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The Non-homologous End-Joining (NHEJ) Mathematical Model for the Repair ofDouble-Strand Breaks: II. Application to Damage Induced by Ultrasoft X Raysand Low-Energy ElectronsAuthor(s): Reza Taleei , Peter M. Girard , Krishnaswami Sankaranarayanan and Hooshang NikjooSource: Radiation Research, 179(5):540-548. 2013.Published By: Radiation Research SocietyDOI: http://dx.doi.org/10.1667/RR3124.1URL: http://www.bioone.org/doi/full/10.1667/RR3124.1

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RADIATION RESEARCH 179, 540–548 (2013)0033-7587/13 $15.00�2013 by Radiation Research Society.All rights of reproduction in any form reserved.DOI: 10.1667/RR3124.1

The Non-homologous End-Joining (NHEJ) Mathematical Model for theRepair of Double-Strand Breaks: II. Application to Damage Induced by

Ultrasoft X Rays and Low-Energy Electrons

Reza Taleei, Peter M. Girard, Krishnaswami Sankaranarayanan and Hooshang Nikjoo1

Radiation Biophysics Group, Department of Oncology- Pathology, Karolinska Institutet, Stockholm SE171 76, Sweden

Taleei, R., Girard, P., Sankaranarayanan, K. and Nikjoo, H.The Non-homologous End-Joining (NHEJ) MathematicalModel for the Repair of Double-Strand Breaks: II. Applica-tion to Damage Induced by Ultrasoft X Rays and Low-EnergyElectrons. Radiat. Res. 179, 540–548 (2013).

We investigated the kinetics of simple and complex types ofdouble-strand breaks (DSB) using our newly proposedmechanistic mathematical model for NHEJ DSB repair. Forthis purpose the simulated initial spectrum of DNA DSB,induced in an atomistic canonical model of B-DNA by low-energy single electron tracks, 100 eV to 4.55 keV, and theelectrons generated by ultrasoft X rays (CK, AlK and TiK),were subjected to NHEJ repair processes. The activityelapsed time of sequentially independent steps of repairperformed by proteins involved in NHEJ repair process werecalculated for separate DSB. The repair kinetics of DSBswere computed and compared with published data on repairkinetics obtained by pulsed-field gel electrophoresis method.The comparison shows good agreement for V79-4 cellsirradiated with ultrasoft X rays. The average times for therepair of simple and complex DSB confirm that double-strand break complexity is a potential explanation for theslow component of DSB repair observed in V79-4 cellsirradiated by ultrasoft X rays. � 2013 by Radiation Research Society

INTRODUCTION

Advances in knowledge of DNA repair processes and cellsignaling pathways, and human genome research haveopened up unprecedented opportunities to develop ‘‘bot-tom-up’’ approaches to targeted cancer therapy andestimates of genetic and carcinogenic risk to humanpopulations exposed to ionizing radiation (1, 2). Theseapproaches are aimed at linking induced DNA double-strand breaks (DSBs) (the principal molecular lesions ofbiological relevance), cellular DNA repair processes (that

repair these and other induced lesions) and deletions,

duplications or other rearrangements (that arise as a result of

such processing). Such rearrangements have the potential to

induce adverse health consequences such as cancer and

hereditary effects. Our current work is focused on forging

links between initial induced DNA damage and the repair

processes with a comprehensive mechanistic computational

model of DNA damage and repair in the human genome.

The model rests on the premise that the cell is a complex

system and radiation insult induces damage in the DNA that

perturbs the system, which activates protective processes of

the cell to restore genome integrity. Activation of the DNA

repair and the cell signaling pathways are among the initial

steps taken by the molecular and cellular protective

processes.

Experimental work over the past two decades has

documented biphasic kinetics for the repair of radiation-

induced DSB with time (referred to as slow and fast repair

hereafter) for c photons (3–5) and ultrasoft X rays (6, 7).

However, the experimental methods available to date are

not capable of revealing the mechanism(s) for the biphasic

characteristic. From biophysical computational modeling

studies of radiation tracks, it has been shown that tracks

from higher-linear energy transfer (LET) radiation induced

much more complex double-strand breaks with higher

frequencies than low-LET photons or electrons (8, 9). It has

been suggested that complexity of the damage could result

in slow repair. More recently, inferences from experimental

DNA repair studies have led researchers to propose that

chromosomal remodeling in the condensed region of the

chromosome known as heterochromatin could also be the

reason for the slow kinetics of repair (10–13).

