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The Role of Oxygen in DNA Damage by Ionizing Particles
J. theor. Biol. (2000) 207, 405}414 doi:10.1006/jtbi.2000.2188, available online at http://www.idealibrary.com on
The Role of Oxygen in DNA Damage by Ionizing Particles J. BARILLA*
AND
M. LOKAJID C[ EK-?
*Czech ¹echnical ;niversity in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department De\ c\ ıH n, Czech Republic and - Institute of Physics, Academy of Sciences, Prague, Czech Republic (Received on 6 December 1999, Accepted in revised form on 31 August 2000)
The actual role of oxygen in inactivation mechanism represents still an open problem, especially when Ewing (1998, Am. J. Clin. Oncol. 21, 355}361) has shown that oxygen "xation hypothesis cannot be regarded as maintainable more and, on the other side, has argued that the oxygen e!ect can be hardly a simple consequence of greater reactivity of oxygen radicals. However, the role of oxygen in DSB formation may be more complicated even during the chemical phase of the radiobiological mechanism, as will be shown by computer simulation of the data concerning DSB number dependence on oxygen concentration (for di!erent gas mixtures) and established experimentally by Blok and Loman in 1973 (Radiat. Res. 9, 165}245) by irradiating DNA water solutions by gamma radiation. 2000 Academic Press
Introduction There are many problems in the radiobiological mechanism that have not been yet satisfactorily solved. Even if much work was already done it is not enough knowledge how the individual phases (i.e. energy transfer, physically chemical processes and biological response of individual cells) actually contribute to the "nal e!ect after the impact of ionizing radiation; especially, when inactivation results di!er often rather strongly according to the radiation kind used. An important problem concerns also the role of oxygen in the radiobiological mechanism, the presence of which enhancing signi"cantly inactivation of cells irradiated by low LET radiation. The given e!ect has played one of the key questions in radiotherapy applications (see e.g. Gray et al., 1953) as the oxygen concentration is ? Author for correspondence. 0022}5193/00/230405#10 $35.00/0
lowered as a rule in solid tumours in comparison to surrounding normal cells. The di!erences in inactivation diminish if the radiation of higher LET is used. However, the actual role of oxygen in inactivation mechanism can be hardly regarded as established. Until recently, the oxygen "xation hypothesis developed about 40 years ago on the basis of the model proposed by Alper & Howard-Flander (1956) has been taken as a satisfactory explanation. However, according to the recent experimental analysis of Ewing (1998) such an idea does not seem to be applicable anymore. On the other hand, having started from the lesser oxygen sensitization of repair-defective strains and from the similarity of maximum insigni"cant doses (i.e. maximum doses that do not reduce the survival from 1.0) in oxygen and nitrogen Ewing has argued that the sensitization cannot be based simply on oxygen's ability to increase the number of DNA lesions. 2000 Academic Press
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J. BARILLA AND M. LOKAJID C[ EK
However, the complexity of radiobiological mechanism should prevent us from doing premature conclusions; especially, when a strong (and not monotone) dependence of SSB and DSB numbers on oxygen concentration seems to exist already in DNA water solutions (Blok & Loman, 1973). Consequently, it should be useful to start with a more detailed analysis of physically chemical processes running after radiation impact in water medium. A greater attention should be devoted to the proper formation of DSB that are regarded generally as main radiobiological damages in a living cell. Recent evidence indicates that two damages are involved in their formation (Milligan et al., 1995; Prise et al., 1993), and consequently that a DSB may be formed only if a greater radical cluster (in which aggressive oxygen radicals may play a role, too) has been formed in the vicinity of a corresponding DNA molecule. However, the probability of DSB formation will be in#uenced not only by e!ective reaction rates of individual radicals with a DNA molecule but also by radical recombination and radical cluster di!usion. Consequently, the ratio of individual radicals being responsible for DSB formation may depend on oxygen concentration in a complex way, as all reactions may be strongly in#uenced by its presence. The following question should be posed: is it possible to explain the experimentally established concentration dependence in di!erent gas mixtures on the basis of the oxygen role in these di!erent reactions? The question concerns before all the DSB formation as in such a case the mentioned di!erent roles of oxygen should be more closely related to other reactions (processes running in a radical cluster after its formation). We will make use of the experimental data of Blok & Loman (1973) and will assume that the ratio of DSB and SSB numbers found by these authors holds under all considered conditions (which should be at lest approximately valid*see experimental points in Fig. 1). We will start from the "nding that one DSB may be formed when a pair damage has occurred in the given part of a DNA molecule (Ward, 1991); a greater number of radicals may be, of course, responsible for damages in individual DNA strands (Michael & Prise, 1996). Anyway,
one radical may form a DSB in an exceptional case, only. And consequently, only su$ciently large radical clusters may be responsible for DSB formation; a necessary pair damage being hardly formed by clusters consisting of very few radicals. A mathematical model will be proposed enabling to comprise mutual reactions of individual radicals in the volume of a corresponding radical cluster as well as the role of cluster di!usion in#uencing the damage probability, too. The model enables to take into account the presence of other radiomodifying agents, too. It allows to follow the physically chemical phase to a greater detail and to use optimization procedures, which might be hardly possible with the help of approaches based on Monte-Carlo method when the values of some free parameters are not known and are to be derived from experimental data. The proposed simulation model will be then applied to the mentioned experimental data (Blok & Loman) obtained by irradiating DNA molecules in a water solution by gamma radiation. The average numbers of DSB formed in individual DNA molecules have been established for di!erent oxygen concentrations in two gas mixtures: O #N , O #N O. The "rst mixture corresponds to changing concentration of oxygen in di!erent cells under standard aerobic conditions (data useful for radiotherapy applications); the other mixture may help in better understanding of the whole mechanism of DSB formation. Especially, the former case exhibiting drastic dependence in the region of very small oxygen concentrations points to the existence of at least two di!erent oxygen roles. Even if the proposed model may be adapted without any greater problems to conditions for any radiation kind the following analysis will concern low-LET radiation where the oxygen e!ect is signi"cantly pronounced. Consequently, the in#uence of multiply damaged sites considered, e.g. by Ward (1994), for higher-LET radiation need not be taken into account. The model may be used in principle for high LET radiation, too, in describing the in#uence of recombination and di!usion processes when some other modifying agents are used. However, the shape of an initial radical clusters might remind a cylinder rather than a sphere when the
THE ROLE OF OXYGEN IN DNA DAMAGE
407
FIG. 1. DSB numbers (per DNA molecule) at di!erent oxygen concentrations; dose of 5 Gy.
