactions [18,40], low-frequency in-

ternal motions of biomacromolecules [41-46], protein

folding kinetics [47,48], analysis of codon usage [49,50],

base distribution in the anti-sense strands [51], hepatitis B

viral infections [52], HBV virus gene missense mutation

[53], GPCR type prediction [54], protein subcellular

location prediction [55], and visual analysis of SARS-

CoV [7,56].

2. METHODS

2.1. Model Review

Under the genome stresses, many efforts have been made

to enhance P53-mediated transcription through some

models [9-12,58,59]. However, the interactions in a real

system would make these models [60] extremely com-

plicated. Therefore, a new feasible model is needed in

order to incorporate more biochemical information. To

realize this, let us take the following criteria or assump-

tions for the new model: 1) only the vital components and

interactions are taken into account; 2) all the localization

issues are ignored; 3) the simple linear relations are used

to describe the interactions among the components con-

cerned; and 4) there are enough substances to keep the

system ‘‘workable’’ [58].

The new integrated model thus established for the P53

stress response networks under radiotherapy is illustrated

in Figure 1. Compared with the previous models [9-12],

the current model contains more vital components, such

as oncogenes, ARF and mP53, as well as their related

regulating pathways. In the DSBs generation and repair

module, the acute IR induces DSBs stochastically and

forms DSB-protein complexes (DSBCs) at each of the

J. P. Qi et al. / HEALTH 2 (2010) 137-146

139

damage sites after interacting with the DNA repair pro-

teins [2,3]. As a sensor of genome stress, ATM is acti-

vated by the DSBCs signal transferred from DSBs.

Meanwhile, the over-expression of oncogenes prompted

by acute IR can trigger the activation of ARF, further

prompting the ATM activation [2,7]. The cooperating

effects of active ATM (ATM*) and active ARF (ARF*)

switch on or off the P53-MDM2 feedback loop [2,7,9],

further regulating the downstream genes to control the

cell-cycle arrest and the cell apoptosis in response to

genome stresses [8]. Here, we use the superscript * to

represent the activate state as done in [61].

2.2. DSBs Generation and Repair

Under the continuous effect of acute IR dose, DSBs occur

and trigger two major repair mechanisms in eukaryotic

cells: homologous recombination (HR) and nonhomolo-

gous end joining (NHEJ) [62,63]. About 60-80% of DSBs

are rejoined quickly, whereas the remaining 20-40% of

DSBs are rejoined more slowly [64,65]. As shown in

Figure 2, the module of DSBs generation and repair

process contains both the fast and slow kinetics, with each

being composed of a reversible binding of repair proteins

and DSB lesions into DSBCs, and an irreversible process

from the DSBCs to the fixed DSBs [62,65]. DSBCs are

synthesized by binding the resulting DSBs with repair

proteins (RP), which is the main signal source to transfer

the DNA damage to P53-MDM2 feedback loop by ATM

activation [2].

Due to the misrepair part of DSBs (Fw) having the

profound consequences on the subsequent cellular vi-

ability and the cellular response in fighting against ge-

nome stresses [1,3], we obviously distinguish between

correct repair part of DSBs (Fr) and Fw [9,10,12].

Moreover, we further deal the total Fw in both repair

processes as a part of toxins within the cell [2,4,11],

which can be eliminated by the regulatory functions of

P53 during and after radiotherapy, and treated as an in-

dicator of outcomes in cellular response to genome

stresses [2].

Some experimental data suggest that the quantity of the

resulting DSBs within different IR dose domains obey a

Poisson distribution [11]. In accordance with the ex-

periments, we assume that the stochastic number of the

resulting DSBs per time scale is proportional to the

number generated by a Poisson random function during

the period of acute radiation [11]. The DSBs generation

process is formulated as follows:

[DT] Poissrnd( IR)

tir

dka

 

(1)

where [DT] is the concentration of total resulting DSBs

induced by IR in both fast and slow repair processes. kt is

the parameter to set the number of DSBs per time scale,

and air is the parameter to set the number of DSBs per IR

dose.

