Nonlinear Dose-Response Mechanisms

Institute of Physics and Biophysics

Helmut SchöllnbergerRonald E.J. Mitchel

Nonlinear Dose-Response MechanismsSimulation with Bio-Mathematical Models

2Institute of Physics and Biophysics

Contents

Introduction to the State Vector Model

Detrimental bystander effects for chromosome aberrations

Protective apoptosis-mediated BE for neoplastic transformation

Update on studies with Two-Stage Cancer model


State Vector ModelFor neoplastic transformation

initiationvia chromosome translocation

promotionclonal expansion of I-cellsloss of contact inhibition

DSB repair

cell killing – dose rate dependent


State Vector Model


Detrimental bystander effects

Included in a dose-dependent way – strongesteffect at low doses

New bystander rates:

1)

k01b_by ×

exp(-λ1by ×

D)

2)

k01r_by ×

DR

×

exp(-λ2by ×

D)

3) (1+km_by

×

exp(-λ2by ×

D))

k01b_by = k01r_by = km_by = 0 at D = 0


Data by Nagasawa and Little Mutation Research 2002

CHO and xrs-5 cells, α-particles,

total chromosome aberrations

First, fit model without BE to control and high dose data

Then, fit model with BE to all data


Data by Nagasawa and Littleα-particle irradiation of CHO and xrs-5 cells

Dose (Gy)

0.0 0.4 0.8 1.2 1.6 2.0

Tota

l Chr

omos

ome

Aber

ratio

ns p

er C

ell

0

1

2

3

4


Fit results

Approaches 1) and 3) worked equally well

Approach 2) did not work initiation due to BE ismostly post-exposure (as expected)

To fit xrs-5 data apply reduction factor for DSB repair rates


Bystander-induced apoptosisIs a protective effectDr. Georg Bauer (Anticancer Res 2000)


Bystander-induced apoptosis For low-LET radiation

Protective Apoptosis-Mediated process (PAM), B.R. Scott et al. (2003)

PAM can eliminate cells in State 4


Bystander-induced apoptosis

PAM = 0 at D = 0PAM = 0 during irradiationPAM activated by 1 mGy low-LET radiationPAM activated for various times after irradiationPAM effective at low doses –no effect at D

> 200 mGy


Data by Redpath et al. Radiat. Res. 2001

CGL1 cells, γ-rays, neoplastic transformation

Irradiation period: 3.3 mGy/min for D ≤ 100 mGycell doubling time of 20 hrs

1 day holding period: 20 hrs10 days exponential growth: 20 hrsConfluent growth until day 26: 38 days


Fit approach

TF/SC =

Fit model without PAM to control and high dose data

for immediate and delayed plating simultaneously

Forward simulation without PAM to all data pointsfor immediate plating

Fit model with PAM to all data points for delayedplating 1 free parameter: kap

2 free parameters: kap

and tap_off

)()()()()()()(

432110

4

endendendendnsendsend

end

tNtNtNtNtNtNtN

+++++


Data by Redpath et al. Forward simulation

Immediate plating

Dose (Gy)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Tran

sfor

mat

ion

Freq

uenc

y pe

r Sur

vivi

ng C

ell (

x105 )

0

2

4

6

8

10

0.000 0.005 0.0100

1

2

3

4

5


Data by Redpath et al. Fit with two free parameters

Delayed plating

Dose (Gy)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0Tran

sfor

mat

ion

Freq

uenc

y pe

r Sur

vivi

ng C

ell (

x105 )

0

2

4

6

8

10

0.000 0.005 0.0100

1

2

3


Fit results

kap = 0.024/day How many State 4 cells killedat day 26 after 100 mGy?

