Can we predict radiation carcinogenesis from first principles?

School of Health Scienceshttp://healthsciences.purdue.eduPurdue

Rob Stewart, Ph.D.Rob Stewart, Ph.D.School of Health SciencesPurdue University550 Stadium Mall DriveWest Lafayette, IN 47907-2051

April 11, 2003

Can we predict radiation carcinogenesis from first principles?

School of Health Scienceshttp://healthsciences.purdue.edu

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Nature of “The Beast”Nature of “The Beast”

Dosimetry

50 keV e- in H2O

In many situations, cells and tissues are exposed to temporally and spatially complex radiation fields


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Radiation field depends on particle Radiation field depends on particle energy energy

1 MeV e- in water

5,000 m

5 MeV e- in water

25,000 m


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… … the type of radiationthe type of radiation

250 keV e+ in water250 keV e- in water

500 m 500 m


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… … and the initial direction(s) of and the initial direction(s) of flightflight

1 MeV photons in water

500,000 m(50 cm)

10 MeV photons in water

500,000 m(50 cm)


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““Dose” is only the first stepDose” is only the first step

Dosimetry

50 keV e- in H2O

Cancer develops through physical, chemical, biochemical and microevolutionary processes that happen over hours, days, months and even years.


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G

C G

CA

T

A

T

T

A

The InfamousThe Infamous

Double Strand Break (DSB) Double Strand Break (DSB)

Pose a major threat to integrity of the genome Created by

• Certain chemotherapeutic drugs (e.g., bleomycine)• “Spontaneously” as a by-productive of cellular processes

Oxidative metabolism Replication fork encounters a single-strand break

• Ionizing radiation (including of course cosmic rays, dental x-rays, radon, 40K, etc.)

Complementary base pairs encode genetic information and provide opportunities for error-free repair.

Guanine (G) Cytosine (C)

Adenine (A) Thymine (T)

Double strand break (DSB)


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Are all DSBs lethal?Are all DSBs lethal?

(0 | ) exp{ }S p n n

( )( | ) exp{ }

!

nnp n n n

n

Some cells survive because they do not sustain critical DNA damage (i.e., a DSB).

DSBs are distributed among identically irradiated cells ~ according to a Poisson distribution

dsbn D

45 Gy h-1

0.5 Gy h-1

0.12 Gy h-1

CHO cells


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Most DSBs are rejoined and non-Most DSBs are rejoined and non-lethallethal

Radiation creates ~ 25-40 DSB Gy-1 cell-1.

Less than 4% of the initial DSBs are lethal.

( ) exp{ }dsbS D D

-1 -10.075 DSB Gy celldsb

-1 -11 DSB Gy celldsb


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Double Strand Break

How are DSBs rejoined?How are DSBs rejoined?

Homologous recombination (HR)• Gene conversion• Single-strand annealing

Non-homologous end joining (NHEJ)


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Homologous DNAHomologous DNA

T G G G C A G A

A C C C G T C T

G A A T C A G C

C T T A G T C G

G A A T C A G C A

C T T A G T C G T

T G G G C A G A

A C C C G T C T

same sequence of base pairs

A T G A C C

T A C T G G

?

Sister chromatid Homologous chromosome Repetitive DNA sequences


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Homologous Recombination (HR)Homologous Recombination (HR)

Double Strand Break

Gene Conversion(no cross over)

Gene Conversion(with cross over)

Resolution

DNA synthesis

resection of 5' end

unwinding of helix/strand invasion

Branch migration/resolutionof Holiday junctions

Requires extensive regions of homology• Allelic recombination

Sister chromatid Homologous chromosome

• Ectopic recombination Other regions of genome with

sequence homology

Holiday junction resolution is not random• Gene conversion without cross

over more frequent than gene conversion with cross over.

