Double strand breaks in DNA resulting from double-electron-emission events

0.13 MB·English

by  Eugene Surdutovich

Double strand breaks in DNA resulting from double-electron-emission events
Eugene Surdutovich1,2 and Andrey V. Solov’yov2∗
1Department of Physics, Oakland University,
Rochester, Michigan 48309, USA
2Frankfurt Institute for Advanced Studies,
Ruth-Moufang-Str. 1, 60438 Frankfurt am Main, Germany
(Dated: January 30, 2012)
Amechanism ofdoublestrandbreaking(DSB)inDNAduetotheaction oftwoelectronsiscon-
sidered. ThesearetheelectronsproducedinthevicinityofDNAmoleculesduetoionizationofwater
2
1 molecules with a consecutive emission of two electrons, making such a mechanism possible. This
0 effect qualitatively solves a puzzle of large yields of DSBs following irradiation of DNA molecules.
2 Thetransportofsecondaryelectrons,includingtheadditionalelectrons,isstudiedinrelationtothe
assessment of radiation damage duetoincidentions. Thiswork isastagein theinclusion of Auger
n
mechanism and like effects into themultiscale approach to ion-beam cancer therapy.
a
J
PACSnumbers: 87.53.-j,61.80.-x,34.50.Gb,36.40.Cg
7
2
The analysis and assessment of radiation damage are by asingle electron. This logichas beenwidely accepted
]
h importantinrelationtoawiderangeofapplicationsfrom andusedbythepresentauthorstocalculatetheyieldsof
p cancer therapy to radiation protection of humans and DSBs due to ions [3]. However, the mechanism of DSBs
- electronics. Studiesofbiodamageduetoirradiationwith due to low-energyelectronsis stillquantitativelyunclear
o
ionbeams, centeredonthe analysis ofpathwaysofDNA despitequalitativearguments,suggestingthatthebreaks
i
b damage, are discussed in a large number of papers ob- in the second strand are due to the action of debris gen-
s. served in reviews [1, 2]; the multiscale approach to the eratedby the first SSB [7]. In Ref. [3], the productionof
c physics of ion-beam cancer therapy [3, 4] is also among DSBs by two separate electrons was alsoconsidered, but
i
s these studies. A double strand break (DSB) in DNA is thatanalysiswasthenshelved,since the numberdensity
y the most pernicious kind of damage that happens as a ofsecondaryelectrons due to primaryionizationwithan
h
resultofradiationimpact. Itisdefinedasthe simultane- ion was not nearly enough for this effect to be consid-
p
ousbreakingofthetwostrandsofaDNAmoleculewithin erable in comparison with DSBs due to single electron
[
thedistanceof10basepairsalongthehelix,whichcorre- action.

1 sponds to a single convolution of a DNA molecule. This
In this work, we argue that additional electrons emit-
v type of lesion is emphasized because of the difficulties
ted in the vicinity of a DNA molecule as a result of the
6
of its repair and thus close connection to cell lethality.
7 Auger-likemechanismaugmenttheaboveeffectandthus
What processes lead to this lesion?
8 constitute amechanismfor aDSB.We explorethe prob-
5 If the primary ionizing projectiles are ions, a substan- ability of two electrons, produced in the vicinity of a
1. tial fraction of damage is done by secondary electrons, DNA molecule, be incident on a single convolution of
0 formed in the process of ionization of the medium. A this molecule. These additionalelectronsemergeasare-
2 number of different pathways of damage due to these sultofdoubleionizationeventssuchastheAugereffectin
1 electronswereconsideredin Refs.[4–6]. The directmea- singlemolecules,e.g.,Refs.[10–13]forwater,ortotheef-
:
v surementsofDNAdamageduetoincidentelectronswere fect of intermolecular coulombic decay (ICD), studied in
i presentedin,e.g.,Ref.[7],whichbroughttolightthepos- Refs. [14–18] for water clusters. The actual mechanism
X
sibility that low energy electrons were important agents of double ionization is not important for our analysis.