slowly moving ionizing particle loses its energy in many smaller amounts (see LokajmH c\ ek et al., 2000). Also the oxygen presence will play a significantly smaller role when the probability of forming a DSB in a given region will tend to one. Dose Dependence of DSB Numbers It follows from experimental data that the number of DSB formed by ionizing radiation depends linearly on the applied dose (see e.g. Frankenberg-Schwager et al., 1980), and therefore, DSB should be formed during the passages of single ionizing particles of a given beam, even for low-LET radiation. It means that one should assume that single radical clusters should be responsible for their formation; the probability of DSB formed by a direct e!ect of a beam particle
may be regarded as quite negligible at doses usually applied to in radiotherapy. It is further evident that very small clusters can be hardly e$cient in forming DSB being a result of two di!erent SSB. Taking into account the diverse e$ciencies of di!erent types of ionizing particles one must conclude that radical clusters corresponding to locally transferred energy of two or more hundreds of eV may form individual DSB (see e.g. Goodhead et al., 1979). Some other analyses concerning correlation between the numbers of radical clusters formed by a given radiation type and corresponding DSB numbers in DNA solutions indicate that even rather distant clusters must be e$cient in DSB formation (LokajmH c\ ek, 1986). That may be explained by assuming that a DNA molecule exhibits thermal motion and encounters a radical cluster before all
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J. BARILLA AND M. LOKAJID C[ EK
radicals recombine and di!use. A DSB is then formed when at least one SSB is created in each of both the strands of a DNA molecule not far one from another, which may occur with a su$cient probability if active radicals belong to the same cluster. The mathematical model being proposed starts from such a basic assumption. It is further assumed that they are water radicals of H) and OH) which are mainly responsible for formation of individual SSB. If oxygen is present some other radicals (e.g. HO) ) are assumed to play a role, too. We will characterize the size of clusters being e$cient in DSB formation by the average numbers of radicals in a given cluster immediately after its formation. These radicals may then recombine and react also with other substances being present in the solution during irradiation; the given cluster di!uses, of course, at the same time. The proposed model enables to take both these basic processes into account: reactions of radicals as well as their di!usion. A SSB is assumed to be formed with a certain probability when a DNA molecule meets the cluster and a radical reacts with it. The probability of SSB formation depends on the instant when a DNA molecule encounters a radical cluster, i.e. on the number and the type of radicals being yet present in the corresponding cluster. A pair of SSB (in di!erent strands) may then form one DSB; the formation of DSB by another mechanism being regarded as negligible. The model makes it possible to include also the in#uence of radiomodifying agents being present during irradiation and to study their e!ects on DSB formation. In the following, the in#uence of O and of N O will be taken into account.
If the energy of a photon is approximately 7 eV the water molecule is excited and the following dissociation leads again to the formation of water radicals: H OPH O*PH)#OH).
(3)
The electron released in reaction (1) may bind to a water molecule: e\#(H O) Pe\, L ?O
(4)
and electron e\ contributes to production of ?O hydrogen radicals: e\#H OPOH\#H). ?O
(5)
Hydrated electrons e\ may, however, exist in this ?O form relatively long; they may di!use to greater distances and react with critical biomolecules. The e!ect of ionizing radiation is known to be signi"cantly modi"ed if oxygen is present in the solution. It represents a source of some radicals which are assumed to be reactive. They may arise by the reaction e\#O PO)#O\,
(6)
minimum electron energy &4 eV, maximum gain at 8 eV. These radicals may react in water medium and form new oxygen radicals: O)#H OPH)#HO) ,
(7)
O\#H OPH)#HO\.
(8)
The oxygen radicals may be formed further in the reactions
Radical Clusters and Processes in the Chemical Phase The formation of radicals during water radiolysis has been described, e.g. in the paper of Sauer et al. (1978). Here a short survey will be given only. When radiation is absorbed the water molecule is ionized (ionizing potential 12, 56 eV):
e\#O PO\, ?O
(9)
O\#H O>PHO) ,
(10)
H)#O PHO) ,
(11)
H OPH O>#e\;
HO) PH O>#O\.
(12)
(1)
H O> ion may decay and produce OH\ radicals: H O>PH>#OH). (2)
At lower concentrations of O (at pH 7) the dissociation (12) is preferred; at higher
409
THE ROLE OF OXYGEN IN DNA DAMAGE
concentrations it is the formation of radicals HO) according to eqn (10) which is preferred (Pikajev, 1986). Thus, the actual content of radicals in individual clusters depends also on oxygen concentration; and the radicals HO) (resp. O ) may be involved in DSB formation in addition to H) and OH). If N O is present in the solution then its reaction with hydrated electrons e\ may be ?O important: e\#N OPN #OH\#OH , ?O
(13)
molecules of N O can be also excited: N OPN O*PN #O
(14)
and the O) radicals react immediately with water molecules according to eqn (7). Some additional radicals H), OH), HO) are formed in a cluster in the dependence of N O concentration (Pikajev, 1986). The ratio of di!erent radicals will depend then also on the concentrations of O and of NO in the solution.
then equal N*"N #N , & & ,& N* "N #N , -& -& , N*"N #N , ,-
(15)
where N , N , N and N depend on the ,& , ,concentrations of O and N O; all being zero if only N is present. However, the cluster size should depend in principle on the energy delivered to a given volume; and we will assume that the total numbers of all radicals will be given by the locally delivered energy, independent of their kinds (i.e. independent of the concentrations of O or N O). The initial composition of an average e!ective cluster may then be characterized generally by N "CN*, & & N "CN* , -& -& N "CN*, -
(16)
where one may put
N U #N U -& & (17) * U #N U #N U #N U U #N U #N -& & - ,& , ,- and U : U : U : U : U : U are the ratios of Mathematical Simulation of energy needed to form individual radicals. Chemical Mechanism We will take into account also the in#uence of Even if the model enables in principle to simuhydrated electrons e\, their initial number being ?O late a very complex structure of the chemical N . Their presence does not seem to in#uence the C mechanism it is useful to introduce some simother initial cluster characteristics. plifying (and averaging) assumptions to facilitate the corresponding analysis. RECOMBINATION AND DIFFUSION PROCESSES C" N
INITIAL SIZE OF EFFICIENT CLUSTERS
Let us assume now the average size of e$cient clusters to be characterized by N and H , i.e. & -& by the numbers of H) and OH) radicals, respectively, being formed in anoxic conditions, when only N is present. When O is present then the &&oxygen'' radicals (e.g. HO) ) will arise, too; their number being denoted as N . If N O is present some additional radicals will arise according to eqns (13), (14) and (7): OH), H) and HO) , their number being N , N , N (respectively). , ,& ) ,-) The numbers of radicals H , OH and HO) will