In this article, we show the results of: (a) simulation

experiments on the spectra of initial DNA damage induced

by ultrasoft X rays and by single tracks of monoenergetic

electrons; (b) application of the mechanistic mathematical

model developed by Taleei and Nikjoo (14), for the repair

of simple and complex DSB by the NHEJ pathway, and (c)

comparisons of the total elapsed repair times calculated

from these studies with published experimental data of

1Address for correspondence: Radiation Biophysics Group, De-partment of Oncology-Pathology, Karolinska Institutet, Stockholm,SE171 76 Sweden; e-mail: hooshang.nikjoo@ki.se.

540

pulsed-field gel electrophoresis studies with V79-4 hamstercells irradiated with CK, AlK and TiK X rays (6, 7).

MATERIALS AND METHODS

In these investigation we first simulated the spectra of initial DNAand then carried out DSB repair studies with our NHEJ model.

Computer Simulation of DNA Damage Spectra

Previously, we have reported on our computer simulation of DNAdamage in cell mimicking conditions for photons, electrons and ions(8, 15–17). Both low-energy electron tracks (100 eV to 4.55 keV), andCK, AlK ultrasoft X rays were simulated with the new version of theKURBUC-liq code (18–21). For the ultrasoft X-ray simulations, theelectron spectrum following the absorption of CK, AlK and TiK X raystakes into account all possible Auger and photoelectron emissionsfrom the K, L, M and N shells. The initial electron spectrum forultrasoft X rays was generated with X-ray interactions in soft tissue(22). The KURBUC-liq code follows all elastic and inelastic electroninteractions in liquid water event by event (23, 24). In ourcomputational modeling of DNA damage we assume electron energyloss distributions are very similar to those of DNA and tissue. Thephysical stage of the simulation takes ;10�15 s. Interactions ofradiation tracks with DNA was considered by noting the position ofthe direct energy depositions, and the indirect reaction of hydroxylradicals generated in the bulk water surrounding the DNA with

nucleobases. In the prechemical stage, the ionized and excited watermolecules undergo several interactions from 10�15 s to 10�12 s thatresults in the production of stable radical species such as OH, H andhydrated electron (eaq) (25).

Full details of the DNA damage modeling have extensively beenreported in earlier publications (8, 15, 26). In this work an atomisticmodel of B-DNA including the hydration shell (27) was used forscoring energy deposition sites.

DNA damage arises either from the direct hits or the indirectreaction of radicals. The direct damage was induced by the energydeposition of the electron tracks. Energy deposition of �17.5 eV by asingle track in a volume of the sugar-phosphate or a base moiety wereconsidered to induce an SSB or a base damage. Full details of theenergetics of DNA damage are given in previous publications (8, 9,26, 28). Indirect damage is produced by reaction of diffused hydroxylradicals with the nucleobases in the time scale 10�12s to 10�9 s. It isassumed that no radical was produced in the first hydration shell, andthe electron interactions with the first hydration shell were consideredas a direct damage. It was also assumed that the probability of reactionof the hydroxyl radicals to produce SSB and base damage were 0.13and 0.8, respectively (26). The model of DNA damage by complexityis shown in Fig. 1. For ease of presentation, helical DNA is presentedwith 4 linear lines. The solid lines present the sugar-phosphate (S-P)backbones and the dashed lines present the bases of the DNA. Thesimple damages include ‘‘DSB’’, ‘‘SSB’’ and base lesions, and thecomplex damages include ‘‘DSBþ’’ and ‘‘DSBþþ’’. By definition (29)‘‘DSBþ’’ is a DSB in close proximity (within 10 bp) to a SSB, and‘‘DSBþþ’’ is a DSB in close proximity to another DSB. The DSBþ and

