Computational modelling of low-energy electron ...

int. j. radiat. biol 1997 , vol. 71 , no. 5 , 467 ± 483

Com putational m odelling of low -energy electron-induced DNA dam age by early physical and chem ical events H . N IK JOO*, P. O ’NEILL, D . T. G OO DH EAD and M . TERRISSOL²

Int J Radiat Biol Downloaded from informahealthcare.com by (ACTIVE) Karolinska Institutet University Library on 07/29/11 For personal use only.

( R eceived 2 0 N ovemb er 1 9 9 6 ; accepted 4 F eb ruary 1 9 9 7 )

A b stract. M odelling and calc ulations are presented as a ® rst step tow ards m echanistic interp retation and prediction of radiation eå ects based on the spec trum of initial DNA dam age produced by low energy elec trons (100eV ± 4´5keV ) that can be com pared w ith exp erim ental inform ation. Relativ e yields of single and clustered strand breaks are presented in term s of com plexity and source of dam age, either by direct energy deposition or by reaction of O H radicals, and depend enc e on the activation probability of O H radicals and the am ount of energy required to give a single strand break (ssb). Data show that the m ajority of interactions in DNA do not lead to dam age in the form of strand breaks and w hen they do occur, they are m ost frequently sim ple ssb. H ow ev er, for double-strand breaks (dsb), a high proportion ( ~ 30 % ) are of m ore com plex form s, even w ithou t consid ering additional com plexity from base dam age. The greater contrib ution is from direct interactions in the DNA but reactions of O H radicals add substantially to this, both in term s of the total num ber of breaks and in increasing the com plexity w ithin a cluster. It has been show n that the lengths of dam aged segm ents of DNA from individual elec tron trac ks tend to be short, indicating that conseq uent deletion length (simply by loss of a fragm ent betw een nearb y dsb) w ould be short, very seldom exceed ing a few tens of base pairs.

1. Intro d u ctio n

The pu rpose of this study is to m ake a theoretical assessm en t of the spectrum of DN A dam age induced by low -LET radiation at early tim es in m am m alian cells, w ith particular em phasis on clustered dam age that m ight result from low -energy secondary elec trons. Su ch electrons are produced in abundance in nearly all typ es of radiation tracks and it has been suggested that the m ore com plex clustered dam age is less rep airable and hen ce m ore likely to lead to biological consequences (G oodhead et al. 1993). Rad iation-quality dep endent diå erences have been dem onstrated in the rep arab ility of dsb in cellu lar DN A (BloÈ cher 1988, Jenner et al. 1993, Prise et al. 1994, B otchway 1996). A m ajor concern in radiation protection is the qu anti® cation of the health hazard s of radiation from *A uthor for corresp ondenc e. M RC Radiation and G enom e Stab ility U nit, H arw ell, O xford shire O X 11 0RD, U .K. ² Centre de Phy sique A tom ique, U niversiteÂ Pau l Sabatier, 188 Route de Narbonne, Toulouse Cedex, France.

low dose and low dose rate exposure. In order to extrapolate available epidem iological and experim ental inform ation from high dose and dose rate, characterised by hu ndreds or thousands of radiation tracks per cell, to the relev ant low levels of single isolated tracks, it is essential to dev elop a m ore m olecu lar and m echanistic approach based on the am ou nts, typ es and rep arab ility of the early m olecu lar dam age that results from the initial physical and chem ical processes. Interac tions of ionizing radiation in m am m alian cells induce a larg e nu m ber and diå erent typ es of m olecu lar dam age in DN A such as single strand breaks (ssb), doub le strand breaks (dsb), base dam age of variou s typ es and DN A-protein cross-links (Franken berg et al. 1981, Oleinick et al. 1987) and local com binations of all of these. A characteristic featu re of ionizing radiations is thought to be their ability to prod uce clustered dam age over the dim ensions of the DN A helix and larg er. The present calculations concentrate on radiation dam age to DN A because of its proven role in induction of m utation (Thacker 1992), chrom osom e aberrations (N atarajan et al. 1994), cell inactivation and other cellu lar eå ects dep endent on genom e integrity (Ward 1988). Sim ilar techniques could be applied to other cellu lar m olecu les if these are dem onstrated to be im portant, initial targets for radiation dam age that can lead indirectly to DN A and cellu lar eå ects possibly via induction of genom ic instability or other cell signalling pathways. Previous studies using M onte-C arlo track-structure techniques have dem onstrated , w ith no a priori assum ptions as to the subcellu lar target structures, that particular ionization clustering prop erties of radiation over dim ensions of 2 ± 10 nm , m ay be of prim e im portance in determ ining the biological eå ectiveness of diå erent radiations (G oodhead and B renner 1983, G oodhead and C harlton 1985) and that clustered dam age occurs in DN A at suæ ciently high frequ encies to be of potential relev ance (N ikjoo et al. 1989, G ood head and Nikjoo 1989, Nikjoo et al. 1991). Su bsequent track analyses using a volum e m odel of DN A in com parison w ith experim ental data

0955 ± 3002/97 $12.00 Ñ 1997 Taylor & Francis Ltd


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allow ed estim ation of the direct energy dep osition req uired for strand breakage (Charlto n and H um m 1988) and of the consequent yield s of ssb and dsb by diå erent radiations (Charlto n et al. 1989). M odelling of radiation-induced DN A dam age using M onteC arlo track-structure m ethods has also been carried out in diå erent w ays at several other centres (e.g H olley et al. 1990, M ichalik 1992, Terrissol 1994, Zaider et al. 1994, Tom ita et al. 1994). The calculations of C harlton et al. (1989) concentrated on the direct interac tions of the tracks w ith DN A and did not explicitly tak e into account the com plem entary eå ects of w ater radicals and in particu lar hydroxyl radicals generated by ionization s and excitations in w ater around the DN A. To provide a m ore advanced m odel of the action of ionizing radiation in DN A the previous approach has been exten ded for low energy elec tron irradiations to includ e the action of radical species generated in w ater around the DN A m olecu le. The tim e dom ain of the present calculations exten ds from about 10 Õ 15s to 10 Õ 9s covering the physical, physico-chem ical and chem ical stages of the interac tion of radiation w ith DN A in a cellu lar environm en t that lim its the radical lifetim es (Ward 1988). The paper consid ers the dam age prod uced by `direct’ energy dep osition in the DN A volum e and also the ìndirect’ contribution of the diå using hydroxyl radicals from the w ater surrounding the DN A, responsib le for the scavengeable com ponent of the DN A dam age (Ward 1991, O’ Neill and Fielden 1993). The role of hydroxyl radicals and their relativ e contribution to the yield s of strand breaks has been rev iew ed (von Sonntag 1987, Ward 1988). A ssum ing that additives added to cells act as OH -rad ical scavengers, the yield of cellu lar strand breaks induced by OH radicals dep ends up on radiation qu ality (Chapm an et al. 1979, deL ara et al. 1995). The reactions of all m ain radical species w ere consid ered, w ith radical diå usion being follow ed around the DN A from distances of ~ 4 nm w hich m im ic the radical diå usion distances in a cellu lar environm en t for low LET radiations ( ~10 Õ 9s) (Roots and Okada 1975, C hapm an and G illespie 1981). In this w ay the com plexity of radiation-induced strand breaks has been estim ated , includ ing the relativ e contributions of direct action and w ater radicals.