Moreover, we assume that the limited repair proteins

are available around DSBs sites, and 70% of the initial

DSBs are fixed by the fast repair process. Each DSB can

be in one of the four states: intact DSB, DSBC, Fr and Fw

[9,10,12]. Thus, we have the following differential equa-

tions:

[D ][D ][C ]

tcd

dak



dc1 1cross12

[RP]([D ]([D ][D]))kk





(2)

2t cd22

[D ][D ][C]

dak



dc2 2cross12

[RP]([D ]([D][D])kk





(3)

dc11 cd11 cf11

[C ][D ][C ][C ]

dkkk



(4)

dc2 2cd22cf22

[] [D ][C ][C ]

dC kkk



(5)

pcd1 1cd22

[RP] [C ][C]

dSk k

 

dc1 1dc22cross12

[RP]([D][D]([D ][D]))kk k



 

(6)

w1 1fw22

[F ][C ][C]

dkk



(7)

where [D], [C], and [Fw] represent the concentrations of

DSBs, DSBCs, and Fw in the fast and the slow repair

kinetics respectively, kdc, kcd, kcf, and kfw are the tran-

sition rates among the above three states; kdc, and kcross

represent the first-order and second-order rate constants in

both the fast and the slow repair kinetics respectively [65].

Srp is the basal induction rate of repair mRNA, and sub-

scripts ‘1’ and ‘2’ refer to the fast and the slow kinetics.

2.3. ATM and ARF Activation

As a DNA damage detector, ATM exists as a dimer in

unstressed cells. After IR is applied, intermolecular

autophosphorylation occurs, causing the dimer to disso-

ciate rapidly into the active monomers. The active ATM

monomer (ATM*) can prompt the P53 expression further

[64]. Meanwhile, ARF, another tumor suppressor, is ac-

tivated by hyperproliferative signals emanating from

oncogenes, such as Ras, c-myc etc., further prompting the

ATM activation [2, 7, 10]. Based on the existing model of

ATM switch [11], we present an ATM and ARF activation

module under IR. Shown in Figure 3 is the module

scheme of ATM and ARF activation, which includes five

components: ATM dimer, inactive ATM monomer, ATM*,

ARF, and ARF*. Compared with the previous studies in

J. P. Qi et al. / HEALTH 2 (2010) 137-146

140

Openly accessible at

AT M

undim

(

DSBCs

)

ARF ARF

Oncogenes over-expression

onf

(

C, [ARF*], [ATM*]

)

dim

Figure 3. Illustration showing the module scheme of ATM and ARF activation under

constant IR. ARF is activated by the over-expression of oncogenes induced by acute

IR, and ATM is activated from ATM monomers under the cooperating effects of

DSBCs, ARF*, and self-feedback of ATM*.

[9-12], ARF, oncogenes, and the related signal pathways

are involved in this module [2,7]. Here, let us assume that

DSBCs is the main signal transduction from DSBs to

P53-MDM2 feedback loop through ATM activation, and

the rate of ATM activation is a function of the amount of

DSBCs, ARF* and the self-feedback of ATM*. Fur-

thermore, the total concentration of ATM is a constant,

including ATM dimer, ATM monomer and ATM, as

treated in {Ma, 2005 #1194].

As a detector of DNA damage, ATM activation plays

an important role in triggering the regulatory mechanisms

of P53 stress response networks [2,65]. After the acute IR

is applied, phosphorylation of inactive ATM monomers is

promoted first by DSBCs and then rapidly by means of

the positive feedback from ATM*, accounting for the

intermolecular autophosphorylation [11]. Meanwhile,

under the circumstance of continuous IR dose, ARF, a

detector of over-expression of oncogenes is activated by

hyperproliferative signals emanating from oncogenes,

further prompting the ATM activation [2,7,10], as can be

formulated as follows:

dim mdim d

[ATM ]1[ATM][ATM ]

2un

dkk



(8)

undimd dimm

[ATM ]2[ATM] [ATM

dkk

]

afmar

[ATM ][ATM*]kf k

(9)

af m

[ATM*] [ATM ][ATM*]

dkf k



(10)

arf adonf

[ARF] [ARF] [Onco][ARF]

dSk k

 

(11)

onf pad

[ARF*] [Onco][ARF] [ARF*]

dkk



(12)

12 3

(, [ATM*])[ATM*][ATM*]fCaC aaC





*][

4ARFa



(13)

where [ATMd], [ATM] and [ATM*] represent the concen-

trations of ATM dimer, ATM monomer, and active ATM

monomer respectively; [Onco], [ARF] and [ARF*] repre-

sent the concentrations of oncogenes, ARF, and active

ARF respectively; kundim, kdim, kar, and kaf are the rates

of ATM undimerization, ATM dimerization, ATM

monomer inactivation, and ATM monomer activation,

respectively. Sarf, konf, kad and kpad are the rates of ARF

basal induction, ARF activation triggered by Oncogenes,

ARF degradation, and ARF* degradation, respetively. In

addition, f is the function of ATM activation, the term a1C

implies the fact that DSBs somehow activate ATM mole-

cules at a distance, a2 [ATM*] indicates the mechanism of

autophosphorylation of ATM, a3C [ATM*] represents the

interaction between the DSBCs and ATM* [9-12,66], and

a4 [ARF*] represents the regulating function of ARF* to

ATM activation [1,3,7].