FIG. 1. Illustrates damage classification according to complexity. The DNA double helix is shown with four lines. The solid lines present thesugar-phosphate (S-P) backbones and the dashed lines present the bases of the DNA. The left column classifies the damages on the S-P backbone.Damage on the (S-P) backbones compose a ‘‘SSB’’ and two tandem SSB in close proximity (,10 bp) is defined as ‘‘SSBþ’’. Two bi-strandedSSBs in close proximity is defined as ‘‘DSB’’ and separated with more than 10 bp is defined as ‘‘2SSB’’. A DSB in close proximity of a SSB anda DSB is defined as ‘‘DSBþ’’ and ‘‘DSBþþ’’, respectively. The complex DSB are defined as ‘‘DSBC’’¼ ‘‘DSBþ’’ and ‘‘DSBþþ’’. The right columnshows the damage on the base. The first damage is a simple base damage (BD). Two base damages are defined as ‘2BD’ and base damage in closeproximity of SSB and DSB. A single-strand break (SSB) or base damage (BD) may arise either from the direct hits or the reaction of an OHradical.

DNA DAMAGE-REPAIR BY LOW-ENERGY ELECTRONS 541

DSBþþ are defined as complex DSB (‘‘DSBc’’). Other forms of DSBc

include additional base damage (not shown in Fig. 1) (30).

DNA DSB Repair

The NHEJ kinetic rate model described in ref. (14) was used for therepair of the DSB produced by ultrasoft X rays and monoenergeticelectrons. The NHEJ repair model was defined by a set of 9 nonlineardifferential equations that explains the biological modification of theDSB ends by repair proteins including Ku70, Ku80, DNA-dependentprotein kinase catalytic subunit (DNA-PKcs), Artemis, Polymerase k,Polymerase l, XRCC4, XLF and ligase IV (LIG IV). Briefly, after theinduction of DSBs by single radiation tracks, the model describes therecruitment of heterodimer proteins Ku70 and Ku80 that find the DSB,and translocate inward to allow more space for DNA-PKcs activity.The recruitment of Ku70/80 heterodimer and DNA-PKcs to form thesynapses is very fast. DNA-PKcs is autophosphorylated at PQR andABCDE clusters and is required to continue the NHEJ repair process.Simple DSB, defined as those DSB that are not in close proximity ofother strand breaks (29, 31), are proposed to be ligated after thesynapses by the (XLF)/XRCC4/LIG IV complex in a fast process. ForDSB that are complex (the DSB that are in close proximity of otherSSB or DSB) (29, 31) the model considers end-processing preligationprocesses, including Artemis endonuclease and Polymerase l or k gapfilling processes. After this processing the ends are ligated with (XLF)/XRCC4/LIG IV complex. The NHEJ repair processes outlined abovewere translated to mathematical equations and solved with the rateconstants presented in Table 1. In our companion article (14), the rateconstants of the proteins were carefully chosen to facilitatecomparison with the kinetics of the total DSB repair computed bythe model with experimental measurements. In this work we assumedthe same rate constants derived in our article (14) is also valid for thepresent calculations. To validate the model for application withultrasoft X rays, the repair kinetic of the NHEJ model were comparedwith that of the CK X ray reported in ref. (7).

To be able to incorporate the repair model in the simulation of therepair kinetics of DSB induced by single tracks of electrons, thecumulative distribution function (CDF) of the proteins were calculatedfrom protein activity kinetics (calculated by solving the NHEJ modelequations) (21). The same method is used in this investigation. Thesolution of the equations in the companion study (14) provides thekinetics of the protein actions shown in Fig. 2 as well as the overallkinetics of the DSB repair for a total dose between 20 to 80 Gy. Theprobability distribution function (PDF) at every step of repair isdefined to be equal to repair activity kinetics in Fig. 2 normalized tothe area under the curve. The PDF is converted to CDF by cumulativeintegration over time. By inverse transform sampling of the CDF, it ispossible to calculate the time required for each protein to perform itsrepair action on each DSB induced by single tracks of radiation. Forthis purpose the DSB were divided into two main categories of simpleand complex types according to our original definition (29). Forsimple DSB, Ku70, Ku80, DNA-PKcs, XRCC4, XLF and ligase IVare involved in the repair and for complex DSB, Ku70, Ku80, DNA-PKcs, Artemis, Polymerase k or l, XRCC4, XLF and ligase IVperform the repair. With this approach we were able to investigate notonly the repair time required for every separate protein to perform endmodifications on the DSB but also the repair kinetics for simple andcomplex DSB separately and therefore the repair time for all types ofdouble-strand breaks.