r ofDNAdamage. Sincethen,themechanismofaSSBdue We will use a generic term “double-ionization-events”to
a
totheactionofasingleelectron,relatedtotheformation describe all relevant events leading to a production of
of a transient negative ion (TNI) as a part of the pro- additional electrons, and we will refer to the additional
cess of dissociative electron attachment (DEA) has been electron as an Auger electron, even if it originates from
widelydiscussedintheliterature,e.g.,Refs.[6,8,9]with ICD.
emphasis on low (under ionization threshold) energy of 1. Auger electrons are produced as a result of non-
the incident electrons. radiative relaxation of holes produced by primary and
secondary ionization. They may emerge consequent to
UnexpectedlyhighyieldsofDSBscomparedwithSSBs
the ionization of water or other molecules or clusters of
in Ref. [7] lead to a hypothesis that DSBs can be caused
the medium. If a secondary electron ionizes a molecule
by kicking out one of its inner-shell electrons, a hole is
formed on this molecule. If this hole then relaxes via a
∗OnleavefromA.F.IoffePhysicalTechnicalInstitute, St. Peters- non-radiativechannel(anAugerelectronisemittedfrom
burg,Russia the same molecule or an adjacent molecule in a cluster)
2
molecule, located a few nm from the path is very small.
However, when ionization of a water molecule (cluster)
producing an Auger electron occurs at a distance from
the path, three electrons emerging from the same spot
substantiallyboost the localnumber density ofelectrons
and, hence, the probability of a nearby DNA convolu-
tion to be hit with two electrons. A similar process may
take place if the primary projectile is a photon. In that
case, two (instead of three) electrons are produced in a
locality and are capable of producing a DSB in a DNA
molecule. Ifincidentphotonsionizethe1a1 state,thena
cascadeofAugerelectronsmayfollow,rapidlyincreasing
the number density of electrons.
In order to give a quantitative example of the effect
causedbytheAugermechanism,letusconsideranevent
ofionizationwith Auger emissioncausedby a secondary
FIG. 1: The schemeof ionization with theAugermechanism
electron, produced by an incident carbon ion. The goal
applied to ICD; e2 and the Auger electron emerge from dif- ofthisexampleistocalculatethetransportofthreeelec-
ferent molecules. The geometry of the problem; ionization
tronsemergingfromtheionizationlocality,whichwewill
happens at the origin; the cylinder represents a DNA convo-
treat as a point, to a nearby DNA convolution.
lution.
Let an event of double ionization of a water molecule
thetotalnumberofelectrons,emergingfromasub-nmlo- (cluster) happen at the origin. We consider a three-
cality,isequaltothree,theionizingelectron,thereleased dimensional random walk of electrons from this point.
electron,andthe Augerelectron,asshowninFig.1. Ifa WerepresentasingleDNAconvolutionwithacylinderof
double-ionization event occurs on a DNA molecule, the radiusa=1.15nmandalengthof3.4nm. Forsimplicity
probability of damage, such as a DSB, comprises the se- and definiteness, we situate this cylinder symmetrically
quence of these processes with a corresponding dynam- with respect to the y-axis, with the cylinder’s axis par-
ics of the DNA molecule and possible further interaction allel to the x-axis and lying in the xy plane, as shown in
with these three electrons. If a water molecule (cluster) Fig.1. Thedistancebetweentheoriginandthecylinder’s
ofthe mediumlocatedinthe vicinityofaDNA molecule axis, ρ, exceeds a so that the Auger electron is emitted
is a host of a double-ionization event, then these three outside the convolution.
electrons can independently diffuse and stumble onto a
DNA convolutionand produce two SSBs, possibly yield- If one electron is emitted from the origin at t = 0,
ing a DSB. Let us consider the latter scenario in more accordingtoRef.[20],itsrate,dp1/dt,ofpassingthrough
detail. the patch, dA~, located at a distance r from the origin,is
It is interesting to notice that the energies of each of given by the expression
the three electrons, emerging from a water molecule or
cluster,arelikelytobe below15eV.Anaverageionizing dp1(~r,t) =dA~·Dnr∂P(t,r) , (1)
electron has the energy around 45-50 eV, corresponding dt ∂r
totheaverageenergyofelectronsproducedbyanion[19].