Adapted from M. van den Bosch, P.H.M Lohman, and A. Pastink, DNA Double-Strand Break Repair by Homologous Recombination, Biol. Chem. 383, 873-892 (2002)

HR has the potential to rejoin DSBs with no loss in genetic information (error-free repair)


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Non-Homologous End Joining Non-Homologous End Joining (NHEJ)(NHEJ)

Adapted from F. Daboussi, A. Dumay, F. Delacote, and B.S. Lopez, DNA double-strand break repair signaling: The case of RAD51 post-translational regulation, Cellular Signaling 14, 969-975 (2002)

NHEJ is an error prone DSB restitution pathway

DSB is recognized by DNA protein kinase (DNA-PK)• KU80/KU70 heterodimer• Catalytic sub-unit DNA-PKcs

Ligase IV and XRCC4 co-factor promote ligation of the DNA break ends

Double Strand Break correct repair

base pair deletion or insertion

XRCC4 andLigase IV

DNA protein kinase(DNA-PKcs)

KU80/KU70 heterodimer

or


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DSB repair in mammalian cellsDSB repair in mammalian cells

HR is potentially error-free. But inappropriate HR can lead to large DNA rearrangements (chromosome aberrations).• Impaired or increased HR has been associated with a predisposition

towards cancer NHEJ is highly mutagenic but consequences are usually less

severe. NHEJ predominates in G0 (quiescent cells) and in G1/early S

phase cells. HR is important in late S/G2 phase.• DSB repair is not the same in quiescent and actively dividing cells.• DSB repair is a function of cell cycle phase.

HR and NHEJ are regulated through a complex set of signaling pathways.• Overall rate and fidelity of DSB repair can be disrupted in many

different ways.


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DNA organized into a chromatin fiber

Track

Local damage complexityLocal damage complexity

Simple double strand break

XXX

Complex double strand break

x

xTrack


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DSB repair may be affected by damage DSB repair may be affected by damage complexitycomplexity

Double Strand Break(complex)

Gene Conversion(no cross over)

Gene Conversion(with cross over)

Resolution

DNA synthesis

resection of 5' end

unwinding of helix/strand invasion

Branch migration/resolutionof Holiday junctions

xxxx

x

xx

xx

xx

xx

xx

Not difficult to imagine that collateral damage near the site of two opposing strand breaks could impair• Resection of damaged break

ends• DNA synthesis• Branch migration and

Holiday junction formation Disruptions in HR would

likely depend on the spatial configuration and types of nearby damage sites.


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Pairwise damage interactionPairwise damage interaction

Free break ends diffuseabout the nucleus

and may encounterother free break ends

mis-rejoinedbreak ends


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Proximity effectsProximity effects

x x

x

Regional Multiply Damaged Sites

Track

One radiation track can create multiple DSB.

Some DSBs may be in close spatial proximity.

Break ends in close temporal and spatial proximity are more likely to interact than ones separated in time or space.• Frequency of pairwise damage

interaction increases with increasing particle LET.


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Repair-misrepair (RMR) modelRepair-misrepair (RMR) model

( )(1 ) ( ) ( ) ( )

dF ta L t L t L t

dt

( )( ) ( ) ( ) ( )dsb

dL tD t L t L t L t

dt

( )(1 )(1 ) ( ) (1 ) ( ) ( )

dM ta L t L t L t

dt

DSBs are created and rejoined

Repair processes convert fraction (1-a) of the initial DSBs to lethal or non-lethal mutations

Non-lethal

Lethal

C.A. Tobias, The repair-misrepair model in radiobiology: comparison to other models. Radiat. Res. Suppl. 8:S77-S95 (1985).

pairwise damage interactionGy h-1 at time t


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Surviving fractionSurviving fraction

S(t) is the fraction of cells free of lethal damage at time t. Lethal damage created during a short time interval dt, whose average is dF/dt, are randomly distributed among cells without regard for which cells already have lethal damage.

For a review, see R.K. Sachs, P. Hahnfeld, and D.J. Brenner, Review: The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. Int. J. Radiat. Biol. 72(4) 351-374 (1997).

( )( ) / ( )

dS tdF t dt S t

dt

( ) exp ( )S t F t Surviving fraction at time t

(0) 1S


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Virtual Cell (VC) SoftwareVirtual Cell (VC) Software Simulates the repair and

misrepair of DNA damage• LPL model (Curtis 1986)• RMR model (Tobias (1985)• TLK model (Stewart 2001)

Predicts endpoints such as• Expected number of DSB as a

function of time• Fraction of cells that survive

irradiation• Fraction of cells that acquire

genetic instability and become unstable (transformed)

• Tumor control probability after radiation therapy

• Expected time of tumor reoccurrence after radiation therapy

45 Gy h-1

0.5 Gy h-1

0.12 Gy h-1

CHO cells


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Split-dose ExperimentSplit-dose Experiment

Time (h)