RESULTS AND DISCUSSIONS

The results are presented under the following subhead-ings: (a) verification of the NHEJ repair model withultrasoft CK X-ray experimental measurements; (b) produc-tion of initial spectra of DNA damage and (c) simulating therepair of the initial DSB. For these studies we utilized theinverse transform sampling method and compared the totalrepair kinetics with experimental measurements.

(a) DSB Repair Model for Carbon K X Ray

Construction of the NHEJ model using the law of massaction for proteins resulted in a set of 9 mathematicalnonlinear equations describing NHEJ repair mechanistically(14). The equations were solved numerically with rateconstants presented in Table 1. The solutions of the 9equations describing the NHEJ model are shown with Y1 toY9 in Fig. 2. Y1 to Y9 present the kinetics of biochemicalrepair processes performed by Ku70, Ku80, DNA-PKcs,Artemis, Polymerase k or l, XRCC4, XLF and LIG IVrepair proteins. Ku 70, Ku80 and DNA-PKcs are very fast

TABLE 1Rate Constants for The NHEJ Kinetic Model

Rate constants (h�1) k1 k2 K3 K4 k5 K6 k7 k8 k9 K10

NHEJ model (mutated in HR) 350 500 50 20 15 5 3.6 8 0.25 0.55

FIG. 2. Kinetics of protein repair Y1 to Y9. The protein repairkinetics is assumed to be the probability distribution function (PDF) ofthe protein activity from which cumulative distribution function(CDF) could be calculated. Y1 presents the kinetics of initial DSB thatstart the repair. Y2 presents the kinetics of DSB that are bound toKu70/80 and form the repair complex. Y3 to Y9 presents the kinetics ofthe further steps of biochemical repair actions of the DSB ends beforeand after the synapses.

542 TALEEI ET AL.

acting on the damage to form synapses. It is very difficult to

verify the kinetics of the protein repair actions experimen-

tally. However, recent experiments using the time-lapse

imaging method provided kinetic data of the initial

recruitment of proteins such as Ku 70/80 and DNA-PKcs

before the synapses of the ends. The initial recruitment

maximum for Ku70/80 and DNA-PKcs was reached in less

than a minute, which is in good agreement with the

experimental measurements (14, 32). However, further end

processing and ligation is required to complete the repair

after the synapses.

The sum of Y1 to Y9 presents the total repair kinetics for

an acute dose of radiation. The total DSB repair kinetics

were compared with the experimental results measured withpulsed-field gel electrophoresis (PFGE) for V79-4 cellsirradiated with CK ultrasoft X rays (7). The repair kinetics ofY1 to Y9 is shown in Fig. 2 in terms of dose equivalent (Deq)in Gy versus time. The probability distribution functions(PDF) of the repair proteins were assumed to be equal to therepair kinetics (Y1 to Y9) presented in Fig. 2.

As shown in Fig. 3, the rate constants used for HRmutated cells were applied for predicting the repair kineticsmeasured from CK irradiation of V79-4 cells (the NHEJmodel with rate constants for HR mutated cells is within themargin of error of CK irradiation of V79-4 cells).

(b) DNA Damage

Monoenergetic electron tracks with energies of 100 eV,200 eV, 300 eV, 400 eV, 500 eV, 1 keV, 1.5 keV, 4.55 keV,and for electron tracks generated by for CK and AlK X rayswere simulated with the Monte Carlo track structure codeKURBUC-liq. The damage produced in the DNA segmentswere scored and classified according to complexity. Thefrequency of damage scored for 500 tracks each ofmonoenergetic electrons and ultrasoft X rays were summa-rized in Table 2. The probability of SSB, DSB and DSBC

induction as a function of electron energy remains nearlyconstant as expected. The relative complexity of the damagewas calculated as the ratio of DSBc (¼ DSBþ þ DSBþþ)over total DSB. The complexity of the DSB has a maximumvalue at about 400 eV. As expected, the number of DSBsinduced by CK X rays is close to that induced by 300 eVelectrons.