2. M etho d s

2.1. M onte C arlo E lectron transport co de for the phy sical and chem ical events The M onte C arlo track structure sim u lation code C PA 100 (Terrissol and B eaud reÂ 1990) w as used to

follow the history of electron interac tions in liquid w ater. The code C PA 100 can generate elec tron tracks w ith initial energies from 10 eV up to 100 keV. The code follow s the prim ary and all the secondary elec trons generated in liquid w ater until they are therm alized , recording the co-ordinates of all inelastic interac tions, the am ou nt of energy dep osited at the point of interac tion, the typ e of interac tion and the tim e of generatio n of initial radical species. The cross-sections used in the physical stage (10 Õ 15s) have been com piled using variou s sources. The ionization cross-sections w ere derived from experim ental data and dielectric response function for the four outer shells of a w ater m olecu le (Terrissol et al. 1989, for a sum m ary see Nikjoo et al 1994b ). In the pre-chem ical stage (10 Õ 15s± 10 Õ 12s) the ionized and excited w ater m olecu les undergo several reactions lead ing to the form ation of free radical species and m olecu lar prod ucts. Su b-excitation elec trons, electrons w ith kinetic energy less than the ® rst excitation potential (7´4 eV ), m ay recom bine w ith the parent ion accord ing to the Onsager-D eb ye theory or therm alize losing their energy by successive scatterin g in the m edium until they are in equ ilibrium w ith the surrounding m olecu les lead ing to the form ation of hydrated elec trons. The calculated yield of radical and m olecu lar species (e aq , OH ¯ , H ¯ , H +, OH Õ , H 2 , H 2O 2 )(B eaudreÂ 1988) at diå erent tim es has been shown to be in reasonable agreem ent w ith the pu blished experim ental data ( Jonah et al. 1976, Su m iyoshi and K afay am a 1982). 2.2. G eneral outline The startin g point of the present calculations of the spectra of DN A dam age is the sim u lation of larg e nu m bers of individu al electron tracks by follow ing, w ith the code C PA 100, all the interac tions that occur stochastically du ring slowing dow n of the elec tron in w ater du ring the physical stage on a tim escale of 10 Õ 15s, follow ed by rapid reactions du ring the physico-chem ical stage and the generatio n of the w ater radical species w ithin 10 Õ 12s. The coordinates and identities of the physical interac tions constitute the `physical track’ and of those of the radical species and m olecu lar prod ucts as the `chem ical track’. The conceptual fram ew ork of the scoring m ethod is then to place a single electron track in both its `physical’ and `chem ical’ form to start at the centre of a virtual sphere, larg e enough to contain any one of the entire tracks (to achieve electronic equ ilibrium ), and then to position random ly a linear segm ent of DN A (or target cylinder) along a chord through the sphere (Figure 1). A search w as m ade of the physical track to ascerta in if any initial physical interac tions (i.e.


M odelling D N A dam age

469

Figure 1. Diagram illustrating the `virtual sphere’ enc losing a sim ulated elec tron trac k and crossed by the scoring cylinders along chord s, positioned at random . The inner cylinder w ith diam eter d = 2´3 nm represents a linear `DNA segm ent’ of canonica l B -DNA . A round this is a `cylindrical shell’ , of thickness `r’ w ithin w hich radical diå usion and reactions are follow ed. The thickness r w as set to 4 nm in the m ain calc ulations.

ionizations and excitations) w ere in the volum e of the DN A. A ny such interac tions w ere classi® ed as a `direct hit’. A round the DN A segm ent, as illu strated in Figure 1, a `cylindrical shell’ w as bu ilt as a w orking volum e for potential diå usion of radical species of the chem ical track towards the DN A. The cylin drical shell lim its the need to follow those radicals w hich start or m ove so far from the DN A that they have little chance of reaching the DN A in the available tim e. The radiu s of the cylin drical shell w as set to m im ic the averag e diå usion length of radicals in a cellu lar environm en t (Roots and Okada 1975) (4 nm , bu t the eå ect of vary ing this param eter w as also investigated). Su bsequently , all radical species in w ater surrounding the DN A, w ithin the boundary of the cylin drical shell, w ere diå used from 10 Õ 12s to 10 Õ 9s. The reactions of radical species w ere assum ed to be diå usion controlled . The rate constants (k) and the reaction distances (R AB ) are sum m arized in Table 1 (Buxton et al. 1988), w ith the reaction distan ces being calculated accord ing to the relatio nship k =4 p (D A + D B )R AB (Chatterjee and H olley 1993, Terrissol and B eaud reÂ 1990). The coeæ cien ts of diå usion (D ) and yield of radical species obtained for tracks generated by the code C PA 100 in w ater for variou s elec tron energies used in this w ork are pre-

sented in Table 2. A ll radical species w ere assum ed to diå use accord ing to Sm oluchowski by allow ing a jum p step du ring a short interval such that L = Ó (6D t), w here L is the step size, D is the diå usion constant and t is the tim e interval for diå usion startin g at 10 Õ 12s. The tim e t w as set such that the step size L w as 0´1 nm . If tw o radicals reacted w ithin the cylindrical shell, both w ere rem oved from the environm en t and the products w ere given a new random position w ithin the reaction radiu s. Sim ilarly, if a radical left the cylindrical shell it w as rem oved from the system . C oordinates w ere recorded of any OH radical reaching the DN A segm ent; these w ere classi® ed as ìndirect hits’ . For good statistical sam p ling the proced ure w as rep eated for a larg e nu m ber of DN A segm ents for each of a larg e nu m ber of elec tron tracks. DN A segm ents w ere generated as cylindrical chord s cutting the virtual sphere using the m ethod of m u-rand om ness (Kellere r 1975). Random ® llings of the virtual sphere w ith suæ cient DN A segm ents w ere m ade such that for each electron track the total volum e of segm ents w as equ al to the volum e of the virtual sphere. These m ethods and consistency tests have been described previously in detail (N ikjoo et al. 1989,1991). A s before, to ensure uniform random