Possible recombination processes and other reactions are summarized in Table 1. For the sake of simplicity, we shall consider in the following only some of them (regarded as more important*see Table 2). As to the di!usion we will start from the mathematical model describing the di!usion in the three-dimensional space going from a singular point. The average radical concentration in different time and space points may be given by
r N exp ! , c(r, t)" 4Dt 8 ((nDt)
(18)
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J. BARILLA AND M. LOKAJID C[ EK
TABLE 1 Recombination reactions (Chaterjee & Maggee, 1983) Reactions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
Rate constants (dm mol\ s\)
H #H PH e\#H PH #OH\ ?O e\#e\PH #2OH\ ?O ?O e\#OH POH\#H O ?O H #OH PH O OH #OH PH O H O>#e\PH #H O ?O H O>#OH\ P H O H #H O PH O#OH e\#H O POH #OH\ ?O OH #H O PH O#HO OH #H PH O#H HO #H PH O e\#O PO\#H O ?O HO #OH PH O#O HO #HO PH O #O H #O PHO O\#H O>PHO H OPH O>#OH\ HO PH O>#O\
1;10 2.5;10 6;10 3;10 2.4;10 4;10 2.3;10 3;10 1;10 1.2;10 5;10 6;10 1;10 1.9;10 1;10 2;10 1;10 3;10 5.5;10\ 1;10
TABLE 2 Recombination reactions chosen from ¹able 1 Reactions
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Reaction rate constants (dm mol\ s\)
H #H PH e\#H PH #OH\ ?O e\#e\PH #2OH\ ?O ?O e\#OH POH\#H O ?O H #OH PH O OH #OH PH O HO #H PH O e\#O PO\#H O ?O HO #OH PH O#O HO #HO PH O #O H #O PHO
1;10 2.5;10 6;10 3;10 2.4;10 4;10 1;10 1.9;10 1;10 2;10 1;10
where r is the distance from the cluster centre, t is the time elapsed, N is the (initial) number of radicals and D is the di!usion coe$cient. The average cluster volume may be given by
Dt . <(t)" n
<(t ) (e.g."10 nm); t being derived from eqn (19). The combined e!ect of the recombination and di!usion may be then described with the help of the following set of di!erential equations: dN &"!N & dt
n (2k N #k N & -& Dt
#k N #k N ) C !N (k [O ]#k [N O]), & dN -&"!N -& dt
n (k N #2k N -& Dt &
#k N #k N ) C !N (k [O ]#k [N O]), -& dN -"!N dt
n (k N #k N -& Dt &
#2k N #k N ) - C !N (k [O ]#k [N O]), - dN C"!N C dt
n (k N #k N -& Dt &
#k N #2k N ) C !N (k [O ]#k [N O]), C
where k ,2, k are rate constant of reactions given in Table 2; D being the average di!usion coe$cient of the radical cluster. CONCENTRATIONS OF O AND N O AND ADDITIONAL RADICALS
The quantities [O ] and [N O] represent mo lecular concentrations of O and N O (respec tively) in given water solutions. One can write [O ]"A +1!exp(!(cp )q-),, -
(19)
We will then assume that the di!usion of an average cluster starts from an initial size
(20)
(21)
A , [N O]" 1#j [O ] , +1!exp(!((1!c)p )q,),, ,
(22)
411
THE ROLE OF OXYGEN IN DNA DAMAGE
where c is the oxygen concentration in either gas mixture, A and A are limit solubilities of O , and N O (respectively) in water (at a given pres sure), p , q , p , q , j are free parameters, (1!c) - - , , , is the concentration of N O in the mixture (O !N O). Formulae (21) and (22) enable to take into account a linear concentration rise of individual gases in water as well as saturation characteristics. We will assume that the number of additional radicals formed together with the basic water radicals [see eqn (15)] are proportional to concentrations of [O ] and [N O]; i.e. N "d [O ], N "d [N O], , , N "d [N O], ,, N "d [N O], ,& ,&
(23)
where d , d , d and d are corresponding - , ,,& coe$cients of proportionality. PROBABILITY OF SSB AND DSB FORMATION
The numbers (N , N , N , N ) of e$cient & -& - C radicals in a cluster decrease from their initial values [see eqns (16)] with rising time [according to eqns (20)]. The probability p of SSB forma1 tion in DNA molecules depends then on the instant of encounter of a molecule with a given cluster. One can write for an average cluster p "p #p #p #p #p , 1 & -& A
(24)
where the individual probabilities are given as averages over di!erent t:
p " &
p " -&
t
a N (t) dt, -& -&
t K t
p" C
a N (t) dt, & &
t
t K
p " -
t K
t K t
a N (t) dt, - a N (t) dt C C
(25)
and parameters a , a , a , a are proportional to & -& - C the reaction rates of individual radicals and of e\ ?O with DNA molecules. The value t should correK spond to cluster di!usion time (e.g. to a time when less than two radicals are present in a given cluster). The parameter p in eqn (24) represents a direct e!ect of the given ionizing radiation. The probability of DSB formation may be then given by p "p, " 1
(26)
which may be correlated to experimentally established numbers of DSB at di!erent oxygen concentrations in the corresponding gas mixtures (O !N , O !N O). A proportionlity coe$ cient should be put into eqn (26) as a greater number of SSB may result in one DSB, which is not necessary if one is interested in mere ratios of parameters a , a , a , a . & -& - C Analysis of Experimental Data We shall now apply the model proposed and described in the preceding section to the already mentioned experimental data taken from the paper of Blok & Loman (1973). They irradiated water solution of UX174-DNA at di!erent oxygen concentrations in two mixtures: (a) N !O ; (b) N O}O . The solution containing 25 lg ml\ of DNA in 0.01 phosphate bu!er at pH 7 was irradiated by photons (&1.25 MeV) of Co-60 isotope by the dose of 5 Gy. They established the ratio of DSB and SSB and measured then the dependence of SSB numbers on oxygen concentrations to a greater detail. To test the proposed model we have derived the concentration dependence of DSB by combining both the experimental data of theirs. The corresponding values are shown in Table 3. Our aim consisted mainly in answering the question whether the model is able to represent the drastic change of DSB numbers at smaller oxygen concentrations (see Fig. 1) and what is the role of individual radicals in DSB formation at di!erent oxygen concentrations. The model (containing a series of free parameters) seems to re#ect complexity of radiobiological mechanism in the chemical phase to a su$cient extent. A part of the parameters (reaction and di!usion
412
J. BARILLA AND M. LOKAJID C[ EK
TABLE 3 Experimental data2number of DSB per 1 DNA molecule in dependence on oxygen concentration
TABLE 4
Concentration
No. of DSB per DNA molecule Experimental values
Theoretical values
(a) N }O solution 1. 0.000 2. 0.000 3. 0.020 4. 0.048 5. 0.092 6. 0.300 7. 0.652 8. 0.900
0.063 0.061 0.022 0.046 0.040 0.040 0.038 0.040
0.062 0.062 0.022 0.046 0.040 0.040 0.040 0.040
(b) N O}O solution 1. 0.000 2. 0.017 3. 0.048 4. 0.090 5. 0.500 6. 0.844 7. 0.906 8. 0.965 9. 1.000
0.060 0.084 0.097 0.085 0.077 0.068 0.060 0.050 0.041
0.060 0.085 0.095 0.087 0.076 0.067 0.060 0.050 0.041
96.77 97.04 1.04 10.70 94.82 1.09 183.98 210.81 603.47 0.02 96.86 994.97 915.05 126.15 0.07
Parameter
Established value
k k k A p q A , p , q , j , d d , d ,d ,&
5.94 949.71 1.56 0.89 ) 10\ 435.82 1.52 0.84 ) 10\ 28.56 3289.20 1.67 108.36 23620.00 18096.00 8658.30
The average initial size of radical clusters may be characterized by the values N "17.05, &
rates) may be established in principle from other experimental data (see e.g. values in Tables 1 and 2). The other part should be regarded as quite free; it is necessary to determine them with the help of an optimization procedure to "t the used experimental data. The MINUIT program (James & Roos, 1975) was made use of. To simplify the numerical approach we have "xed the ratios of energy needed to form corresponding radicals by putting U : U : U : U : U : U "1 : 1 : 0 : 0.75 : 0 : 0. (27) The average coe$cient determining the cluster di!usion has been put according to Pikajev (1986): D"3.5 [nm ns\].
k k k k k k k k k k k k k k k
Established value
(28)
The values of other parameters involved in eqns (20)}(25) have been established with the help of the mentioned optimization approach; they are shown in Table 4.