The number of SSB and DSB in DNA segments per trackwas used to calculate the number of SSB and DSB in thecell nucleus per Gy. For this purpose, the mean molecularweight of a chromosome was calculated by considering anaverage number of 245 Mbp per chromosome, and 22chromosomes with a relative mass of 650 g/mol.bp (33).The comparison of the number of damage induced per cellper Gy with the experimental results is shown in Table 3.The number of SSB remains almost constant with thechange of energy (;700). The number of DSB increases

FIG. 3. Unrejoined DSB kinetics calculated for the NHEJ modeland observed with pulsed-field gel electrophoresis experiment with CK

X ray inducing damage in V79-4 cells (7). Sum of Y1 to Y9 repairkinetics results in the total number of unrejoined DSB. The solid lineshows the NHEJ model calculations with the rate constants derived forHR mutated cells (14).

TABLE 2Frequency of Damage Induced by Monoenergetic Electrons, CK and AlK, and TiK X Rays

Type of damage

Monoenergetic electrons (eV) X ray

100 200 300 400 500 1000 1500 CK 278 eV AlK 1.5 keV TiK 4.55 keV

No Strand break (%) 75.3 72.9 72.4 72.3 72.4 72.7 73.4 73.4 73.4 75.2SSB (%) 22.7 23.3 23.7 23.0 22.9 23.1 22.6 22.7 22.8 21.9SSBþ (%) 0.9 1.9 1.7 2.1 2.1 1.9 1.7 1.7 1.8 1.32SSB (%) 0.1 0.2 0.4 0.6 0.6 0.6 0.6 0.4 0.4 0.4DSB (%) 0.8 1.3 1.3 1.4 1.5 1.3 1.3 1.5 1.3 0.9DSBþ (%) 0.13 0.36 0.36 0.51 0.45 0.34 0.33 0.31 0.33 0.22DSBþþ (%) 0.00 0.08 0.07 0.10 0.04 0.03 0.06 0.06 0.05 0.02DSBc 0.13 0.44 0.43 0.61 0.49 0.37 0.39 0.37 0.38 0.24Total DSB 0.93 1.74 1.73 2.01 1.99 1.67 1.69 1.87 1.68 1.14DSBc/total DSB 15 25 25 29 24 22 23 20 23 21

DNA DAMAGE-REPAIR BY LOW-ENERGY ELECTRONS 543

with energy from 100–300 eV and decreases for energieshigher than 300 eV. The 60Co source induces around 30DSB/Gy/cell (6), that is about 3 times less than that for low-energy electrons and ultrasoft X rays, and 1,000 SSB/Gy/cell (6) which is around the same number for low-energyelectrons and ultrasoft X rays. For ultrasoft X rays, thenumber of DSB per cell per Gy increased with the decreasein energy as expected.

(c) Simulation of The Repair of DSB Induced by SingleTrack of Electrons

The scored DSB were subjected to the NHEJ repairmodel. To utilize the repair model for the DSB induced bysingle track of electron or ultrasoft X ray, an inversetransform sampling of the protein kinetics were carried out.For this purpose the cumulative distribution function (CDF)for all biochemical repair processes were calculated. Figure4 shows the CDF of Y2 to Y9. Inverse transform sampling ofthe CDF computes the elapsed time for repair of biophysicalprocesses on the DSB ends by each protein.

By using the inverse transform sampling method therepair times were calculated for simple (DSBs) and complex

(DSBc) double-strand breaks produced by low-energy

electrons and ultrasoft X rays. Figure 5A shows a summary

of the repair times for five illustrative examples of simple

types of double-strand breaks produced by single tracks of

4.55 keV electrons. In Fig. 5B the repair times are shown

for five examples of complex types of double-strand breaks

produced by single tracks of 4.55 keV electrons. The post-

synapses process is the main difference between simple and

complex types of double-strand breaks. The biochemical

protein repair end processing times estimated by simulations

remain to be verified by experimental measurements. To

date, the available experimental methods are not able to

make such measurements.