470

H . N ikjoo et al. Table 1.

k dm 3m ol Õ 1s Õ

Reaction ¯ OH + ¯ OH

6Ö 2´5 Ö 2´0 Ö 4´5 Ö 2´3 Ö 1´0 Ö 2´5 Ö 2´5 Ö 1´7 Ö 1´9 Ö 1´3 Ö 2´0 Ö 1´3 Ö 1´0 Ö 2´0 Ö 2´0 Ö 2´0 Ö 1´0 Ö 2´0 Ö

H 2O 2 OH Õ aÕ q ¯ OH + H ¯ H O 2 ¯ OH + H H + H O 2 2 ¯ OH + H O H O + H O 2 2 2 2 ¯ OH + H O O + H O 2 2 2 eaqÕ + eaÕ q H 2 + O H Õ eaqÕ + ¯ H H 2 + O H Õ eaqÕ + H + H eaqÕ + O2¯Õ eaqÕ + H 2O 2 OH + O H Õ eaqÕ + H O 2 H O 2Õ eaqÕ + O2Õ H O2Õ + O H Õ ¯H + ¯H H 2 ¯H + O H O 2 2 ¯H + O H Õ eaqÕ + H 2O ¯H + H O H O 2 2 2 ¯ H + H O ¯ OH + H O 2 2 2 ¯H + O H O 2Õ 2Õ


¯ OH + e

Table 2. 10 Õ ¯ OH

5

D cm 2s Õ

2´8 4´5 7´0 9´0 5´0 2´2 2´0 2´1 5´0

eaqÕ ¯H Haq+ H2 H 2O 2 H O2 O2 OHÕ

1

M axim um reaction distance nm

1

10 9 10 10 10 10 10 7 10 7 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 7 10 10 10 8 10 10

Referenc es

0´2820 0´9054 0´5395 0´0015 0´0012 0´5500 0´1620 0´5740 0´3320 0´7600 0´5120 0´8120 0´5200 0´1899 0´5810 0´0004 0´5860 0´0028 0´5810

Schw arz 1969 Schw arz 1969 Schw arz 1969 Dorfm an and M atheson 1965 B urns et al . 1981 Farhataz iz 1977 Schw arz 1969 Schw arz 1969 Schw arz 1969 A nbar and Farhataz iz 1975 Schw arz 1969 B urns et al . 1981 A nbar et al . 1973 Schw arz 1969 Dorfm an and M atheson 1965 A nbar et al . 1973 A nbar et al . 1973 A nbar et al . 1973 B oyd et al . 1980

Coeæ cients of diå usion* and yields of radicals and m olecu lar spec ies at 10 Õ

100eV

300eV

500eV

1keV

4´95 5´17 1´88 4´17 0´45 0´99 ± ± ±

4´98 4´65 1´83 4´31 0´39 0´97 ± ± ±

4´97 4´54 1´78 4´34 0´39 0´96 ± ± ±

4´98 4´45 1´81 4´34 0´38 0´95 ± ± ±

12

s

1´5keV

4´5keV

4´95 4´44 1´77 4´37 0´37 0´97 ± ± ±

4´96 4´41 1´77 4´38 0´38 0´98 ± ± ±

*Data from Schw arz 1969 and B urns et al . 1981.

® lling of the sphere, sam p lin g of interac tions by DN A segm ents w as tested by com paring the ratio of total energy dep osited in the virtual sphere to that dep osited directly in all segm ents. Other tests to ensure good statistical sam p ling includ ed com parison of the frequ ency-averaged m ean speci® c energy, zÅ F , calculated from the scored frequ ency distribution, in DN A segm ents of length 2´3 nm and 2´3 nm diam eter, as zÅ F =

P

2

0

z f (z) dz /

P

2

0

f (z) dz w ith the scored absolute

frequ ency of all energy dep ositions, f ( >0). For perfect scoring f ( >0) should be identical to 1/zÅ F . A lso com puted w as the dose-w eighted m ean speci® c energy

zÅ D =

P

22

z f (z)dz /

0

P

2

f (z) dz (ICRU36 1983, Goodhead

0

1987). Figure 1 dem onstrates the conceptual fram ew ork of the m ethod used for scoring both the direct energy dep ositions and the diå usion of radical species. In this w ay a com plete record of locations of all hits in DN A, eith er by direct ionization s and excitations or by OH radicals w ere m ade on each DN A segm ent. These scoring calculations provide the initial positions of the variou s hits, and then from these the consequent DN A dam age is estim ated and classi® ed as described in §2´4 ± 2´6. Figure 2 shows the dep endence of DN A



Figure 2. Variation of the num ber of O H radical-induced DNA breaks w ith the thickness of the diå usion shell as show n in Figure 1. Radical spec ies generate d by 1´5 keV elec trons at 10 Õ 12s and contained in the diå usion shell w ere diå used from 10 Õ 12s to 10 Õ 9s. A ny O H radical reaching the DNA volum e w as assigned a probability 0´13 to produce a strand break (see Sec tion 2.5).

interac tions w ith OH radicals on the assum ed thickness of the cylin drical shell around the DN A (using the DN A m odel and pathway assum ptions described in §2´3 ± 2´5). A ll com putations w ere carried out on a very fast cpu includ ing the Su percom puter C ray at the Rutherford-A ppleton Laboratory. 2.3. M odel of D N A The volum e m odel of DN A is as used in our previous calculations (Charlto n et al. 1989, Nikjoo et al. 1994a). The DN A m odel, w hich has the sam e dim ensions as a canonical decam er B -DNA (Dickerson et al. 1982), consists of a cylin der divided into regions of sugar-p hosphate m oiety and bases w ithout specifying the detailed atom ic structure of the oligonucleotide. The sugar-p hosphate chain w hich w raps helically around the central cylinder w ith a diam eter of 1 nm has a helical tw ist of 36 ß . The diam eter of the DN A m olecu le is 2´3 nm and the rise for each doub le helical turn is 0´34 nm per base pair. The m odel structure im plicitly includ es the ® rst hydration shell of the DN A. In these calculations w e assum e the charge resulting from any reaction/ intera ction w ith the bound w ater layer is transferred to the DN A (La Vere et al. 1996) 2.4. E nergy to produce a strand b reak b y direct interactions For the m ain calculations the criter ion assum ed for the prod uction of a ssb by `direct’ action is that breakage occurs w hen energy dep osited by a track