N "18.23 -&
(29)
and the initial number of e\ has been established ?O as N "38.91. C
(30)
The reaction-rate ratios of di!erent radicals with DNA are a : a : a : a "0.01 : 0.10 : 0.07 : 0.03. (31) & -& - C The probability of a direct e!ect is approximately p "0.0007,
(32)
indicating to be practically negligible. Theoretical results as well as experimental data are given in Table 3; they are represented graphically in Fig. 1, too. The percentage e$ciency of individual radicals in formation of individual SSB is shown in Table 5. The direct e!ect of radiation seems to be quite negligible, which is in harmony with probability estimates that beam particles (secondaries included) hits directly a DNA molecule at the given doses. The proposed model has been able to reproduce the given experimental data exhibiting not
413
THE ROLE OF OXYGEN IN DNA DAMAGE
TABLE 5 Ratio (in %) of individual radicals in DSB formation at di+erent oxygen concentrations c (%)
0.0 0.1 1.0 2.0 10.0 100.0
N }O
N O}O
H
OH
HO
e\ ?O
Direct e!ect
H
OH
HO
e\ ?O
Direct e!ect
0.00 0.00 4.43 1.33 0.00 0.00
16.21 3.73 0.00 0.00 0.00 0.00
0.00 0.00 48.18 94.52 99.99 99.99
83.79 96.26 47.30 4.10 0.00 0.00
0.00 0.01 0.09 0.05 0.01 0.01
0.00 0.00 0.17 0.00 0.00 0.00
99.84 98.60 0.00 0.00 0.00 0.00
0.00 0.00 99.24 99.99 99.99 99.99
0.13 1.37 0.55 0.00 0.00 0.00
0.03 0.03 0.04 0.01 0.01 0.01
only the steep decrease of DSB in the close vicinity of zero oxygen concentration but also a small excess of DSB exhibited by experimental data approximately at 5% of oxygen in the mixture with nitrogen. The values of "tted parameters will be in#uenced only insigni"cantly if this e!ect will correspond to mere statistical #uctuations, as they are given mainly by global dependence on oxygen concentration. Conclusion There is a lot of di!erent chemical agents which may strongly in#uence the radiobiological e!ect of ionizing particles when present in cells during irradiation. However, it is not clear very often in which phase of the radiobiological mechanism they are active; whether in the chemical phase in#uencing cell damages or in the biological phase when the damages are being repaired. The proposed mathematical model enables to study the processes of the chemical phase to a greater detail and to analyse the actual role of individual substances in this phase of radiobiological mechanism with the help of experiments performed on DNA molecules in water solutions. The results following from such analyses might contribute to improving radiotherapy approaches by making use of suitable radiomodifying agents. Analyses based on the proposed model might help also in distinguishing between the processes running in the chemical phase and governed fully by laws of non-living nature and those belonging to processes of the biological phase. Our results
have shown that the oxygen may play di!erent roles at di!erent concentrations; the given characteristic being explained fully on the basis of chemical processes (or physical ones when the saturation is taken into account, too). Some other agents in#uencing the oxygen e!ect may be present in living cells (see e.g. van der Schans et al., 1986). However, if the "xation hypothesis is to be doubted the proposed model may be helpful also in such a case. It might be applied directly to the data concerning DSB formation. An eventual extension of the model to cover corresponding modi"cations should not represent a very di$cult task, either. Only more exact data with a greater number of experimental points should be probably needed. As to its possible application to survival curves the model should have to be supplemented by additional assumption concerning the way how cell inactivation depends on the number of DSB and their distribution in the chromosomal system (direct inactivation, repair, misrepair). The corresponding analyses might help also in understanding better the links and di!erences between the laws governing non-biological and biological processes in living matter. The given experiments and theoretical results have shown the role of oxygen radicals in DSB (or SSB) formation to be rather complicated if the high number of DSB obtained by Blok & Loman (1973) at zero oxygen concentration in nitrogen mixture corresponds to reality. Such an e!ect has not been reported in experiments based on inactivation of living cells. It has been always demonstrated and argued that the cell survival has
414
J. BARILLA AND M. LOKAJID C[ EK
increased when oxygen concentration has been diminished. However, it is necessary to assume that if such a survival decrease were observed after rinsing out the oxygen from cell medium it would be attributed to cell dying due to oxygen de"ciency, as cells cannot remain alive being in anoxic conditions for a longer time. The problem should be questioned to a greater detail with the help of more sophisticated experiments at low oxygen concentrations as the similarity of maximum insigni"cant dose may be hardly decisive in this point. The presented model analysis has been based on some simplifying assumptions. A de"nite answer to all opened questions will require a more detailed theoretical analysis involving all possible chemical reactions playing a role in the given mechanism, and of course, more experimental data, too. The model may provide, however, a new tool for solving a series of corresponding problems. REFERENCES ALPER, T. & HOWARD-FLANDERS, P. (1956). Role of oxygen in modifying the radiosensitivity of E. colli. Nature 178, 978}979. BLOK, J. &. LOMAN, H. (1973). The e!ects of c-radiation in DNA. Radiat. Res. 9, 165}245. CHATTERJEE, A., MAGGEE, J. L. & DEX, S. K. (1983). The role of homogeneous reaction in the radiolysis of water. Radiat. Res. 96, 1}19. EWING, D. (1998). The oxygen "xation hypothesis. A reevaluation. Am. J. Clin. Oncol. 21, 355}361. FRANKENBERG-SCHWAGER, M., FRANKENBERG, D., BLOECHER, D. & ADAMCZY, C. (1980). The linear relationship between DNA double-strand breaks and radiation dose 30 MeV electrons is converted into a quadratic function by cellular repair. Int. J. Radiat. Biol. 37, 207}212.