Dos

e ra

te (

Gy

h-1)

4 hour

Time (h)

0 10 20 30 40 50

Let

hal m

utat

ions

(ce

ll-1

)

0.0

0.5

1.0

1.5

2.0

2.5

S = 0.12

RMR parameters for CHO cells


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External beam radiation therapyExternal beam radiation therapy

Time (h)

0 200 400 600 800 1000

Exp

ecte

d nu

mbe

r of

DS

B (

cell

-1)

0

10

20

30

40

50

60

Time (h)

0 200 400 600 800 1000

Let

hal m

utat

ions

(ce

ll-1

)0

1

2

3

4

5

6


S = 5.4×10-3

A 60 Gy radiation treatment (2 Gy × 30) delivered over 6 weeks (M-F skipping weekends). The 2 Gy daily doses are delivered at 6 Gy h-1 (= 2 Gy/20 minutes).

SF2 = 0.849

S (SF2)30 = 7.27 × 10-3


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BrachytherapyBrachytherapy

Time (h)

100 101 102 103 104

Exp

ecte

d nu

mbe

r of

DS

B (

cell

-1)

0

2

4

6

8

10

12

14

16

18

Time (h)

100 101 102 103 104

Let

hal m

utat

ions

(ce

ll-1

)0

2

4

6

8

10

S = 3.9×10-4

A 125I seed that delivers 150 Gy in 1.1 years. Dose rate decreases exponentially with a half-life of 1,443 h (peak dose rate = 72.4 mGy h-1).



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Combined radiation treatmentsCombined radiation treatments

Time (h)

100 101 102 103 104

Exp

ecte

d nu

mbe

r of

DS

B (

cell

-1)

0

10

20

30

40

50

60

70

Time (h)

100 101 102 103 104

Let

hal m

utat

ions

(ce

ll-1

)0

2

4

6

8

10

12

14

Hypothetical combined external beam and brachytherapy radiation treatment (160 Gy total delivered dose).


Scombined = 7.4×10-6

Sebrt(60 Gy) = 5.4×10-3

Sbrachy(100 Gy) = 8.9×10-3

Sebrt × Sbrachy= 4.8×10-5


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RMR and LQ survival models are relatedRMR and LQ survival models are related

The widely used linear-quadratic (LQ) survival model may be written as

2( ) exp GS D D D

2

2( ) ( )exp ( )

t

dt D t d D tD

G t t t

2( ) exp ( ) expS D DGF

Equating S(D) and S() gives

2( )F D GD

See M. Guerrero, R.D. Stewart, J. Wang, and X.A. Li. Phys. Med. Biol. 47, 3197–3209 (2002) and RK Sachs, P. Hahnfeld, DJ Brenner. Int. J. Radiat. Biol. 72(4), 351-74 (1997).


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{

A mechanistic interpretation of the A mechanistic interpretation of the LQLQ

2( ) (1 ) / 2dsb a (1 ) dsba

Accuracy of repair process

-1 -1~ 40 DSB Gy celldsb

Rate of DSB rejoining

Pairwise damage interaction process alwayscreates a mutation (chromosome aberration). But not all of them are lethal.

2 (1 )

/(1 )dsb

a

a

Expect / ratio to increase asrate of DSB rejoining () increases.


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Prediction of LQ parameters from “first Prediction of LQ parameters from “first principles” – a tantalizing possibilityprinciples” – a tantalizing possibility

(Gy-1)10-2 10-1 100

(G

y-2)

10-3

10-2

10-1

100

Small black filled symbols generated using Monte Carlo sampling methods

Large red symbols parameter values obtained from the direct analysis of measured survival data

2( ) (1 ) / 2dsb a

(1 ) dsba


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Lack of a dose rate effect is insufficient Lack of a dose rate effect is insufficient evidence to infer ‘no repair’evidence to infer ‘no repair’

2( ) exp GS D D D

dose rate effects

/ (1 )

2.27%dsb a

2( ) (1 ) / 2dsb a

Lack of a dose rate effect implies A small fraction of the initial

damage is unrepairable (< 2%)• complex DSBs?

Rapid DSB rejoining• G → 0 (large )• (/) << 1

Rapid DSB fixation competes with 1st and 2nd order repair.

Other possibilities


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Damage formation and repair is still Damage formation and repair is still only the beginningonly the beginning

Dosimetry

50 keV e- in H2O

Cancer develops through physical, chemical, biochemical and microevolutionary processes that happen over hours, days, months and even years.