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stochastically in one sugar-p hosphate volum e of the m oiety exceeds an energy dep osition threshold of E ssb= 17´5 eV . This valu e has previously been estim ated by m odellin g of the 125I experim ental data of M artin and H aseltine (1981) by C harlton and H um m (1988). U sing a diå erent scoring proced ure and 125I A uger electron spectrum (Terrissol 1994) Pom plun (1992) re-ev aluated E ssb and qu oted a valu e of about 18 eV w hich is not signi® cantly diå erent. Recent analysis of m ore exten sive data (Kandaiya et al. 1996) showed good agreem ent w ith the valu e of about 17´5 eV (N ikjoo et al. 1996). The present calculation assum es no m igration of energy along the DN A. Som e prelim inary estim ates have been m ade also of base `dam age’ , using the sim p li® ed assum ption that this results w hen direct energy dep osition reaches a threshold of 17´5 eV in the base. Variation of strand break yield w ith threshold energy E ssb w ill be discussed further in §4. 2.5. Pathw ay to induce a strand b reak b y O H radicals Once the OH radicals reach the DN A, they are no longer diå used and are assum ed to react eith er w ith the sugar phosphate or the nu cleobase to yield sugar or base radicals. Not all sugar radicals lead to strand breaks (von Sonntag 1987, M urthy et al. 1988). A n assum ption is m ade that the subsequen t dam age distribution betw een the sugar-p hosphate and nu cleobase is 20 580 based up on the ® ndings of Scholes et al. (1969). That 20 % of OH radicals react w ith sugar-p hosphate w as also ded uced from phosphate end -group s releas ed. M illigan et al. (1993) estim ated that the eæ ciency of ssb form ation per OH radical interac tion is about 13 % (see Section 3.4). Other estim ates for ssb per ¯ OH interac tion range from 0´14 to 0´22 (van Rijn et al. 1985). Our m ain calculation assum ed an activation prob ability of 0´13 as the eæ ciency for induction of ssb per OH radical interac tion w ith DN A. This is im plicitly com posed of a 20 % probability that an ¯ OH that reaches the DN A w ill react w ith a sugar-p hosphate (i.e. 80 % w ith a base) and a 65 % probability that the resulting sugar radical w ill lead to a strand break. A range of activation eæ ciencies for the induction of strand breaks per OH radical reaction w ith the DN A (O H activation probability ) via the sugar-p hosphate has been investigated, by vary ing the valu e from 0´002 to 0´20 in the calculations. It w as assum ed that hydrated elec trons and H atom s react m ainly w ith the bases (von Sonntag 1987) to produce base radicals and therefo re do not prod uce strand breaks (Deeble et al. 1990). A dditional m echanism s such as charge and energy transfer w ithin the DN A or collective excitation w ere not consid ered. For this paper it has

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been assum ed that base m odi® cation does not lead to sugar dam age. For prelim inary estim ates of base dam age it is assum ed that all the OH radicals that react w ith a base (i.e. 80 % ) result in `dam age’ .


2.6. C lassi® cation of D N A b reaks The tw o altern ative classi® cation schem es used for DN A breakage, Figure 3, consid er dam age in DN A as (A ) the patter ns of breaks accord ing to the com plexity of dam age (single, doub le and their m ajor com binations) on one or both strand s and in (B) the breaks have been classi® ed accord ing to the origin of the breaks eith er from direct energy dep osition or reactions of OH radicals. The top and bottom lines in each diagram of Figure 3 rep resent a 2-dim ensional projection of the doub le helix sugarphosphate backbone and the tw o m iddle dashed lines rep resent the individu al bases. Vertically the tw o centre dashes and the corresponding sugarphosphates on the top and bottom strand s form a 2-dim ensional projection of a nu cleotide pair. The m axim u m distance betw een tw o ssb on com plem entary strand s w hich are classed as producing a doub le strand break w as set at 10 base-pairs (see Discussion). In each of the tw o schem es only one class of dam age w as assigned to each linear segm ent of DN A through the virtual sphere. A related qu antity is the ratio of yield of base `dam age’ (BD) (base radicals) to sugar-p hosphate dam age (SPD ). In a third classi® cation schem e (h and i of Figure 3(B )) the dam age to sugar or base has been shown by a cross. Prelim inary estim ates of the ratio B D/SPD w ere calculated eith er by counting independ ently all hits that lead to dam age in bases or sugar-p hosphates (diagram (h)), or by counting those segm ents of DN A that contain at least one base dam age or at least tw o strand breaks, one on each strand w ithin < 10bp (diagram i)). This latter ratio should be m ore com parable w ith the experim entally m easurable qu antity . 3. R e sults

3.1. S tochastic distrib ution of energy depo sition in D N A The track sim u lation s w ere used ® rst to evalu ate the cum u lative absolute frequ ency distributions of direct energy dep osition in short (2´3 nm long) DN A segm ents random ly positioned in liquid w ater uniform ly irradiated by m onoenergetic low energy elec trons (Figure 4). These liquid-w ater results allow com parison w ith earlier calculations using w atervapour codes (N ikjoo et al. 1991) and con® rm that there are signi® cant nu m bers of severely -h it segm ents

of cellu lar DN A. It is, therefo re, w orthwhile to investigate in detail the spectrum of m olecu lar dam age that m ay result from this direct action, plus the additional dam age from diå using hydroxyl radicals. In addition, Figure 4 shows that the frequ encies for m oderate energy dep ositions of a few tens of eV are fairly independ ent of prim ary electron energy bu t that larg er energy dep ositions are m ost likely to occur w ith the low er energy elec trons, subject to their inherent lim itation of total energy. Table 3 provides basic inform ation from the track structure codes and the scoring on the nu m bers of ionization s, total nu m bers of inelastic interac tions (ionizations and excitations), nu m bers and frequ encies of 2´3 nm long segm ents hit and consequent frequ ency m ean and dose-w eighted m ean speci® c energies in the targets. C alculations have been m ade for longer DN A segm ents in m ultiples of 2´3n up to n = 8. For a good approxim ation and segm ents lengths longer than 36´8nm scaling is applied. The m ean speci® c energies presented agree w ith the theoretical criter ia presented in §2.2. 3.2. R ange and distrib ution of dam age in D N A segm ents The hypothesis underly ing the biological signi® cance of clustered dam age is that the m ore com plex the dam age to DN A the m ore diæ cult it is to rep air and the m ore likely it is to lead to perm anent consequences (G oodhead et al. 1980, Ward 1988, G ood head 1991). Therefor e, in this section w e exam ine the spatial exten t and distribution of hits in long DN A segm ents for irradiation w ith m onoenergetic elec trons of 100 eV to 4´5 keV. For each hit in a random ly oriented DN A segm ent (Figure 1) from a track interac tion (ionization, excitation and OH radical), a set of spatial coordinates, energy dep osited , and typ e of interac tion (direct or OH ), w as recorded . Figure 5 shows a variety of illu strative exam ples of diå erent typ es of DN A dam age found in long segm ents (216 base pairs or 73 nm long) of DN A caused by direct energy dep osition or diå usible OH radicals. The selected exam ples show hits w ithout breakage and w ith sim p le and m ore com plex typ es of ssb and dsb. A strik ing featu re of the full set of data is the larg e variability of the typ es of clustered dam age that result ev en from sim ilar nu m bers of hits or sim ilar qu antities of energy dep osited in a DN A segm ent (data not shown). To obtain the distribution of lengths of the dam aged sites, long segm ents of DN A (216 base pairs) containing hits w ere analysed. The frequ ency distribu tions of the lengths of dam age sites w ere obtained by m easuring the nu m ber of base pairs betw een the