The inverse transform sampling method permits the

calculation of the total repair time for all DSB induced by

low-energy electrons and ultrasoft X rays. The kinetics for

the repair of DSB induced by 500 tracks of low-energy

electrons and ultrasoft X rays is shown in Fig. 6, showing

the number of repaired DSB after every 10 min. Most of the

damages were repaired in less than 1 h and the highest

repair activity was seen in about 15 min. The repair kinetics

for 300 eV and 1.5 keV electrons are similar to CK and AlK

ultrasoft X rays, respectively.

Table 4 summarizes the total number of initial, complex

and simple double-strand breaks with the average repair

times for 500 tracks of low-energy electrons and ultrasoft X

rays. The average time for the repair of simple DSB is

around 20 min, while the average time for complex DSB is

around 6 h. Before the synapses of the DSB ends by DNA-

PKcs the protein repair kinetics is the same for the complex

and simple damage. Therefore the difference in the repair

time arises after the synapses in the way the complex DSB

require more end processing and a longer ligation activity to

clear the damage.

Figure 7 shows unrejoined DSB kinetics. The repair

kinetics were normalized to the total (initial) number of

DSB for 500 tracks of low-energy electrons or ultrasoft X

rays. The symbols and the lines present the experimental

measurements, and calculations, of repair kinetics for the

DSB induced by CK, TiK and AlK X rays, respectively. The

simulation results are in good agreement with the

experimental measurements. The slow part of the repair

for AlK X rays is more pronounced in comparison to TiK and

CK X rays, due to the fact that DSB induced by AlK X rays

show slightly higher fraction of complex DSB (23%) in

comparison to TiK (21%) and CK (20%) X rays.

TABLE 3Yield of DSB and SSB per Cell per Gy

Energy (eV) 100 200 300 400 500 1000 1500 CK 278 eV AlK 1.5 keV TiK 4.55 keV

SSB/Gy/cell (calculated, this work) 650 717 739 786 698 781 774 746 746 776SSB/Gy/cell (experimental) - - - - - - - - 935 (6) -DSB/Gy/cell (calculated, this work) 33 81 99 94 79 86 65 101 91 81DSB/Gy/cell (experimental) - - - - - - - 112 (7) 77 (7) 56 (7)

FIG. 4. Cumulative probability distribution (CDF) function of Y2–Y9. To do inverse transform sampling for calculating biochemicalrepair processes times, the CDF of all repair activities is calculated.

544 TALEEI ET AL.

FIG. 5. Panel A: Five examples of simple DSB (DSBs) simulated for 4.55 keV electrons. Repair time required for biochemical repair processesof each of the five DSBs examples, and average repair time required for biochemical repair processes of all simple DSBs (simulated 500 times)induced by 4.55 keV electrons. Panel B: Five examples of the complex DSB (DSBc) simulated for 4.55 keV electrons. Repair time required forbiochemical repair processes of each of the five DSBc examples, and average repair time required for biochemical repair processes of all DSBc

(simulated 500 times) induced by 4.55 keV electrons.

DNA DAMAGE-REPAIR BY LOW-ENERGY ELECTRONS 545

DISCUSSION

In this study we employed the new version of track

structure code KURBUC-liq for simulation of electron track

in condensed media to model DNA damage spectra induced

by low-energy electrons (100 eV to 1.5 keV monoenergetic

electrons, and CK, AlK and TiK ultrasoft X rays). Table 2

presents the spectrum of damage for 500 tracks of radiation.

To limit the statistical uncertainty of the results the

calculations were repeated 500 times for each radiation.

However, even then another source of uncertainty arose

from the systematic uncertainties in track structure simula-

tions. The DSB generated by simulation for electrons and

soft X rays were subjected to repair with the NHEJ model.