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Tumor growth kineticsTumor growth kinetics

( ) ( )dN

N tdt

Exponential cell kinetics are sometimes observed

Cell birth rate (h-1) Cell death rate (h-1)

( ) (0)exp ( )

(0)exp 0.693 / d

N t N t

N t T

ln(2)

( )dT

Cell Doublings

N(t)Tissue

Volume (cm3)

0.00 1.00E+00 5.24E-101.00 2.00E+00 1.05E-092.00 4.00E+00 2.09E-093.00 8.00E+00 4.19E-094.00 1.60E+01 8.38E-095.00 3.20E+01 1.68E-086.00 6.40E+01 3.35E-087.00 1.28E+02 6.70E-088.00 2.56E+02 1.34E-079.00 5.12E+02 2.68E-07

10.00 1.02E+03 5.36E-0715.00 3.28E+04 1.72E-0520.00 1.05E+06 5.49E-0425.00 3.36E+07 1.76E-0230.00 1.07E+09 5.62E-0135.00 3.44E+10 1.80E+0140.00 1.10E+12 5.76E+0245.00 3.52E+13 1.84E+0450.00 1.13E+15 5.90E+05

Doubling time


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Time (h)

10-1 100 101 102 103 104 105

Exp

ecte

d nu

mbe

r of

cel

ls

10-1

100

101

102

103

104

105

106

107

108

109

60 Gy EBRT60 Gy EBRT (no repopulation)

145 Gy 125I brachytherapy

Effective treatment time ~ 234 days

Radiation therapy for the treatment of Radiation therapy for the treatment of prostate cancerprostate cancer

Prostate tumor composed of 107 tumor cells.

Wang et al. (2003) radiosensitivity parameters

JZ Wang, M. Guerrero, XA Li. How low is the alpha/beta ratio for prostate cancer? Int. J. Radiat. Oncol. Biol. Phys. 55(1), 194-203 (2003).

( ) ( )exp ( )N t S t t


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Tumor control probability (TCP)Tumor control probability (TCP)

JZ Wang, M. Guerrero, XA Li. How low is the alpha/beta ratio for prostate cancer? Int. J. Radiat. Oncol. Biol. Phys. 55(1), 194-203 (2003).

Dose in parentheses is the treatment dose that gives a TCP of 90%

Prostate tumor composed of 107 tumor cells.

Wang et al. (2003) radiosensitivity parameters


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Multi-stage cancer model(s)Multi-stage cancer model(s)

MalignantTumor

tlag

Stem Cells

Minor G.I.

Enhanced G.I.

Transformed(neoplastic)

Through a series of mutational events, stem cells acquire minor and enhanced genetic instability and other traits.

Tumor forms through the clonal expansion of the unstable cell population.

Cell birth/death processes may change as cells progress towards malignancy.


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Incidence of lung cancerIncidence of lung cancer

Total absorbed dose delivered in 75 years (mGy)

1 10 100 1000 10000

Can

cer

inci

denc

e at

75

year

s, N

5(75

yr)

10-4

10-3

10-2

10-1

100

Estimated lung cancer incidence with and without DNA damage caused by endogenous processes.

H. Schöllnberger, R.D. Stewart, R.E.J. Mitchel, and W. Hofmann, An examination of radiation hormesis mechanisms using a multi-stage carcinogenesis model. In progress. Abstract submitted to ICRR 2003 Brisbane, Australia (2003).

At background radiation levels (75 to 225 mGy), endogenous processes may account for 70 to 90% of lung cancers.

At 1 Gy, endogenous processes may account for as much as 30% of lung cancers.


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Induction of cellular defense Induction of cellular defense mechanismsmechanisms

Estimated lung cancer incidence with and without low dose (rate) adaptations in radical scavenging and DNA repair.

H. Schöllnberger, R.D. Stewart, R.E.J. Mitchel, and W. Hofmann, An examination of radiation hormesis mechanisms using a multi-stage carcinogenesis model. In progress. Abstract submitted to ICRR 2003 Brisbane, Australia (2003).

A 3-fold low dose (rate) enhancement in DNA repair and radical scavenging would provide support for an effective threshold.