2.4. Regulation of P53-MDM2 Feedback Loop

As shown in Figure 4, P53 and its principal antagonist,

MDM2 transactivated by P53, form a P53-MDM2 feed-

back loop, which is the core part in the integrated networks

[9-12]. ATM* elevates the transcriptional activity of P53

by prompting phosphorylation of P53 and degradation of

MDM2 protein [67]. Also, ARF* can indirectly prompt the

transcriptional activity of P53 by inhibiting the expression

of MDM2 and preventing P53 degradation [2,7,9]. With

the cooperating regulations of ATM* and ARF*, this

negative feedback loop can produce oscillations in re-

sponse to the sufficiently strong IR dose [11].

Especially, the mutation of P53 (mP53) triggered by

oncogenes is added in this module, and mP53 is further

dealt as another detector of outcomes in cellular response

J. P. Qi et al. / HEALTH 2 (2010) 137-146

141

Openly accessible at

Onco

P53

mP53

MDM2

Toxin

ATM

ARF

P53

MDM2

Figure 4. The directed graph of P53-MDM2 feedback loop under radiotherapy. P53 is translated from

P53mRNA and phosphorylated by ATM* and ARF*. MDM2 protein promotes a fast degradation of

P53 protein and a slow degradation of P53*. In addition, ATM*and ARF* stimulate the degradation of

MDM2, and then indirectly increase the regulatory activation of P53* further. Especially, oncogenes,

toxins and mP53 are decreased directly by the regulatory functions of P53*.

to acute IR. To account for a decreased binding affinity

between inactive P53 and P53*, we assume that

MDM2-induced degradation of inactive P53 is faster than

that of P53*, and only P53* can induce target genes to

depress the over-expression of oncogenes and further

eliminate the toxins within the cell [3,4,9-12]. The main

differential equations used in this module are as follows:

P53rp Rrp R

[P53 ][P53 ][P53 ]

dSdk

 

(14)

rp Rp*ppp P

[P53 ][P53][P53*][P53 ]

dkk d

 

app*mp P

Pp Pd

[P53 ][P53 ]

[ATM*][MDM2 ]

[P53 ]+[P53 ]+



(15)

app*p*p pp*

[P53]

[P53*] [ATM*][P53*] [P53*]

[P53]+

dkk

dt k

d

p*ppp*mp* P

[P53*]

[P53*][P53*][MDM2][P53*]+

kdk k

 

(16)

mdm2 p*mnn

[MDM2 ][P53*]

+[P53*] +

dSk

dt k



mrpR mrR

[MDM2 ][MDM2]kd

(17)

mrp Rmp P

[MDM2 ][MDM2][MDM2 ]

dkd



mat marP

at ar

[ATM*] [ARF*]

(

[ATM*]+ [ARF*]+

)[MDM2]

(18)

onIR onp

[Onco] [Onco][IR] [Onco][P53*]

dkk



(19)

tfw wpt

[Toxin ][F][P53*][Toxins]



(20)

mp Rpmd P*

[mP53] [P53 ][Onco][P53][mP53]

dkk



(21)

where [P53R], [P53P], [P53*], [MDM2R], and [MDM2P]

represent the concentrations of P53 mRNA, P53 protein,

active P53, MDM2 mRNA, and MDM2 protein, respec-

tively; [Onco], [Toxins], and [mP53] represent the con-

centrations of oncogenes, Fw and mP53, respectively.

SP53, and SMDM2 represent the basal induction rates of

P53 mRNA and MDM2 mRNA, respectively; k, and d

represent the regulation and degradation rates among

genes and proteins, respectively. The other parameters are

presented in Tables 1-3.

3. RESULTS AND DISCUSSIONS

3.1. Kinetics of DSBCs Synthesizing

During the simulation process, the continuous 2, 5, and

7Gy IR are applied into a cell respectively. As shown in

Figure 5(a), owing to the condition that many DSBs

occur and the limited RP are available around damage

sites, the concentration of RP begins to decrease as IR

dose overtakes 5Gy, and trends to zero versus radiation

time. Meanwhile, the kinetics of DSBCs synthe sizing is

shown in Figure 5(b). We can see that the rates of DSBCs

synthesis keep increasing under 2, and 5Gy IR, whereas,

it begins to decrease and trend to constant after about

120min under 7Gy IR dose.