To employ the repair model, inverse transform sampling

method was used to calculate the repair time from the CDF

of the protein repair kinetics. The method is capable of

calculating the overall repair time for every single DSB. The

overall DSB repair kinetic for DSB induced by 500 tracks of

radiation for CK, TiK and AlK X rays were compared with

experimental measurements. The uncertainty of the repair

kinetics arise from many sources including the simplifyingmodel assumptions by ignoring homologous recombinationpathway; classification of double-strand breaks into twobroad classes of simple and complex; the juxtaposition ofDSB in the cell nucleus (that are not in 10 bp proximity);uncertainties arising from estimating the rate constants; andfinally statistical uncertainties. In future work we plan toreduce the uncertainty of the repair results by combining allpossible known DSB repair pathways, and assign the rateconstants more accurately. For this purpose dedicatedbiological experiments applying fluorescently repair proteintagged cells method needs to be performed. RecentlyReynolds et al. (34), using fluorescently repair proteintagged in mammalian cells, have shown the complexity ofdamage slows down the repair, and identified Ku70/80 wererecruited at the site of damage in less than 1 min, inagreement with the result shown in Fig. 5.

In future work, we plan to extend this work byconsidering biological end points such as DNA deletions,

TABLE 4Yield and Repair Time of DSB Ultrasoft X Rays and Monoenergetic Electrons

Energy (eV) 100 200 300 400 500 1000 1500 CK AlK TiK

Total number of DSB 61 195 280 417 523 905 1360 271 1487 3235Number of DSBs 52 146 211 294 397 709 1044 217 1099 2568Number of DSBc 9 49 69 123 126 196 316 54 388 667Average time for DSBs repair (min) 20 20 20 20 20 20 20 20 20 19Average time for DSBc repair (min) 348 349 341 340 328 344 348 338 341 349

FIG. 7. Unrejoined DSB kinetics calculated for 500 tracks of CK,AlK X rays and 4.55 keV electrons and compared to the pulsed-fieldgel electrophoresis experiment measurements with CK (7), AlK (6) andTiK (7) X rays inducing damage in V79-4 cells. The solid line presentsthe modeling results. Inverse transform sampling method of theprotein repair kinetics is used to calculate the repair kinetics of DSB.

FIG. 6. Number of DSB repaired for 500 electron tracks of 100 eV–4.55 keV monoenergetic electrons, CK and AlK X rays. The number ofrepaired DSB is calculated every 10 min. It is shown that the peak ofrepair is achieved around 15 min for all radiation qualities.

546 TALEEI ET AL.

and the mechanism resulting in chromosome aberration. Forthis purpose, a more complex form of the DNA in the cellnucleus (15) will be used to allow modeling the spatiotem-poral modification of the DSB ends. Recently, manybiology experiments have focused on the spatiotemporalmodification by repair induced foci (RIF) experiments (35–39). We will also include other repair pathways includingbase excision repair (BER) and homologous recombinationrepair (HRR), and consider the distribution of damage in theeuchromatin and heterochromatin and their effect in repairkinetics.

CONCLUSIONS

By employing the track structure simulation tools, wewere able to follow the physical processes of energydeposition of the tracks and chemical reactions of OHradicals in DNA model to simulate initial forms of simpleand complex double-strand breaks in cellular mimickingenvironment. It is important to note that the presentbiophysical computer simulation method is the only wayto precisely identify and quantify forms and frequencies ofsimple and complex DSB. To access the reparability of theinduced DSB, a mechanistic mathematical model of theNHEJ kinetic repair was implemented and applied tosimulated DNA DSB induced by low energy electrons andultrasoft X rays. From the latter we calculated the kinetics ofthe DSB repair. For this purpose we solved a set ofequations describing the NHEJ biophysical repair activitieson the DSB ends to derive the proteins activity kinetics for atotal dose of 15 Gy of CK X rays. The protein activities weresampled to estimate the repair time required for DSBinduced by 1 track of radiation at a time. Finally, the totalDSB repair kinetics for CK, AlK and TiK showed goodagreement with experimental measurements and modelcalculation. This approach provides details of repair timingthat are not easily measured for protein activities on theDSB ends. The average time for the repair of simple andcomplex DSB confirms that complex DSB are the potentialexplanation for slow repair kinetics and may help explainhow this impacts the maintenance of genomic integrity inirradiated cells.

ACKNOWLEDGMENTS

The work was partially supported by SSM the Swedish Radiation

Safety Authority and Karolinska Institutet.

Received: July 13, 2012; accepted: January 14, 2013; published online:

April 5, 2013

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15. Nikjoo H, Girard P. A model of the cell nucleus for DNA damagecalculations. Int J Radiat Biol 2012; 88: 87–97.

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