GOODHEAD, D. T., THACKER, J. & COX, R. (1979). E!ectiveness of 0.3 keV carbon ultrasoft X-rays for the inactivation and mutation of cultured mammalian cells. Int. J. Radiat. Biol. 36, 101}114. GRAY, L. A., CONGER, A. D., EBERT, M., HORNSEY, S. & SCOTT, O. C. A. (1953). The concentration of oxygen in tissues at the time of irradiations as a factor in radiotherapy. Brit. J. Radiol. 26, 638}648. JAMES, F. & ROOS, M. (1975). MINUIT*a system for function minimization and analysis of parameter errors and correlations. Comput. Phys. Commun. 10, 343}367. LOKAJID C[ EK, M. (1986). Biophysical mechanism of cell inactivation by ionizing particles. Report ICT/86/399. International Centre for Theoretical Physics. Trieste. LOKAJID C[ EK, M. V., EE ECHAD K, T., JUDAS, L., KLUSOOE , J., KUNDRAD T, V. & PROKESS[ , K. (2000). Inactivation of individual cells by divers ions at di!erent LET values. Contribution to 1st International =orkshop on Space Radiation Research, Arona, Italy, 27}31, May. MICHAEL, B. D. & PRISE, K. M. (1996). A multiple-radical model for radiation action on DNA and the dependence of OER on LET. Int. J. Radiat. Biol. 69, 351}358. MILLIGAN, J. R., NG, J.Y-Y., WU, C. C. L., AGUILERA, J. A., FAHEY, R. C. & WARD, J. F. (1995). DNA repair by thiolos in air shows two radicals make a double-strand break. Radiat. Res. 143, 273}280. PIKAJEV, A. K. (1986). Sovremennaja Radiacionnaja Chimija. Moskva: Nauka. PRISE, K. M., DAVIES, S. & MICHAEL, B. D. (1993). Evidence for induction of DNA double-strand breaks at paired radical sites. Radiat. Res. 134, 102}106. SAUER, C. M., SCHMIDT, K. H., JONAH, CH. D., NALEWAY, C. A. & HART, E. (1978). High-LET Pulse Radiolysis: O and oxygen production in tracks. Radiat. Res. 75, 519}528. VAN DER SCHANS, G. P., VOST, O., ROOS-VERHEIJ, W. S. D. & LOHMAN, P. H. M. (1986). The in#uence of oxygen on the induction of radiation damage in DNA in mammalian cells after sensitization by intracellular glutathion depletion. Int. J. Radiat. Biol. 50, 453}465. WARD, J. F. (1991). Mechanisms of radiation action on DNA in model system*their relevance to cellular DNA. NA¹O Advanced Research =orkshop on Cell Biology: ¹he Early E+ects of Radiation on DNA (Fielden, E. M. & O'Neill, P., eds), pp. 1}16. Berlin: Springer. WARD, J. F. (1994). The complexity of DNA damage: relevance to biological consequences. Int. J. Radiat. Biol. 66, 427}432.
The Role of Oxygen in DNA Damage by Ionizing Particles J. BARILLA*
AND
M. LOKAJID C[ EK-?
*Czech ¹echnical ;niversity in Prague, Faculty of Nuclear Sciences and Physical Engineering, Department De\ c\ ıH n, Czech Republic and - Institute of Physics, Academy of Sciences, Prague, Czech Republic (Received on 6 December 1999, Accepted in revised form on 31 August 2000)
The actual role of oxygen in inactivation mechanism represents still an open problem, especially when Ewing (1998, Am. J. Clin. Oncol. 21, 355}361) has shown that oxygen "xation hypothesis cannot be regarded as maintainable more and, on the other side, has argued that the oxygen e!ect can be hardly a simple consequence of greater reactivity of oxygen radicals. However, the role of oxygen in DSB formation may be more complicated even during the chemical phase of the radiobiological mechanism, as will be shown by computer simulation of the data concerning DSB number dependence on oxygen concentration (for di!erent gas mixtures) and established experimentally by Blok and Loman in 1973 (Radiat. Res. 9, 165}245) by irradiating DNA water solutions by gamma radiation. 2000 Academic Press
Introduction There are many problems in the radiobiological mechanism that have not been yet satisfactorily solved. Even if much work was already done it is not enough knowledge how the individual phases (i.e. energy transfer, physically chemical processes and biological response of individual cells) actually contribute to the "nal e!ect after the impact of ionizing radiation; especially, when inactivation results di!er often rather strongly according to the radiation kind used. An important problem concerns also the role of oxygen in the radiobiological mechanism, the presence of which enhancing signi"cantly inactivation of cells irradiated by low LET radiation. The given e!ect has played one of the key questions in radiotherapy applications (see e.g. Gray et al., 1953) as the oxygen concentration is ? Author for correspondence. 0022}5193/00/230405#10 $35.00/0
lowered as a rule in solid tumours in comparison to surrounding normal cells. The di!erences in inactivation diminish if the radiation of higher LET is used. However, the actual role of oxygen in inactivation mechanism can be hardly regarded as established. Until recently, the oxygen "xation hypothesis developed about 40 years ago on the basis of the model proposed by Alper & Howard-Flander (1956) has been taken as a satisfactory explanation. However, according to the recent experimental analysis of Ewing (1998) such an idea does not seem to be applicable anymore. On the other hand, having started from the lesser oxygen sensitization of repair-defective strains and from the similarity of maximum insigni"cant doses (i.e. maximum doses that do not reduce the survival from 1.0) in oxygen and nitrogen Ewing has argued that the sensitization cannot be based simply on oxygen's ability to increase the number of DNA lesions. 2000 Academic Press
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J. BARILLA AND M. LOKAJID C[ EK
However, the complexity of radiobiological mechanism should prevent us from doing premature conclusions; especially, when a strong (and not monotone) dependence of SSB and DSB numbers on oxygen concentration seems to exist already in DNA water solutions (Blok & Loman, 1973). Consequently, it should be useful to start with a more detailed analysis of physically chemical processes running after radiation impact in water medium. A greater attention should be devoted to the proper formation of DSB that are regarded generally as main radiobiological damages in a living cell. Recent evidence indicates that two damages are involved in their formation (Milligan et al., 1995; Prise et al., 1993), and consequently that a DSB may be formed only if a greater radical cluster (in which aggressive oxygen radicals may play a role, too) has been formed in the vicinity of a corresponding DNA molecule. However, the probability of DSB formation will be in#uenced not only by e!ective reaction rates of individual radicals with a DNA molecule but also by radical recombination and radical cluster di!usion. Consequently, the ratio of individual radicals being responsible for DSB formation may depend on oxygen concentration in a complex way, as all reactions may be strongly in#uenced by its presence. The following question should be posed: is it possible to explain the experimentally established concentration dependence in di!erent gas mixtures on the basis of the oxygen role in these di!erent reactions? The question concerns before all the DSB formation as in such a case the mentioned di!erent roles of oxygen should be more closely related to other reactions (processes running in a radical cluster after its formation). We will make use of the experimental data of Blok & Loman (1973) and will assume that the ratio of DSB and SSB numbers found by these authors holds under all considered conditions (which should be at lest approximately valid*see experimental points in Fig. 1). We will start from the "nding that one DSB may be formed when a pair damage has occurred in the given part of a DNA molecule (Ward, 1991); a greater number of radicals may be, of course, responsible for damages in individual DNA strands (Michael & Prise, 1996). Anyway,
one radical may form a DSB in an exceptional case, only. And consequently, only su$ciently large radical clusters may be responsible for DSB formation; a necessary pair damage being hardly formed by clusters consisting of very few radicals. A mathematical model will be proposed enabling to comprise mutual reactions of individual radicals in the volume of a corresponding radical cluster as well as the role of cluster di!usion in#uencing the damage probability, too. The model enables to take into account the presence of other radiomodifying agents, too. It allows to follow the physically chemical phase to a greater detail and to use optimization procedures, which might be hardly possible with the help of approaches based on Monte-Carlo method when the values of some free parameters are not known and are to be derived from experimental data. The proposed simulation model will be then applied to the mentioned experimental data (Blok & Loman) obtained by irradiating DNA molecules in a water solution by gamma radiation. The average numbers of DSB formed in individual DNA molecules have been established for di!erent oxygen concentrations in two gas mixtures: O #N , O #N O. The "rst mixture corresponds to changing concentration of oxygen in di!erent cells under standard aerobic conditions (data useful for radiotherapy applications); the other mixture may help in better understanding of the whole mechanism of DSB formation. Especially, the former case exhibiting drastic dependence in the region of very small oxygen concentrations points to the existence of at least two di!erent oxygen roles. Even if the proposed model may be adapted without any greater problems to conditions for any radiation kind the following analysis will concern low-LET radiation where the oxygen e!ect is signi"cantly pronounced. Consequently, the in#uence of multiply damaged sites considered, e.g. by Ward (1994), for higher-LET radiation need not be taken into account. The model may be used in principle for high LET radiation, too, in describing the in#uence of recombination and di!usion processes when some other modifying agents are used. However, the shape of an initial radical clusters might remind a cylinder rather than a sphere when the
THE ROLE OF OXYGEN IN DNA DAMAGE
407
FIG. 1. DSB numbers (per DNA molecule) at di!erent oxygen concentrations; dose of 5 Gy.