3.2. Kinetics of ARF and ATM Activation

The ARF activation is used to describe the mechanisms in

cellular response to the over-expression of oncogenes

J. P. Qi et al. / HEALTH 2 (2010) 137-146

142

Openly accessible at

020406080100120140160180200

the dynamic traces of RP avaliable around DSBs under 2,5,7Gy, respectively

(a) Radiation Time(Min)

Concentration

under IR=2Gy

under IR=5Gy

under IR=7Gy

(a)

050 100 150 200 250 300

the kinetics of DSBCs synthesizing under 2,5,7Gy IR, respectively

(b) Radiation Time(Min)

Concentration

under IR=2Gy

under IR=5Gy

under IR=7Gy

Under 7Gy IR, the rate of DSBCs

synthesizing begin to decrease

after this plausible time threshold

(b)

Figure 5. The kinetics of DSBs repairing and transferring under

continuous effect of 2, 5, 7Gy IR. (a) The dynamics of RP

available around the resulting DSBs under different IR dose

domains. (b) The kinetics of DSBCs synthesized by DSBs and

RP versus continuous radiation time under different IR dose

domains.

induced by acute IR [2,7]. The kinetics of ARF activation

is shown in Figure 6(a). Owing to the over-expression of

oncogenes without depressing functions of P53*, ARF is

activated fast and ARF* keeps increasing followed by

trending to dynamic equilibrium versus radiation time.

Meanwhile, the ATM activation module was estab-

lished to describe the switch-like dynamics of the ATM

activation in response to DSBCs increasing, and the

regulation mechanisms during the process of the ATM

transferring DNA damage signals to the P53-MDM2

feedback loop. Under the cooperative function of DSBCs,

ARF*, and the positive self-feedback of ATM*, the ATM

would reach the equilibrium state within minutes due to

the fast phosphorylation [2,11,67]. Kinetics of ATM ac-

tivation is shown in Figure 6(b). ATM is activated rap-

idly and switches to “on” state with respective rates, and

then trends to the saturation state. The step- like traces

suggest that the ATM module can produce an on-off

switching signal, and transfer the damage signal to the

P53-MDM2 feedback loop [3]. Furthermore, under the

cooperation effects of ATM* and ARF*, DNA damage

0100 200300 400 500 600 700800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

the kinetics of ARF activation under different IR dose domains

(a) Radiation Time(Min)

Concentration

under IR=2Gy

under IR=5Gy

under IR=7Gy

(a)

0100 200300 400 500 600 700 800

0.2

0.4

0.6

0.8

Concent ration

(b) Radiation Time(Min)

the kinetics of ATM activation under different IR dose domains

under IR=2Gy

under IR=5Gy

under IR=7Gy

the rate of ATM activation begin to decrease

after this plausible time threshold under 7Gy IR

(b)

Figure 6. The kinetics of ARF and ATM activation under 2, 5,

7Gy IR. (a) The kinetics of ARF activation in response to

over-expression of oncogenes induced by different IR dose. (b)

The switch-like kinetics of ATM activation, ATM* reach satu-

ration and trend to constant state in response to continuous

radiation time of different IR dose domains.

signals can be further transferred to the downstream

genes and their signal pathways more efficiently [2,7].

3.3. Outcomes of Cellular Responding

Radiotherapy

The P53-MDM2 feedback loop is a vital part in control-

ling the downstream genes and regulation pathways to-

fight against the genome stresses [6,67,68]. In response to

the input signal of ATM* and ARF*, the P53-MDM2

module generates one or more oscillations. The response

traces of P53 and MDM2 protein under continuous appli-

cation of 2, 5, and 7Gy IR from time 0 are shown in Figure

7(a). Upon the activation by ATM*, ARF* and decreased

degradation by MDM2, the total amount of P53 proteins

increases quickly. Due to the P53-dependent induction of

MDM2 transcription, the increase of MDM2 proteins is

sufficiently large to lower the P53 level, which in turn

reduces the amount of the MDM2 proteins.

J. P. Qi et al. / HEALTH 2 (2010) 137-146

143

The oscillation pulses shown in Figure 7(a) have a pe-

riod of 400 min, and the phase difference between P53

and MDM2 is about 100 min. Moreover, the first pulse is

slightly higher than the second, quite consistent with the

experimental observations [2,7,11] as well as the previous

simulation results [9,10,12,69].