473

Figure 3. Classi® cation schem e of DNA breaks accord ing to com plexity (A). These include: segm ents that w ere hit but have `no break’ (NB) i.e. none of the hits by direct energy deposition or by hydroxyl radicals lead to a strand break, ssb alone (`ssb’ ), two ssb on the sam e strand (`ssb +’ ), two or m ore ssb on opposite strand s but suæ ciently separated ( > 10 bp) as not to be classi® ed as a double strand break (`2ssb’), two single strand breaks on opposite strand s but w ith a separation < 10 base pairs to constitu te a double strand break (`dsb’ ), a double strand break accom panied by one (or m ore) additional single strand break w ithin ten base pair separation (`dsb +’ ), and ® nally m ore than one double strand break on the segm ent w hether w ithin the ten base pair separation or further apart (`dsb ++’ ). Each hit DNA segm ent is allocate d to only one class of dam age, w ith the m ost com plex option (as ordered in Figure 3(A )) having precedence. O nly one assignm ent, starting from the bottom of the diagram , w as given to any one full-length segm ent of hit DNA . Various exam ples are show n in Figure 5. B ase dam age is not consid ered at all in this classi® cation schem e. Classi® cation schem e of the DNA breaks accord ing to their cause (B), either from direct energy deposition (D) or from the diå using O H radicals (I). `ssb D’ and `ssb I’ w ere assigned for one or m ore single strand breaks in the segm ent by direct eå ect (D) alone or by O H radical (I) alone, respectively, on one of the two strand s. In a sim ilar m anner dsb (break s on opposite strand s w ithin < 10 bp) w ere classed as arising solely from direct eå ect (`dsb D’ ) or solely from indirect eå ect of O H radicals (`dsb I’ ). A dditional classes of ssb and dsb arise from a m ixture of breaks originating from direct energy deposition and the O H radicals on one or both strand s. If on the sam e strand only there w ere direct and indirect breaks this w as classed as m ixed (`ssb m’ ). The hybrid dsb (`dsb hyb’ ) w as consid ered to be depend ent on a direct break in com bination w ith an indirect break. This w ould include sim ple cases such as one break of each type, on opposite strand s, or m ore breaks. The essentia l featu re of `dsb hyb’ is that total elim ination of indirect processes w ould elim inate this from being a dsb. If a com plex double strand break arose from any other com bination of direct and indirect breaks w ithin 10 bp, it w as classi® ed as m ixed (`dsb m’ ). O nly one assignm ent, starting upw ards from (g ) to (a), w as given to any one full-length segm ent of hit DNA . Exam ples of ssb I , ssb D , ssb m are show n in the 4th, 6th and 8th segm ents, respectively, of Figure 5. B ase dam age is not consid ered at all in this classi® cation schem e. Diagram s (h) and (i) are not part of this schem e, but are for prelim inary estim ation of the total am ount of base dam age relativ e to strand breaks (see text).

tw o farthest dam age sites in a larg e nu m ber ( >10 4 ) of segm ents. Figure 6 shows the frequ ency distribution for 1´5 and 0´3 keV electrons. The data show

that m ost DN A segm ents have a very short hit region w ith m ost dam age being in a single base pair, bu t 38 % of hit segm ents have dam age exten ding


474

H . N ikjoo et al.

Figure 4. Frequenc y distributions of energy deposition in a target corresp onding in size to a short linear segm ent of a canonica l B -DNA , 2´3 nm diam eter and 2´3 nm length, in w ater irradiated w ith m onoener getic elec trons of initial energies 100 eV, 300 eV, 500 eV, 1 keV , 1´5 keV and 4´5 keV . The left ordinate gives the absolute frequency f ( > E ) of deposition events greater than the energy E in the target volum e w hen random ly placed in w ater uniform ly irradiated w ith 1 G y of the given radiation. The right ordinate is the corresp onding averag e num ber of events in such DNA segm ents in a typical m am m alian cell, assum ing the nucleus contains 6 pg of DNA and is com posed of base pairs of m olecu lar w eight 660 and length 0´34 nm (G ood head and Nikjoo 1989). Table 3. Prim ary elec tron energy

Track scoring and energy deposition param eters in a 2´3 nm by 2´3 nm DNA segm ent

No. of interactions ( per prim ary elec tron)

(eV )

A

B

M

100 300 500 1000 1500 4500

12´7 36´8 128´2 249´9 373´2 1121´2

5´0 15´5 25´5 49´9 72´7 200´4

5´837 16´164 27´604 55´384 86´139 266´25

f( > 0) (G y Õ 1 target Õ 1 ) 3´486 Ö 10 Õ 6 3´216 Ö 10 Õ 6 3´294 Ö 10 Õ 6 3´304 Ö 10 Õ 6 3´426 Ö 10 Õ 6 3´529 Ö 10 Õ 6

zÅ F (G y) 2´8 Ö 3´0 Ö 2´9 Ö 2´9 Ö 2´9 Ö 2´7 Ö

10 5 10 5 10 5 10 5 10 5 10 5

zÅ D (G y) 5´7 Ö 6´8 Ö 6´4 Ö 6´4 Ö 6´2 Ö 4´8 Ö

10 5 10 5 10 5 10 5 10 5 10 5

Total num ber of trac ks scored : 1000 for each prim ary energy excep t 100 for 4´5 keV . A -M ean num ber of inelastic interactions (ionizations +excitatio ns) per prim ary elec tron (therm alized and dead elec trons not included). B -M ean num ber of ionizations per prim ary elec tron. M -M ean num ber of short (2´3 nm long) DNA segm ents receiving direct hits per prim ary elec tron for total random ® lling of the virtual sphere.