Simulation performed starting with 1 cell: N4 (26) - N4 (26;kap

=0) = 9 cells

N0 (26) + N1s (26) +…+ N4 (26) = 8⋅105

tap_off = 22 daysJamali and Trott (1996): two week induction of apoptosis after 1 Gy X-irradiation


Data by Miller et al. Radiat. Res. 1995

200 keV/μm

Dose (Gy)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Tran

sfor

mat

ion

Freq

uenc

y pe

r Sur

vivi

ng C

ell

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

α-particle irradiation (150 keV/μm) of C3H 10T1/2 cells

Dose (Gy)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Tran

sfor

mat

ion

Freq

uenc

y pe

r Sur

vivi

ng C

ell

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025


Conclusions

SVM can describe detrimental and protectivebystander effects

The experimentally proven phenomenon of bystander-induced apoptosis can explain protectiveeffects of low doses of low-LET radiation

SVM can also explain LNT-shaped data sets

Work towards a model than contains all essential mechanisms that work at low doses: inducible repairand radical scavenging, bystander effects …


Four age-independent stochastic rates (μ1, μ2, α, β)

μ1 a function of dose-rate - also included endogenous DNA damage

Two Stage Clonal Expansion Model (TSCE)


Total absorbed dose delivered in 75 years [mGy]

0 100 200 300 400 500 600 700 800 900 1000

Life

time

prob

abili

ty fo

r lun

g ca

ncer

at 7

5 ye

ars

10-5

10-4

10-3

10-2

Lifetime probability for lung cancer Low-LET radiation at low dose rates


Total absorbed dose delivered in 75 years [mGy]

0 200 400 600 800 1000

Life

time

prob

abili

ty fo

r lun

g ca

ncer

at 7

5

10-5

10-4

10-3

10-2

G = F = const. = 1Gmax = Fmax = 1.4Gmax = Fmax = 3Gmax = Fmax = 5

Lifetime probability for lung cancer With repair and scavenger induction


Rossi and Zaider: “Radiogenic lung cancer: the effects of low doses of low LET radiation” REB 1997


Rate of change in the expected number of simple or complex lesions per cell at time t

-∞

birth Δt 75

30

)()( tLDdt

tdLii

radi

endoi

i λ−Σ+Σ=•

Mutation models for high dose rates


)()(

)()(

)(1 tLLG

tLLG

t clclcl

clslsl

sl

sl λϕ

+λϕ

∝μ

ϕi

probability ith type (simple or complex) of lesion is misrepaired

Misrepair probability modifiedwith..

[ ])(11)( tLeLG Δ−−+= γδ

age (yrs)30.000 30.002 30.004

G(L

)

0.0

0.5

1.0

1.5

2.0


[ ])(11)( tLeLG Δ−−+= γδ

Dx = 100 mGy

Δt = 1 day

dose (mGy)

0 50 100 150 200 250 300

L i( t)

- Li( 0

)

0

2

4

6

8

10

12

14

Lsl(t)-Lsl(0)Lcl(t)-Lcl(0)

•

bD = 3 mGy/yr


dose (mGy)

0 50 100 150 200 250 300 350

μ 1

0.0

2.5e-6

5.0e-6

7.5e-6

1.0e-5without repair inductionwith repair induction

age (yrs)

30.000 30.002 30.004

μ 1

0.0

2.5e-6

5.0e-6

7.5e-6

1.0e-5without repair inductionwith repair induction

)()(

)()(

)(1 tLLG

tLLG

t clclcl

clslsl

sl

sl λϕ

+λϕ

∝μ


AcknowledgementsCollaborator: Dr. Robert D. StewartAustrian Science Foundation FWF (project P18055-N02)RISC-RAD project, EC Contract No. FI6R-CT-2003-508842EU Marie Curie Individual Fellowship, EC Contract No. FIGH-CT-2002-50513Marie Curie European Reintegration Grant, EC Contract No. MERG-CT-2004-006610Atomic Energy of Canada LimitedUS Department of Energy, Grant Nos. DE-FG02-03ER63541 and DE-FG02-03ER63665

Nonlinear Dose-Response Mechanisms

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