slowly moving ionizing particle loses its energy in many smaller amounts (see LokajmH c\ ek et al., 2000). Also the oxygen presence will play a significantly smaller role when the probability of forming a DSB in a given region will tend to one. Dose Dependence of DSB Numbers It follows from experimental data that the number of DSB formed by ionizing radiation depends linearly on the applied dose (see e.g. Frankenberg-Schwager et al., 1980), and therefore, DSB should be formed during the passages of single ionizing particles of a given beam, even for low-LET radiation. It means that one should assume that single radical clusters should be responsible for their formation; the probability of DSB formed by a direct e!ect of a beam particle
may be regarded as quite negligible at doses usually applied to in radiotherapy. It is further evident that very small clusters can be hardly e$cient in forming DSB being a result of two di!erent SSB. Taking into account the diverse e$ciencies of di!erent types of ionizing particles one must conclude that radical clusters corresponding to locally transferred energy of two or more hundreds of eV may form individual DSB (see e.g. Goodhead et al., 1979). Some other analyses concerning correlation between the numbers of radical clusters formed by a given radiation type and corresponding DSB numbers in DNA solutions indicate that even rather distant clusters must be e$cient in DSB formation (LokajmH c\ ek, 1986). That may be explained by assuming that a DNA molecule exhibits thermal motion and encounters a radical cluster before all
408
J. BARILLA AND M. LOKAJID C[ EK
radicals recombine and di!use. A DSB is then formed when at least one SSB is created in each of both the strands of a DNA molecule not far one from another, which may occur with a su$cient probability if active radicals belong to the same cluster. The mathematical model being proposed starts from such a basic assumption. It is further assumed that they are water radicals of H) and OH) which are mainly responsible for formation of individual SSB. If oxygen is present some other radicals (e.g. HO) ) are assumed to play a role, too. We will characterize the size of clusters being e$cient in DSB formation by the average numbers of radicals in a given cluster immediately after its formation. These radicals may then recombine and react also with other substances being present in the solution during irradiation; the given cluster di!uses, of course, at the same time. The proposed model enables to take both these basic processes into account: reactions of radicals as well as their di!usion. A SSB is assumed to be formed with a certain probability when a DNA molecule meets the cluster and a radical reacts with it. The probability of SSB formation depends on the instant when a DNA molecule encounters a radical cluster, i.e. on the number and the type of radicals being yet present in the corresponding cluster. A pair of SSB (in di!erent strands) may then form one DSB; the formation of DSB by another mechanism being regarded as negligible. The model makes it possible to include also the in#uence of radiomodifying agents being present during irradiation and to study their e!ects on DSB formation. In the following, the in#uence of O and of N O will be taken into account.
If the energy of a photon is approximately 7 eV the water molecule is excited and the following dissociation leads again to the formation of water radicals: H OPH O*PH)#OH).
(3)
The electron released in reaction (1) may bind to a water molecule: e\#(H O) Pe\, L ?O
(4)
and electron e\ contributes to production of ?O hydrogen radicals: e\#H OPOH\#H). ?O
(5)
Hydrated electrons e\ may, however, exist in this ?O form relatively long; they may di!use to greater distances and react with critical biomolecules. The e!ect of ionizing radiation is known to be signi"cantly modi"ed if oxygen is present in the solution. It represents a source of some radicals which are assumed to be reactive. They may arise by the reaction e\#O PO)#O\,
(6)
minimum electron energy &4 eV, maximum gain at 8 eV. These radicals may react in water medium and form new oxygen radicals: O)#H OPH)#HO) ,
(7)
O\#H OPH)#HO\.
(8)
The oxygen radicals may be formed further in the reactions
Radical Clusters and Processes in the Chemical Phase The formation of radicals during water radiolysis has been described, e.g. in the paper of Sauer et al. (1978). Here a short survey will be given only. When radiation is absorbed the water molecule is ionized (ionizing potential 12, 56 eV):
e\#O PO\, ?O
(9)
O\#H O>PHO) ,
(10)
H)#O PHO) ,
(11)
H OPH O>#e\;
HO) PH O>#O\.
(12)
(1)
H O> ion may decay and produce OH\ radicals: H O>PH>#OH). (2)
At lower concentrations of O (at pH 7) the dissociation (12) is preferred; at higher
409
THE ROLE OF OXYGEN IN DNA DAMAGE
concentrations it is the formation of radicals HO) according to eqn (10) which is preferred (Pikajev, 1986). Thus, the actual content of radicals in individual clusters depends also on oxygen concentration; and the radicals HO) (resp. O ) may be involved in DSB formation in addition to H) and OH). If N O is present in the solution then its reaction with hydrated electrons e\ may be ?O important: e\#N OPN #OH\#OH , ?O
(13)
molecules of N O can be also excited: N OPN O*PN #O
(14)
and the O) radicals react immediately with water molecules according to eqn (7). Some additional radicals H), OH), HO) are formed in a cluster in the dependence of N O concentration (Pikajev, 1986). The ratio of di!erent radicals will depend then also on the concentrations of O and of NO in the solution.
then equal N*"N #N , & & ,& N* "N #N , -& -& , N*"N #N , ,-
(15)
where N , N , N and N depend on the ,& , ,concentrations of O and N O; all being zero if only N is present. However, the cluster size should depend in principle on the energy delivered to a given volume; and we will assume that the total numbers of all radicals will be given by the locally delivered energy, independent of their kinds (i.e. independent of the concentrations of O or N O). The initial composition of an average e!ective cluster may then be characterized generally by N "CN*, & & N "CN* , -& -& N "CN*, -
(16)
where one may put
N U #N U -& & (17) * U #N U #N U #N U U #N U #N -& & - ,& , ,- and U : U : U : U : U : U are the ratios of Mathematical Simulation of energy needed to form individual radicals. Chemical Mechanism We will take into account also the in#uence of Even if the model enables in principle to simuhydrated electrons e\, their initial number being ?O late a very complex structure of the chemical N . Their presence does not seem to in#uence the C mechanism it is useful to introduce some simother initial cluster characteristics. plifying (and averaging) assumptions to facilitate the corresponding analysis. RECOMBINATION AND DIFFUSION PROCESSES C" N
INITIAL SIZE OF EFFICIENT CLUSTERS
Let us assume now the average size of e$cient clusters to be characterized by N and H , i.e. & -& by the numbers of H) and OH) radicals, respectively, being formed in anoxic conditions, when only N is present. When O is present then the &&oxygen'' radicals (e.g. HO) ) will arise, too; their number being denoted as N . If N O is present some additional radicals will arise according to eqns (13), (14) and (7): OH), H) and HO) , their number being N , N , N (respectively). , ,& ) ,-) The numbers of radicals H , OH and HO) will
Possible recombination processes and other reactions are summarized in Table 1. For the sake of simplicity, we shall consider in the following only some of them (regarded as more important*see Table 2). As to the di!usion we will start from the mathematical model describing the di!usion in the three-dimensional space going from a singular point. The average radical concentration in different time and space points may be given by
r N exp ! , c(r, t)" 4Dt 8 ((nDt)
(18)
410
J. BARILLA AND M. LOKAJID C[ EK
TABLE 1 Recombination reactions (Chaterjee & Maggee, 1983) Reactions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.