occasionally out to > 30 bp . H olley and C hatterjee 1996 have recently calculated the frequ ency of larg er fragm ents obtained by heavy ion irradiation of chrom atin DN A. Figure 7 shows the frequ ency distribution of the total nu m ber of dam aged sites in the segm ents of DN A. The distributions show that the

averag e nu m ber of dam ages is usually sm all, being m ost frequ ent for a single dam age and decreasing qu ite rapid ly for clusters of higher order. Nev ertheless about 33 % of dam aged sites have tw o or m ore lesions. Figures 6 and 7 tak en together dem onstrate that the predom inant dam age is sim p le (e.g. lone ssb)



475

Figure 5. Various exam ples of sites hit directly and indirectly by a trac k of 300 eV elec trons. The diagram s show only the hit regions of the DNA . In these diagram s the three horizontal dashed lines represent the two sugar-phosphate s (S-P) and the base regions (B) of the DNA . A set of vertical pixels represents a nucleotid e base pair. The top and bottom pixels represent the two sugarphosp hate backbones and the m iddle show s the com plem entary bases com bined. The closed rectangles show the sites w here direct hits of energy deposition > 17´5 eV caused a ssb. The open rectangles show the sites w here a ssb is induced by a diå usible O H radicals on reaction w ith DNA w ith a probability of 0´13. Sites of direct hits w ith energy deposition below the threshold energy are show n as `1’ for 10 ± 17´5 eV and `-’ for < 10 eV. Classi® cation of dam age is desc ribed in legend for Figure 3(A ).

bu t that there is a signi® cant proportion of m ore com plex dam age. 3.3. F req uencies of sim ple and co m plex strand b reaks The exam ples of dam aged segm ents in Figure 5 illu strate the variety of typ es of DN A dam age induced

by ionizing radiations. These w ere then classi® ed for com plexity of com binations of strand breaks. A larg e nu m ber of random DN A segm ents, about 10 4 , such as those in Figure 5, containing at least one hit, w ere analysed and classi® ed accord ing to the schem e of Figure 3(A ) (Section 2.6) to obtain statistically m eaningful nu m bers on the yield of strand breaks and


476

H . N ikjoo et al.

Figure 6. Frequenc y distribution of length of dam aged sites for 1´5 and 0´3 keV elec trons. For this diagram `dam age’ w as evalu ated as: any direct hit that induces a break (i.e. > 17´5 eV), any O H that reache s the DNA and induces a break (activation probability 0´13) or that reacts w ith base ( probability 0´80) to form a base radical.

Figure 7.

Frequenc y distribution of num ber of dam age sites in segm ents of DNA by 1´5 and 0´3 keV elec trons. `Dam age’ w as evalu ated as in Figure 3.

477


M odelling D N A dam age their typ es for each electron energy. The yield of strand breaks from these calculations is a function of the assum ed threshold energy (E ssb ) and of the OH activation prob ability of giving a ssb on interac tion w ith DN A. E ssb w as set at 17´5 eV (see Discussion) and the activation prob ability varied from 0´002 to 0´20. Table 4 presents data for the relativ e yield s of diå erent typ es of strand breakage by 300 eV elec trons as a function of OH activation probability . In all cases 1000 electrons w ere set in m otion to obtain statistically m eaningful sam p lin g of electron tracks and DN A segm ents, except at 4´5 keV w ith 100 elec trons because scoring of longer range electrons is rather tim e-consum ing w ith the m ethod used. For the latter, a com prom ise betw een scoring tim e and nu m ber of elec trons w as m ade (see Nikjoo et al. 1991). Table 5 shows the calculated relativ e yield s of diå erent typ es of strand breaks for other prim ary elec tron energies, w ith the OH activation probability ® xed at 0´13. The data in Tables 4 and 5 show that Table 4.

the m ajority of hits in DN A do not lead to dam age in the form of strand breaks. W hen breaks do occur, they are m ost frequ ently sim p le ssb, bu t for dsb a substantial proportion are eith er dsb + or dsb ++, w hich are the m ore com plex form s of a dsb accom panied by at least one additional strand break w ithin 10 bp . This is the case for all prim ary elec tron energies tested , from 100 eV to 4´5 keV. The data in Tables 4 and 5 do not tak e into accou nt any role of base dam age in DN A strand break induction or dam age com plexity nor do they record the base m odi® cations. Therefor e these data provide only a low er lim it to the com plexity of the clustered dam age. 3.4. R elative co ntrib utions to strand b reak y ield b y direct and indirect eå ects The scoring m ethod (Section 2.2) also allow s for the source of each hit in DN A to be identi® ed. The hit DN A segm ents w ere analysed for dam age typ e

Relativ e yields of strand breaks of diå erent com plexity as a function of ¯ OH activation probability for 300 eV elec trons

O H activation probability

`No B reak ’

ssb

ssb +

2ssb

dsb

dsb +

dsb ++

%

#DNA segm ents hit

62´9 66´4 69´8 73´0 75´7 76´1

29´7 26´6 24´5 21´1 19´7 18´7

3´97 3´29 3´23 2´28 2´72 2´48

0´478 0´425 0´348 0´282 0´209 0´212

2´79 2´38 2´17 2´06 1´84 1´77

1´07 0´849 0´807 0´659 0´743 0´696

0´141 0´091 0´098 0´054 0´061 0´048

15655 15300 15241 14873 14805 14657

%

0´20 0´13 0´10 0´04 0´02 0´002

%

%

%

%

%

A ll percentages are relativ e to the total num ber of DNA segm ents hit. Elec tron Energy = 300 eV. E ssb= 17´5 eV. Table 5.

Relativ e yield of strand breaks classi® ed by com plexity (see Figure 3)

No break

ssb

ssb +

2ssb

dsb

dsb +

dsb ++

com plex dsb/ total dsb

Y ssb G y Õ 1Da Õ 1 Ö 10 Õ 10

Ydsb G y Õ 1Da Õ 1 Ö 10 Õ 11

100

73´9

22´4

1´86

0´089

1´39

0´269

0´0149

17´0

300

66´4

26´6

3´29

0´425

2´38

0´849

0´0915

28´3

500

68´7

25´4

2´78

0´469

1´86

0´792

0´0697

29´1

1000

68´9

25´2

2´75

0´501

1´81

0´712

0´0814

31´7

1500

70´5

24´3

2´39

0´400

1´68

0´626

0´0739

29´4

4500

71´4

24´1

2´13

0´288

1´47

0´553

0´0411

28´8

2´5 ± 2´5 ± 2´5 ± 2´4 ± 2´4 1´5b 4´4 ±

1´5 ± 2´3 1 .6 a 2´0 ± 2´0 ± 1´8 1´3b 2´9 ±

Energy eV

%

%

E ssb= 17´5 eV. A ctivation Prob ability = 0´13. Experim ental data in italic. b Franken berg et al . 1986. b O’Neill et al . 1997.