After this ionization event, it loses about 30 eV [15].1 whereD =v¯l/6isthe diffusioncoefficient, v¯isthe speed
ofthe electron,nr isaunitvectorintheradialdirection,
Thus, the ionizing electron is left with less than 15 eV
and
while the other two will have even smaller energies [16].
These low-energy electrons are likely to be engaged into 3 3/2 3r2
theDEAchannelleadingtoSSBs. Howdoesthisscenario P(t,r)= exp − (2)
(cid:18)2πv¯tl(cid:19) (cid:18) 2v¯tl(cid:19)
make a difference in the DSBs production?
The number density of secondary electrons, produced
is the probability density to observea randomly walking
on the ion’s path, reduces rather steeply with the in-
electron at a time t and a distance r from the origin.
creasing distance from the path, so that the probability Eq. (1) should be integrated over both the time and dA~,
oftwoelectronsincidentonasingleconvolutionofaDNA
in order to calculate the probability for the electron to
encounter the cylinder.
The time dependence in Eqs. (1, 2) can be translated
1 Inordertokickoutanelectronfrom1a1 MOofH2Omolecule, intothedependenceonnumberofsteps,k,usingv¯t=kl,
thesecondaryelectronhastohavetheenergyabove540eV.Such
where l is the elastic mean free path of electrons in the
electronsereveryrare. Ionizationofotherstatecannotproduce
Augerelectronbecauseofthelackofenergy. medium. Then, we rewrite Eq.(1), substituting (2), and
3
Auger emission, but still, a substantial quantity of this
fluence makes the Auger-mechanism influence on DSB
0.7
yield viable.
0.6 2. Augerelectronsemittedfromtheion’spathasaresult
of primary ionization propagate similarly to secondary
0.5 electrons, so the correction to the number of agents in-
y teracting with a DNA molecule situated at a distance
bilit 0.4 from the path can be made after the calculation of the
a
b probability of Auger electron emission during the pri-
o
Pr 0.3 mary ionization. Our goal in this section is to consider
the Auger electrons emitted as a result of the ionization
0.2
of water molecule clusters by secondary electrons.
The scenario is as follows: Secondary electrons orig-
0.1
inate on the ion’s path and diffuse (through a random
walk)awayfromthe path. Theirinteractionswithwater
0.0
0 1 2 3 4 molecules are primarily elastic until they ionize a wa-
rHnmL ter molecule (cluster). This happens about once per ev-
ery 30 elastic collisions at relevant energies of secondary
FIG. 2: The probability for two electrons to pass through a electrons. A typical secondary electron ionizes one wa-
single convolution of DNA (solid line) compared to that of ter molecule before it becomes thermalized and finally
one electron (dashed line).