Rate constants (dm mol\ s\)
H #H PH e\#H PH #OH\ ?O e\#e\PH #2OH\ ?O ?O e\#OH POH\#H O ?O H #OH PH O OH #OH PH O H O>#e\PH #H O ?O H O>#OH\ P H O H #H O PH O#OH e\#H O POH #OH\ ?O OH #H O PH O#HO OH #H PH O#H HO #H PH O e\#O PO\#H O ?O HO #OH PH O#O HO #HO PH O #O H #O PHO O\#H O>PHO H OPH O>#OH\ HO PH O>#O\
1;10 2.5;10 6;10 3;10 2.4;10 4;10 2.3;10 3;10 1;10 1.2;10 5;10 6;10 1;10 1.9;10 1;10 2;10 1;10 3;10 5.5;10\ 1;10
TABLE 2 Recombination reactions chosen from ¹able 1 Reactions
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Reaction rate constants (dm mol\ s\)
H #H PH e\#H PH #OH\ ?O e\#e\PH #2OH\ ?O ?O e\#OH POH\#H O ?O H #OH PH O OH #OH PH O HO #H PH O e\#O PO\#H O ?O HO #OH PH O#O HO #HO PH O #O H #O PHO
1;10 2.5;10 6;10 3;10 2.4;10 4;10 1;10 1.9;10 1;10 2;10 1;10
where r is the distance from the cluster centre, t is the time elapsed, N is the (initial) number of radicals and D is the di!usion coe$cient. The average cluster volume may be given by
Dt . <(t)" n
<(t ) (e.g."10 nm); t being derived from eqn (19). The combined e!ect of the recombination and di!usion may be then described with the help of the following set of di!erential equations: dN &"!N & dt
n (2k N #k N & -& Dt
#k N #k N ) C !N (k [O ]#k [N O]), & dN -&"!N -& dt
n (k N #2k N -& Dt &
#k N #k N ) C !N (k [O ]#k [N O]), -& dN -"!N dt
n (k N #k N -& Dt &
#2k N #k N ) - C !N (k [O ]#k [N O]), - dN C"!N C dt
n (k N #k N -& Dt &
#k N #2k N ) C !N (k [O ]#k [N O]), C
where k ,2, k are rate constant of reactions given in Table 2; D being the average di!usion coe$cient of the radical cluster. CONCENTRATIONS OF O AND N O AND ADDITIONAL RADICALS
The quantities [O ] and [N O] represent mo lecular concentrations of O and N O (respec tively) in given water solutions. One can write [O ]"A +1!exp(!(cp )q-),, -
(19)
We will then assume that the di!usion of an average cluster starts from an initial size
(20)
(21)
A , [N O]" 1#j [O ] , +1!exp(!((1!c)p )q,),, ,
(22)
411
THE ROLE OF OXYGEN IN DNA DAMAGE
where c is the oxygen concentration in either gas mixture, A and A are limit solubilities of O , and N O (respectively) in water (at a given pres sure), p , q , p , q , j are free parameters, (1!c) - - , , , is the concentration of N O in the mixture (O !N O). Formulae (21) and (22) enable to take into account a linear concentration rise of individual gases in water as well as saturation characteristics. We will assume that the number of additional radicals formed together with the basic water radicals [see eqn (15)] are proportional to concentrations of [O ] and [N O]; i.e. N "d [O ], N "d [N O], , , N "d [N O], ,, N "d [N O], ,& ,&
(23)
where d , d , d and d are corresponding - , ,,& coe$cients of proportionality. PROBABILITY OF SSB AND DSB FORMATION
The numbers (N , N , N , N ) of e$cient & -& - C radicals in a cluster decrease from their initial values [see eqns (16)] with rising time [according to eqns (20)]. The probability p of SSB forma1 tion in DNA molecules depends then on the instant of encounter of a molecule with a given cluster. One can write for an average cluster p "p #p #p #p #p , 1 & -& A
(24)
where the individual probabilities are given as averages over di!erent t:
p " &
p " -&
t
a N (t) dt, -& -&
t K t
p" C
a N (t) dt, & &
t
t K
p " -
t K
t K t
a N (t) dt, - a N (t) dt C C
(25)
and parameters a , a , a , a are proportional to & -& - C the reaction rates of individual radicals and of e\ ?O with DNA molecules. The value t should correK spond to cluster di!usion time (e.g. to a time when less than two radicals are present in a given cluster). The parameter p in eqn (24) represents a direct e!ect of the given ionizing radiation. The probability of DSB formation may be then given by p "p, " 1
(26)
which may be correlated to experimentally established numbers of DSB at di!erent oxygen concentrations in the corresponding gas mixtures (O !N , O !N O). A proportionlity coe$ cient should be put into eqn (26) as a greater number of SSB may result in one DSB, which is not necessary if one is interested in mere ratios of parameters a , a , a , a . & -& - C Analysis of Experimental Data We shall now apply the model proposed and described in the preceding section to the already mentioned experimental data taken from the paper of Blok & Loman (1973). They irradiated water solution of UX174-DNA at di!erent oxygen concentrations in two mixtures: (a) N !O ; (b) N O}O . The solution containing 25 lg ml\ of DNA in 0.01 phosphate bu!er at pH 7 was irradiated by photons (&1.25 MeV) of Co-60 isotope by the dose of 5 Gy. They established the ratio of DSB and SSB and measured then the dependence of SSB numbers on oxygen concentrations to a greater detail. To test the proposed model we have derived the concentration dependence of DSB by combining both the experimental data of theirs. The corresponding values are shown in Table 3. Our aim consisted mainly in answering the question whether the model is able to represent the drastic change of DSB numbers at smaller oxygen concentrations (see Fig. 1) and what is the role of individual radicals in DSB formation at di!erent oxygen concentrations. The model (containing a series of free parameters) seems to re#ect complexity of radiobiological mechanism in the chemical phase to a su$cient extent. A part of the parameters (reaction and di!usion
412
J. BARILLA AND M. LOKAJID C[ EK
TABLE 3 Experimental data2number of DSB per 1 DNA molecule in dependence on oxygen concentration
TABLE 4
Concentration
No. of DSB per DNA molecule Experimental values
Theoretical values
(a) N }O solution 1. 0.000 2. 0.000 3. 0.020 4. 0.048 5. 0.092 6. 0.300 7. 0.652 8. 0.900
0.063 0.061 0.022 0.046 0.040 0.040 0.038 0.040
0.062 0.062 0.022 0.046 0.040 0.040 0.040 0.040
(b) N O}O solution 1. 0.000 2. 0.017 3. 0.048 4. 0.090 5. 0.500 6. 0.844 7. 0.906 8. 0.965 9. 1.000
0.060 0.084 0.097 0.085 0.077 0.068 0.060 0.050 0.041
0.060 0.085 0.095 0.087 0.076 0.067 0.060 0.050 0.041
96.77 97.04 1.04 10.70 94.82 1.09 183.98 210.81 603.47 0.02 96.86 994.97 915.05 126.15 0.07
Parameter
Established value
k k k A p q A , p , q , j , d d , d ,d ,&
5.94 949.71 1.56 0.89 ) 10\ 435.82 1.52 0.84 ) 10\ 28.56 3289.20 1.67 108.36 23620.00 18096.00 8658.30
The average initial size of radical clusters may be characterized by the values N "17.05, &
rates) may be established in principle from other experimental data (see e.g. values in Tables 1 and 2). The other part should be regarded as quite free; it is necessary to determine them with the help of an optimization procedure to "t the used experimental data. The MINUIT program (James & Roos, 1975) was made use of. To simplify the numerical approach we have "xed the ratios of energy needed to form corresponding radicals by putting U : U : U : U : U : U "1 : 1 : 0 : 0.75 : 0 : 0. (27) The average coe$cient determining the cluster di!usion has been put according to Pikajev (1986): D"3.5 [nm ns\].