Also, by comparing these simulation results, we can

see that the strength and swing of these oscillations begin

to decrease as IR overtakes 7Gy, suggesting that the

ability of cellular responding genome stresses begin to

0100 200300 400 500 600 700800

0.5

1.5

2.5

3.5

4.5

the kinetics of Fw elimination with the regulating functions of P53* under different IR

(b) Radiation Time(Min)

Concentration

Fw under IR=2Gy

Fw under IR=5Gy

Fw under IR=7Gy

(a)

0100 200 300 400 500600 700 800

0. 1

0. 2

0. 3

0. 4

0. 5

0. 6

0. 7

0. 8

0. 9

the oscillating kinetics of P53* and MDM2 in response to different IR dose domains

(a) Radiation Time(Min)

Conce ntratio n

P53* under IR=2Gy

P53* under IR=5Gy

P53* under IR=7Gy

MDM2 under IR=2Gy

MDM2 under IR=5Gy

MDM2 under IR=7Gy

(b)

0100 200 300 400 500600 700 800

0.1 5

0.1 6

0.1 7

0.1 8

0.1 9

0.2

0.2 1

0.2 2

0.2 3

0.2 4

0.2 5

the kinetics of Oncogenes depressed by the functions of P53* in response to different IR

Concentration

Onco under IR=2Gy

Onco under IR=5Gy

Onco under IR=7Gy

(c)

0100 200 300 400 500 600 700 800

0.48

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

the kinetics of mP53 degradated by P53* under different IR dose domains

(d) Radiation Time(Min)

Concentration

mP53 under IR=2Gy

mP53 under IR=5Gy

mP53 under IR=7Gy

(d)

Figure 7. The outcomes of cellular responding 2, 5, 7Gy IR

under radiotherapy. (a) The oscillating kinetics of P53* and

MDM2 in response to the cooperative effect of ATM* and

ARF* under different IR dose domains; (b) The kinetics of

toxins elimination triggered by the functions of P53*; (c) The

depressing dynamics of oncogenes over-expression with the

regulations of P53*; (d) The kinetics of mP53 elimination

triggered by the effect of P53*.

decrease as IR dose exceeds a certain threshold.

Furthermore, because in the current model the toxins,

mP53 and oncogenes can be degraded directly by P53* in

this module, we can plot the predictable outcomes of

cellular response in fighting against genome stresses

under different IR dose domains. As shown in Figure

7(b), Fw remaining within the cell keeps decreasing with

respective rate, and trends to zero versus continuous

radiation time under 2 and 5Gy IR. Whereas, when IR

exceeds 7Gy, Fw begins to increase slightly with some

oscillations. Also, the kinetics of oncogenes degrading is

plotted in Figure 7(c). As we can see, owing to the nega-

tive regulations of P53*, the expression level of onco-

genes keeps decreasing after the first climate under 2 and

5Gy IR dose, and then begins to increase slowly under

7Gy IR dose. Meanwhile, as shown in Figure 7(d), quite

similar to the results in Figure 7(b) and Figure 7(c),

mP53 keeps decrease after reaching the first maximum

under 2 and 5Gy IR dose, and then begins to increase

slowly under 7Gy IR dose. All these results obtained by

the above simulations based on the new model indicate

that that P53* indeed acts an important role in regulating

downstream genes and their signal pathways, whereas its

capabilities in cellular responding DNA damage under

radiotherapy begin to decrease as the strength of IR ex-

ceeds a certain maximal threshold.

4. CONCLUSIONS

A new model was proposed to simulate the P53 stress

response network under radiotherapy. It is demonstrated

according to our model that ATM and ARF exhibits a

strong sensitivity and switch-like behavior in response to

J. P. Qi et al. / HEALTH 2 (2010) 137-146

144

Openly accessible at

the number of DSBs, fully consistent with the experi-

mental observations. Interestingly, it is shown in this

study that after the DNA damage signals transferring,

P53-MDM2 feedback loop will produce oscillations, then

triggering the cellular self-defense mechanisms to de-

grade the toxins remaining within the cell, such as Fw,

oncogenes, and mP53. Particularly, under different IR

dose domains, the new model can reasonably predict

outcomes of cellular response in fighting against genome

stresses, and hence providing a framework for analyzing

the complicated regulations of P53 stress response net-

works, as well as the mechanisms of the cellular self-

defense under radiotherapy.

5. ACKNOWLEDGMENT

The current work was supported in part by Specialized Research Fund

for Natural Science Foundation of Shanghai (No.10ZR1401600), the

Doctoral Program of Higher Education from Ministry of Education of

China (No.20060255006), Project of the Shanghai Committee of Sci-

ence and Technology (No. 08JC1400100), and the Open Fund from the

Key Laboratory of MICCAI of Shanghai (06dz22103).

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