bound. More rare energetic δ-electrons are not consid-
eredinthis discussion. Forsimplicity, letusassumethat
ionizationhappens on a certainstep in the randomwalk
switching from variable t to k as
of a 45-eV electron. At that time, this electron is most
likely situated at a distance from the path, given by the
r 3 3/2 3r2
dp1(~r,k)=dkdA~·nr2k (cid:18)2πkl2(cid:19) exp(cid:18)−2kl2(cid:19) (3) expression,
3
ρ¯= ρP(k,r)d r , (5)
and integrate it over k (from the minimal number of Z
steps necessary to reach the surface of the cylinder to
infinity) and dA over the surface of the cylinder. As where k = 30 and ρ is the radial distance from the
was noticed above, these electrons are very near or be- path. The calculations, with the above parameters for
low the ionization threshold and their interactions with secondary electron propagation in water, give ρ¯approx-
watermolecules will be, by andlarge,elastic. Therefore, imately equal to 1 nm. This means that the locus of
we integrate Eq. 3 without including attenuation due to firstionizationevents is a cylinder with a radius of1 nm
inelastic collisions and using the value for the mean free on the axis of the ion path. Then, we can calculate the
path, l=0.15 nm [21]. fluence at a distance ρ from the path due to Auger elec-
TheresultsofthisintegrationofarepresentedinFig.2. tronsemittedfromthesurfaceofthiscylinder. Itisgiven
The probabilitydecreaseswithincreasingr. This proba- by the integration of Eq. (3) normalized by dA over the
bilityisproportionaltothatofproducingastrandbreak surface of the cylinder:
oradifferenttypeoflesiononthelengthofagivenDNA
convolution. The corresponding coefficient is the proba- p (ρ)= ~r ·n dp1(r,k)dσ (6)
bility of inducing an SSB in a single electron action, Γ, A ZS(cid:12)(cid:12)r ρ(cid:12)(cid:12) dA S
remains largely unknown and its calculations and mea- (cid:12) (cid:12)
surements remaina task for atomic physicists and quan- where r2 = ρ¯2+ζ2+ρ(cid:12)2−2ρ¯(cid:12)ρcosφ, ζ is the coordinate
tum chemists. alongthepath,φistheazimuthalangle,andnρ isaunit
vector in the radial direction. The rest of the geometry
The second and third electrons from the three, pro-
is shown in Fig. 3 along with the results for p (ρ). The
duced in the double ionization event, are independent A
fluenceperoneelectronfromthecylinderiscomparedto
fromthefirstoneand,hence,theprobabilityoftwoelec-
that of electron coming from the path. Starting from a
trons to impact the cylinder, p2, is given by
small distance from the cylinder, the fluences are equal,
p2(r)=3p21(r) . (4) whichmeansthatoutsidesomedomain,thetotalfluence
is equal to the fluence of secondary electrons emitted on
The dependence of this probability on the distance of thepathmultipliedby(1+2ψ),whereψistheprobability
the cylinder axis from the origin is shown in Fig. 2. It of the double-ionization event on impact and the factor
is remarkable, that for r < 2nm the probability of the oftwoisduetoanextraelectronemittedinthisprocess.
impact of two electrons is comparable to that of one. 3. ThequintessenceofthispaperisthatduetotheAuger
Of course, Fig. 2 includes neither the value of Γ, nor mechanism, events in which two or more electrons inter-
the probability of an ionization event with the following act with a single DNA convolution are not rare. Double
4
contributeto the DSB yieldconsequenttoanirradiation
of tissue with photons.
Weconsideredthemajorconceptsrelatedtothetrans-
port of Auger electrons and made first steps to includ-
ing the Auger electrons in the multiscale approach to
the calculation of radiation damage by ions. Besides
the considerationofatwo-electronmechanismforDSBs,
our findings also correct the fluence of secondary elec-
trons through the DNA convolution due to the Auger
mechanism. The inclusion of this effect into the mul-
tiscale approach is an important step, since, in general,
theAugermechanismplaysasignificantroleinradiation
damage [22].
Future research in this route will be based on the
calculations and measurements of the cross sections of
ionization of water molecules and clusters with a conse-
quent emission of Auger electrons and the cross sections
of DSBs due to two incident electrons.
The calculation of the fluence of Auger electrons pre-
FIG. 3: The dependence of the fluence of an Auger electron sented in the previous section gives a framework for the
from ionization by asecondary electron on thedistancefrom calculation of the transport of free radicals formed due
the path (solid line) compared to that of a single electron
to anion’s traversethroughamedium. This calculation,
emitted from thepath (dashed line).
withouttheuseofMonteCarlosimulationshaslongbeen
desired. Finally, the analysis presentedin this paper can
be extended to the calculation of complex damage as in
strand breaks or other types of complex damage may
Ref. [4] with the inclusion of the Auger mechanism.
result from these interactions. Thus, this effect quali-
Acknowledgments
tatively provides a solution to the puzzle of high yields
of DSBs by finding sources of high local electron den-
sity near sites of damage. Since the Auger emission may ES is grateful to J.S. Payson who critically read the
resultfromthe ionizationofawatermoleculebyaninci- manuscript and the support of COST Action MP1002
dentphoton, the abovetwo-electronmechanismcanalso “Nano-scale insights in ion beam cancer therapy.”