k k k k k k k k k k k k k k k
Established value
(28)
The values of other parameters involved in eqns (20)}(25) have been established with the help of the mentioned optimization approach; they are shown in Table 4.
N "18.23 -&
(29)
and the initial number of e\ has been established ?O as N "38.91. C
(30)
The reaction-rate ratios of di!erent radicals with DNA are a : a : a : a "0.01 : 0.10 : 0.07 : 0.03. (31) & -& - C The probability of a direct e!ect is approximately p "0.0007,
(32)
indicating to be practically negligible. Theoretical results as well as experimental data are given in Table 3; they are represented graphically in Fig. 1, too. The percentage e$ciency of individual radicals in formation of individual SSB is shown in Table 5. The direct e!ect of radiation seems to be quite negligible, which is in harmony with probability estimates that beam particles (secondaries included) hits directly a DNA molecule at the given doses. The proposed model has been able to reproduce the given experimental data exhibiting not
413
THE ROLE OF OXYGEN IN DNA DAMAGE
TABLE 5 Ratio (in %) of individual radicals in DSB formation at di+erent oxygen concentrations c (%)
0.0 0.1 1.0 2.0 10.0 100.0
N }O
N O}O
H
OH
HO
e\ ?O
Direct e!ect
H
OH
HO
e\ ?O
Direct e!ect
0.00 0.00 4.43 1.33 0.00 0.00
16.21 3.73 0.00 0.00 0.00 0.00
0.00 0.00 48.18 94.52 99.99 99.99
83.79 96.26 47.30 4.10 0.00 0.00
0.00 0.01 0.09 0.05 0.01 0.01
0.00 0.00 0.17 0.00 0.00 0.00
99.84 98.60 0.00 0.00 0.00 0.00
0.00 0.00 99.24 99.99 99.99 99.99
0.13 1.37 0.55 0.00 0.00 0.00
0.03 0.03 0.04 0.01 0.01 0.01
only the steep decrease of DSB in the close vicinity of zero oxygen concentration but also a small excess of DSB exhibited by experimental data approximately at 5% of oxygen in the mixture with nitrogen. The values of "tted parameters will be in#uenced only insigni"cantly if this e!ect will correspond to mere statistical #uctuations, as they are given mainly by global dependence on oxygen concentration. Conclusion There is a lot of di!erent chemical agents which may strongly in#uence the radiobiological e!ect of ionizing particles when present in cells during irradiation. However, it is not clear very often in which phase of the radiobiological mechanism they are active; whether in the chemical phase in#uencing cell damages or in the biological phase when the damages are being repaired. The proposed mathematical model enables to study the processes of the chemical phase to a greater detail and to analyse the actual role of individual substances in this phase of radiobiological mechanism with the help of experiments performed on DNA molecules in water solutions. The results following from such analyses might contribute to improving radiotherapy approaches by making use of suitable radiomodifying agents. Analyses based on the proposed model might help also in distinguishing between the processes running in the chemical phase and governed fully by laws of non-living nature and those belonging to processes of the biological phase. Our results
have shown that the oxygen may play di!erent roles at di!erent concentrations; the given characteristic being explained fully on the basis of chemical processes (or physical ones when the saturation is taken into account, too). Some other agents in#uencing the oxygen e!ect may be present in living cells (see e.g. van der Schans et al., 1986). However, if the "xation hypothesis is to be doubted the proposed model may be helpful also in such a case. It might be applied directly to the data concerning DSB formation. An eventual extension of the model to cover corresponding modi"cations should not represent a very di$cult task, either. Only more exact data with a greater number of experimental points should be probably needed. As to its possible application to survival curves the model should have to be supplemented by additional assumption concerning the way how cell inactivation depends on the number of DSB and their distribution in the chromosomal system (direct inactivation, repair, misrepair). The corresponding analyses might help also in understanding better the links and di!erences between the laws governing non-biological and biological processes in living matter. The given experiments and theoretical results have shown the role of oxygen radicals in DSB (or SSB) formation to be rather complicated if the high number of DSB obtained by Blok & Loman (1973) at zero oxygen concentration in nitrogen mixture corresponds to reality. Such an e!ect has not been reported in experiments based on inactivation of living cells. It has been always demonstrated and argued that the cell survival has
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increased when oxygen concentration has been diminished. However, it is necessary to assume that if such a survival decrease were observed after rinsing out the oxygen from cell medium it would be attributed to cell dying due to oxygen de"ciency, as cells cannot remain alive being in anoxic conditions for a longer time. The problem should be questioned to a greater detail with the help of more sophisticated experiments at low oxygen concentrations as the similarity of maximum insigni"cant dose may be hardly decisive in this point. The presented model analysis has been based on some simplifying assumptions. A de"nite answer to all opened questions will require a more detailed theoretical analysis involving all possible chemical reactions playing a role in the given mechanism, and of course, more experimental data, too. The model may provide, however, a new tool for solving a series of corresponding problems. REFERENCES ALPER, T. & HOWARD-FLANDERS, P. (1956). Role of oxygen in modifying the radiosensitivity of E. colli. Nature 178, 978}979. BLOK, J. &. LOMAN, H. (1973). The e!ects of c-radiation in DNA. Radiat. Res. 9, 165}245. CHATTERJEE, A., MAGGEE, J. L. & DEX, S. K. (1983). The role of homogeneous reaction in the radiolysis of water. Radiat. Res. 96, 1}19. EWING, D. (1998). The oxygen "xation hypothesis. A reevaluation. Am. J. Clin. Oncol. 21, 355}361. FRANKENBERG-SCHWAGER, M., FRANKENBERG, D., BLOECHER, D. & ADAMCZY, C. (1980). The linear relationship between DNA double-strand breaks and radiation dose 30 MeV electrons is converted into a quadratic function by cellular repair. Int. J. Radiat. Biol. 37, 207}212.
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