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CommentsComments

Multi-stage models that use exponential cell growth kinetics are extremely sensitive to the selection of a net cell birth rate (-) and have conceptual difficulties• For lung cancer, (-) ~ 0.012 + 0.001.• Cell density < ~ 108 to 109 cells cm-3.• Tumor size has a finite upper bound ~ 1014 or 1015 cells.

Over extended periods of time (months or years), age, health status, etc., etc., will impact on cancer development• Cell birth/death parameters will change over time and most likely has

a stochastic (chaotic) element.• Wounds or disease may temporarily alter the tissue microenvironment

and accelerate the clonal expansion of aberrant cells. Normal cells affect behavior of transformed cells and vice

versa• Cell signaling (bystander) effects.


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Maybe I’ve got the virus and just don’t know it

yet

Cell signalingCell signaling

Cells in higher animals coordinate cellular activities using hundreds of different kinds of signaling molecules• Proteins, small peptides, amino acids, nucleotides, steroids, retinoids, fatty acid

derivatives, and gases such as nitric oxide (NO) and carbon monoxide

Signaling can be long range (synaptic and endocrine signaling) or short range (autocrine and paracrine signaling)

Direct cell-to-cell communication through gap junctions

Goodbye friends. I’ve caught a virus and must leave you.

Autocrine and paracrine signaling through excreted messengers


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Why do we care?Why do we care?

Cell birth, differentiation and death processes are highly regulated through multiple signaling networks.

Medium transfer and single-cell irradiator experiments demonstrate that radiation-damaged cells emit signals that cause radiation-like changes in nearby undamaged cells• changes in gene expression, mutations, increases in sister chromatid exchanges, induction

of chromosomal instability, and cell transformation


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Growth InhibitionGrowth Inhibition

Cell growth in vivo is limited (at a minimum) by the availability of space, nutrients, and growth factors

Cells compete with each other for resources

Diameter (um) (um3) (cm3)

Peak density

(cell cm3)1 0.524 5.24E-13 1.91E+122 4.189 4.19E-12 2.39E+113 14.137 1.41E-11 7.07E+104 33.510 3.35E-11 2.98E+105 65.450 6.54E-11 1.53E+106 113.097 1.13E-10 8.84E+097 179.594 1.80E-10 5.57E+098 268.083 2.68E-10 3.73E+099 381.704 3.82E-10 2.62E+09

10 523.599 5.24E-10 1.91E+0915 1,767.146 1.77E-09 5.66E+0820 4,188.790 4.19E-09 2.39E+0825 8,181.231 8.18E-09 1.22E+08

Volume( ) ( )

( ) ( )dN t N t

N tdt

Life support capacity

( ) ( )( ) ( ) / ( )

dN t N tdS t dt N t

dt

Radiation killing


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Microevolution of a tumorMicroevolution of a tumor

Normal and transformed cells vie for resources

0 0 10 0 0 0

0

( ) ( ) ( )( ) ( ) / ( )

dN t N t N tdS t dt N t

dt

Normal cells

Tumor cells

1 0

1 0 11 1 1 1

1

( ) ( ) ( )( ) ( ) / ( )

dN t N t N tdS t dt N t

dt

Crowding effects:

Over-expression of growth factor receptors


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Virtual Tissue Model (VTM)Virtual Tissue Model (VTM)

System of 6 or 7 differential equations describe the in vivo cell system (i.e., the Virtual Tissue).

Normal cells and transformed cells vie for resources.

Tissue microenvironment is re-shaped as the relative number of normal and transformed cells changes.

Stem Cells(N0)

CommittedProgenitor

(N1)

Minor G.I.(G0)

Enhanced G.I.(G1)

Transformed(neoplastic)

(G2)

Malignant(Gm)

in vitro

in vivo

Terminallydifferentiated (N2)

( ) 1( ) ( ) / ( ) ( )i

i i i j iji

dN tdS t dt N t N t

dt


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Can we simulate cancer from first Can we simulate cancer from first principles?principles?

Yes! No! Maybe…

What’s a first principle?

Mechanisms and

parameters

Computational issues


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A lot more can be doneA lot more can be done

http://healthsciences.purdue.edu/vc/

Acknowledgement: The Virtual Cell software development effort is supported in part by the U.S. Department of Energy's Low Dose Radiation Research Program through the Office of Science (BER), Grant Number DE-FG02-03ER63541.

Can we predict radiation carcinogenesis from first principles?

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