%

%

%

%

%

%


478

H . N ikjoo et al.

accord ing to the classi® cation in Figure 3(B ) (§2.4). Table 6 presents data for the relativ e yield s of strand breakage for irradiation by elec trons of initial energies 100 eV ± 4´5 keV. The data presented here are from the analysis of the identical hit segm ents as in Table 5 (§3.3), bu t regrouped for this diå erent classi® cation schem e. A s before, the threshold energy to induce a ssb w as set at 17´5 eV and the activation prob ability at 0´13 for OH radicals. Data are presented for total nu m bers of single and doub le strand breaks by OH radicals and by direct energy dep osition in sugar-p hosphate. The data show that for all these low energy electrons, the m ain contribution to strand breakage in a cell-lik e environm en t em anates from direct energy dep ositions. H owever, there is a signi® cant contribution from OH radicals both to the total nu m bers of ssb and dsb and also to increases in their com plexity . B ase dam ages have not been includ ed in any of the above analyses, ev en though they can add to the local com plexity of strand breaks. A prelim inary estim ate of the ratio of base `dam age’ to sugarphosphate breakage is includ ed in Table 6, based on classi® cation ì’ of Figure 3. Dep endence on assum ed activation probability , re¯ ecting diå erent environm en tal scavenging conditions, w as investigated by obtaining strand break Table 6.

E (eV ) 100 300 500 1000 1500 4500

data for activation probabilities from 0´002 to 0´20 for diå erent electron energies. Table 7 presents the data for 300 eV electrons showing how red uction of activation probability decreases the OH radical contribution to total strand break yield and in the lim iting case m im ics the situation w hen OH radicals are entirely absent from the system or have been entirely scavenged before reaching the DN A. For direct eå ects, the dep endence on the threshold energy param eter, E ssb , w as investigated. Table 8 dem onstrates the variation of yield of strand breaks w ith the valu e of E ssb from 12´6 eV to 30 eV for elec trons of initial energy 300 eV . For this com parison the OH activation probability w as set at zero to allow analysis of direct-action breaks only. Sim ilar trend s w ere obtained for other elec tron energies. It Table 8.

Variation of num bers of strand breaks w ith threshold energy for direct eå ect only

E

E ssb (eV )

ssb

ssb +

300eV ` ` ` `

12´6 15´0 17´5 21´1 30´0

3727 2892 2730 1852 848

1050 445 374 115 18

Total ssb/ 2ssb dsb dsb + dsb ++ Total dsb 68 39 33 12 1

645 305 252 8 16

607 153 110 14 0

154 13 7 0 0

3´4 7´2 8´5 90 54

Relativ e yields of strand breaks classi® ed by cause of breaks (Figure 3B)

ssb OH

ssb D

ssb M

dsb OH

dsb D

dsb hyb + dsbm*

%

B D/SPD

total ssb

total dsb

33 32 34 35 37 37

66 66 65 62 62 62

1 2 2 2 2 1

11 10 11 11 12 15

75 71 77 73 73 74

14 19 12 16 15 11

2´2 2´0 2´1 2´1 3´2 3´4

1856 5719 9430 18513 27554 4209

112 510 744 1408 2039 236

%

%

%

%

%

Percentages are relativ e to total ssb or total dsb as appropriate. E ssb= 17´5 eV. A ctivation Prob ability = 0´13. *dsb m m ake only a sm all contrib ution. Table 7. OH A ctivation Prob ability 0´20 0´13 0´10 0´04 0´02 0´002 Elec tron Energy = 300 eV. E ssb= 17´5 eV.

Depende nce of strand breaks yields on activation probability for 300 eV elec trons ssb OH

%

40 32 26 13 7 ±

ssb D

ssb m

dsb OH

56 66 71 86 93 99

3 2 2 1

17 10 7 1 1 ±

%

%

±

±

%

dsb D

%

58 71 79 88 95 100

dsb hyb+ dsb m

%

B D/SPD

24 19 14 11 4 ±

1´8 2´0 2´2 2´5 2´7 2´9



is seen that as the valu e of E ssb increases the yield of ssb decreases qu ite rapid ly and the yield of dsb decreases even m ore rapid ly, resulting in an overall increase in the ratio ssb 5dsb from 3´4 to 90. In view of this strong dep endence on E ssb it is interesting to note that each of the E ssb valu es listed in Table 8 has been used by diå erent w orkers in other m odellin g studies of dam age to DN A. It is apparent that their results m ay have been heavily dep endent on their assum ed param eter valu e. 4. D isc ussion a nd co nclusio ns

The m odellin g and calculations presented here w ere carried out as a ® rst step towards m echanistic interp retatio n and prediction of radiation eå ect based on the spectrum of initial DN A dam age that can be com pared w ith experim ental inform ation by inclusion of dam age induced by diå usible w ater radicals prod uced near to the DN A. In principle there are three stages in the w ork. First, transport of the ionizing particle in the DN A environm en t; secondly, sim u lation of the biological target and thirdly, pathw ays lead ing to the induction of initial biological lesions. U ncertainties in each of these w ill be brie¯ y discussed. A nu m ber of com puter codes exist for sim u lation , at the m olecu lar level, of electron and ion transport in w ater. The ® rst approxim ation in these calculations and indeed in alm ost all m odellin g w ork of this nature assum es a close correlation betw een the physical prop erties of w ater and DN A (Inagaki et al. 1974, Ritchie et al. 1991) so that the track interac tions in w ater can be applied to direct eå ects in DN A. A sum m ary and com parison of w ater codes has been m ade by Nikjoo et al. (1994b) and Nikjoo and U ehara (1994). U se of liquid, rather than vapour code is essential for m eaningful consid eration of indirect eå ects, startin g w ith the initial yield s of w ater radicals. B iophysical calculations have used a variety of geom etrical volum es such as spheres and cylin ders to rep resent target biological m acrom olecules such as DN A, nu cleosom e and chrom atin ® bre. A s m ost biophysical m odels start on a sem i-em pirical basis, the sim p le geom etrical rep resentations have served a useful pu rpose to highlight featu res of potential relev ance, such as the critical im portance on patter ns of interac tion on the scale of a few nanom etres and of clustered dam age in DN A (G oodhead and B renner 1983, G ood head and Nikjoo 1989, Nikjoo et al. 1991). B ut advancing knowled ge and techniques now invite a m ore detailed m echanistic and m olecu lar approach and the degree of sophistication of m odels of biological targets have also increased (G oodfellow et al. 1994, U m ran ia et al. 1995). H owever, to apply in