[1] E. Fokas, G. Kraft, H. An, and R. Engenhart-Cabillic, A. Ausmees, et al., Chem. Phys.Lett. 334, 151 (2001).
Biochim. Biophys. Act.1796, 216 (2009). [13] M.Mitani,O.Takahashi,K.Saito,andS.Iwata,J.Elec.
[2] D.Schardt,T.Els¨asser,andD.Schulz-Ertner,Rev.Mod. Spect. Relat. Phen. 128, 103 (2003).
Phys.82, 383 (2010). [14] L. S. Cederbaum, J. Zobeley, and F. Tarantelli, Phys.
[3] A.V.Solov’yov,E.Surdutovich,E.Scifoni,I.Mishustin, Rev. Lett.79, 4778 (1997).
and W. Greiner, Phys. Rev.E79, 011909 (2009). [15] I. Mu¨ller and L. S. Cederbaum, J. Chem. Phys. 125,
[4] E. Surdutovich, D. C. Gallagher, and A. V. Solov’yov, 204305 (2006).
Phys.Rev.E 84, 051918 (2011). [16] S. Stoychev, A. Kuleff, and L. S. Cederbaum, J. Am.
[5] J. Kiefer, Biological Radiation Effects (Springer-Verlag, Chem. Soc. 133, 6817 (2011).
Berlin, Heidelberg, New York,1990). [17] T. Jahnke,H.Sann,T.Havermeier,et al., Nat.Phys.6,
[6] A. Kumar and M. D. Sevilla, Chem. Rev. 110, 7002 139 (2010).
(2010). [18] M. Mucke,M. Braune, S. Barth, M. F¨orstel, T. Lischke,
[7] M. A. Huels, B. Bouda¨ıffa, P. Cloutier, D. Hunting, and V.Ulrich,T.Arion,U.Becker,A.Bradshaw,andU.Her-
L. Sanche,JACS 125, 4467 (2003). genhahn, Nat. Phys.6, 143 (2010).
[8] F.A.Gianturco,F.Sebastianelli,R.R.Lucchese,I.Bac- [19] E.Surdutovich,O.Obolensky,E.Scifoni,I.Pshenichnov,
carelli, and N. Sanna, J. Chem. Phys. 128, 174302 I.Mishustin,A.V.Solov’yov,andW.Greiner,Eur.Phys.
(2008). J. D 51, 63 (2009).
[9] Y. Park, Z. Li, P. Cloutier, L. Sanche, and J. Wagner, [20] S. Chandrasekhar, Rev.Mod. Phys. 15, 1 (1943).
Radiat. Res. 175, 240 (2011). [21] C. Tung, T. Chao, H. Hsieh, and W. Chan, Nucl. Inst.
[10] W. Moddeman, T. Carlson, M. Krause, and B. Pullen, Meth B 262, 231 (2007).
J. Chem. Phys. 55, 2317 (1971). [22] S. McMahon, W. Hyland, M. Muir, J. Coulter, S. Jain,
[11] H. Siegbahn, L. Asplund, and P. Kelfve, Chem. Phys. K. Butterworth, G. Schettino, G. Dickson, A. Hounsell,
Lett.35, 330 (1975). J. O’Sullivan,et al., Sci. Rep.1, 18 (2011).
[12] I. Hjelte, M. Piancastelli, R. Fink, O. Bjo¨rneholm,
M. B¨assler, R. Feifel, A. Giertz, H. Wang, K. Wiesner,