479

detail all these advances sim u ltaneously w ou ld im plicitly introduce m any m ore assum ptions and uncertain param eters . The present calculations w ere carried out w ith the volum e m odel of DN A (Charlto n et al. 1989) w hich identi® es the general geom etric featu res of a B -DNA structure. In this m odel it w as assum ed that the w ater of hydration in the m ajor and m inor grooves is associated w ith the sugar-p hosphate. Therefor e, the m odel over-estim ates the volum e and m ass of the sugar-p hosphate m oiety . H owev er, this w as to som e degree com pensated for since radicals form ed in the prim ary hydration shell of DN A are believ ed to be transferred to the DN A (La Vere et al. 1996) thereb y acting essentially as direct eå ect. Furtherm ore, the param eter (E ssb ) for conversion of energy dep osition to breaks w as derived from experim ental data m odelled w ith this sam e volum e m odel of DN A (Charlto n and H um m 1988, Nikjoo et al. 1996). Ratio of ssb/dsb in Table 8 shows the sensitivity of the energetics of the DN A dam age w ith variation of threshold energy for induction of a ssb. The data con® rm s the choice of 17´5 eV as the m ost probable energy involved in production of a ssb by direct energy dep osition. The pathways to strand breakage w ere divided into tw o classes of direct (unscaven geab le) and indirect (scavengeable) eå ects on the basis of the volum e m odel of DN A, w ith the prim ary hydration shell of DN A im plicitly includ ed in the direct com ponent. W hat is the origin of the clusters of energy dep osition that lead to m ost doub le strand breaks? We have previously highlighted the role of low energy electrons (i.e. track end s) in the studies based on w ater-v apour track codes (N ikjoo and G oodhead 1991), suggested that clusters of energy dep osition of >~100 eV in DN A-like volum es correlate w ith dsb yield s for diå erent radiations (G oodhead and Nikjoo 1989, Nikjoo et al. 1991) and show that such energy dep ositions in low -LET irradiations arise m ostly from the com ponent of low energy secondary elec trons (G oodhead and B renner 1983, Nikjoo et al. 1989, 1991). From the present analyses w ith a liquid-w ater code, Table 9 shows the percentage of total energy dep ositions in short segm ents of DN A (216 bp length and 2´3 nm diam eter) from clusters of diå erent energy m agnitu de and the corresponding yield of dsb. It is seen that about 90 % of total energy dep ositions are du e to events less than 60 eV bu t the larg est dsb yield is du e to energy dep ositions in the range 60± 150 eV for all three electron energies. These are m ost likely to occur w ith the low er energy elec trons, w hich have the highest ionization den sity, and their strand breakage capability is increased through associated OH radicals w ithin the sam e cluster.

480 Table 9.

H . N ikjoo et al. Relativ e frequency of direct energy deposition in a DNA segm ent 216 bp long and of dsb for 300 eV, 1´5 keV and 4´5 keV elec trons Relativ e frequency of energy depositions

Relativ e frequency of dsb

%

Prim ary elec tron energy


300 eV 1´5 keV 4´5 keV

%

0 ± 60 eV

60 ± 150 eV

> 150 eV

0 ± 60 eV

60 ± 150 eV

> 150 eV

86 89 92

13 10 7

1 1 1

21 27 30

74 65 64

5 8 6

The ® rst attem pts to calculate absolute yield s of strand breaks from direct energy dep osition only, by C harlton et al. (1989) and H olley et al. (1990), produ ced results sim ilar to each other, and w ere encouragingly close to the pu blished experim ental data, despite diversity in approaches and assum ptions and uncertain ty in experim ental dep endence of dsb on LET. On the other hand, a recent rep ort (Tom ita et al. 1994) on relativ e yield of strand breaks using M onte C arlo track structure studies concludes that the m ajor contribution to the total yield is by OH radicals. C alculations of this nature are closely associated w ith the assum ptions m ade in the m odellin g. It is therefo re essential to identify the critical assum ptions and to obtain experim ental and theoretical data to validate the choices m ade. A long-stand ing qu estion in radiobiology has been the role of diå using radicals in DN A dam age by ionizing radiation ( see rev iew by C hapm an and G illespie 1981). This w ork has attem pted to shed ligh t on a nu m ber of qu estions by a system atic study of the role of OH radicals in and around DN A. A notab le featu re of the present results is the appreciable, bu t not dom inant, contribution by diå using OH radicals to the strand breakage of DN A irradiated by low energy elec trons (Table 6). M ore strik ingly, the data on the com plexity of dam age (Table 5) show clearly the featu re of ionizing radiation that m any dsb are com plex, involving m ore than tw o breaks. The proportion of these is about 30 % for all bu t the low est electron energy investigated. The present evalu ations have concentrated on strand breakage only. It is expected that the inclusion of base dam age w ill substantially increase the com plexity of dam age to DN A w ithin the sites of clustered ionization s that contain the dsb. The m odelling approach is being exten ded to ev alu ate the contribution of base dam age. C om parison of experim ental data for the yield of strand breaks and ratio of ssb/dsb have been m ade in Table 5 for A lK U SX (Botchway 1996) in V-79 cells and C K U SX (Franken berg et al. 1986) for yeast cells. A lthough there are som e variations in the yield of strand breaks for diå erent cell lines (O ’Neill et al. 1997) the expected valu es calculated are in reason-

able agreem ent w ith the experim ental data. The expected ratio of ssb/dsb for 1´5 keV elec trons from the current calculations is about 13 w hich is in good agreem ent w ith the experim ental ratio of 12 for A l K U SX (Botchway 1996, O’ Neill et al. 1997). The yield of strand breaks obtained from the present calculation for A l K U SX is higher than those obtained for direct dam age only (Charlto n et al. 1989). The additional contribution from the OH radicals seem s to have a bigger eå ect on the yield of ssb than dsb. Su ch diå erences should be observed in the ligh t that the calculated data here present an up per lim it for the expected valu es. This study has shown that the lengths of dam aged sections of DN A tend to be qu ite short (Figure 6), indicating that the length of deletio ns sim p ly by loss betw een nearby dsb should be short. This suggests that w here substantial proportion s of larg e deletio ns are observed in m utated genes after low LET irradiation, som e other m echanism m ay be involved such as non-hom ologous recom bination from one dam aged site w ithin the gene (Thacker 1994) or by association of dsb du e to higher order DN A structure. A cknow led gem e nts

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