TOWARD A THEORY OF THE INITIATION OF CANCER BY IONIZING RADIATION: THE TWIN DOUBLET PAIR MODEL

by

John H. Marshall and Antonio Pagnamenta

Prepared for

Seventh Symposium on Microdosimetry

Oxford, England

September 8-12, 1980

MTMBUTIOM Of THIS O0CU«Hrt II

ARGONNE NATIONAL LABORATORY, ARGONNE, ILLINOIS

Operated under Contract W-31-109-Eng-38 for the U. S. DEPARTMENT OF ENERGY TOWARD A THEORY OF THE INITIATION OF CANCER BY IONIZING RADIATION: THE TWIN DOUBLET PAIR MODEL*

John H. Marshall* and Antonio Pagnamenta**

•Center for Human Radiobiology, Argonne National Laboratory, Argonne, 111. 60639, USA, **Department of Physics, University of Illinois, Chicago, 111. 60680, USA.

Introduction Growing knowledge about the basic mechanisms of interaction of radiation with matter at both the cellular and the molecular levels may now be sufficient to allow us to localize the targets for the initiation of cancer at the level of indi- vidual particle tracks, ionizations, and particular bonds in the DNA molecule. It seems clear that the explanation for the LET-dependence of cancer initiation lies at the molecular level whereas the explanation for the dose-dependence lies at the cellular level. The finding of a simple mechanism that yielded the correct ratios of the cross sections for initiation of cancer by x rays, beta, alpha particles would greatly strengthen our knowledge of RBE and dose-response and would allow us to extrapolate more accurately than we do with the pure linear model from existing data in cell culture, animals, and man to the low doses and low dose rates of our radioactive environment. In the following, it Is assumed that dose rates are low enough no longer to affect incidence rates. In the Marshall-Groer theory of the induction of bone cancer by alpha 1 2 radiation, ' it was shown that two initiation events in one flattened endosteal cell at or near bone surface, together with a promotion event, cell killing, and cell replacement, provide an excellent fit over the whole dose-time-response surface to data for induction of osteosarcoma in dog and in man by the alpha particles from radium (Ra-226, Ra-228, and Ra-224). There appears to be a dose range (between 20-40 rads and 140 rads) in which even alpha particles yield a dose-squared response. The finding by Rowland, Stehney, and Lucas that the human osteosarcomas (number of tumors per person-year at risk) caused by long-lived radium are well fit by a square-exponential function of

*Work performed under the auspices of the U. S. Department of Energy. - 2 - injected activity, and that they are not fit (p = 0.03) by a linear-exponential function, strengthens that conclusion. That the csteosarcoma response to radium 4 is much steeper than linear was first pointed out by Evans. Recent data on the stimulation of lymphocytes by mitogens in 45 radium cases showed no significant dependence on radium dose, so the possible effect of immune surveillance on the shape of the dose-response curve due to alpha particles can be tentatively eliminated. The cross section In one cell for each of the two initiation events by -5 radium alpha particles in man found by Marshall and Groer was about 9 x 10 J O O um", which is equivalent to an area 20 A wide and 450 Along, the "diameter of the DNA molecule and the length of about 130 pairs of letters of the genetic code. When factors of geometry and target blackness are taken into account, the actual target may be about 1000 letter-pairs in man (10,000 letter-pairs in g dog). The size of the typical gene is about 1000 letter-pair. Our estimate of this cross section depends on other parameters of the model, particularly the number of cells at risk and the promotion rate; but the order of magnitude is probably right. The target for one initiation is so small that it seems likely the target is about one gene on one DNA molecule. If RNACjr an enzyme or other molecule were the target, it Vtouii exist in so many copies that one disruption could hardly matter to the cell. Is this what is really happening? Is a deletion of information (the loss of one or two letter-pairs) from one gene on one DNA molecule, together with the deletion of the same information on the twin (homologous) DNA molecule somewhere else within the cell nucleus (Figure 1), actually the primary event in the induction of cancer by radiation?" We believe this may be so. The Two-Target Model and the Linear-Square Dose Response? — The Twin Model The statistics of the two-target model (Figure 1) have been worked out 2 and published. At doses greater than about 40 rads, the two DNA targets are more likely to be hit by two independent alpha particles than by one, a square dose response. However, below 40 rads, it becomes more likely that both DNA molecule targets will be hit with one alpha particle, a linear dose - 3 -•

QOR/3

CELL NUCLEUS

J

FIG. 1.—Two-target model of the initiation of cancer by radiation. Each of the two DNA targets is here being considered to require four ionizations per initiation event. The four black dots within adjacent base-pairs represent the postulated ionizations. The energetics of coulomb repulsion between positive charges left in adjacent pyrimidine or purine rings probabL requires four rather than two ionizations per track per double helix to disrupt.

response. (This result corresponds to an endosteal target cell that is flattened and parallel to a bone surface with a nuclear thickness of 1.5 um and a nuclear volume of 180 urn irradiated by a volume source of alpha particles.) This low result of 40 rads for eta (the dose at which the linear and square terms intersect) depends upon our assumption, that each of the two DNA targets may be anywhere within a given cell nucleus. If the two targets were constrained 7 8 to a smaller site, such as 0.5 um, as assumed by Brown or Xellerer and Rossi, then it would be impossible to find a dose range in vivo with a square response for alpha particles: such a square region would only occur for endosteal doses much above 1000 rads and would be unobservable in vivo due to cell killing. The observed square response for the induction of osteosarcoma by radium in man would have to be explained by a systemic effect rather than by the statistics of two targets within the nucleus. - 4 -

If we are correct that there are two targets and that the whole nucleus is the volume within which they are randomly contained, then low LET radiation would show a square dose response down to below one rad and would be about two orders of magnitude less dangerous at environmental levels than is currently estimated on the basis of the linear model. For practical purposes, one beta particle or one x ray photon could not produce both initiations (Figure 1). A Two-Ionization Model for Each Target In our two-target analysis, we used a cross section for initiation to relate the fluence of alpha particles through a cell nucleus to the probability of each of our two initiation events. We did not specify whether one initiation event involved one ionization, two ionizations, or a cluster of ionizations within or near a DNA target region. The fact that cancer induction by radiation depends strongly on LET makes it likely that one initiation event depends on more than one ionization within an extremely small critical region. The shape of g the curve of biological effectiveness versus LET for processes such as mutation and cell killing makes it promising to assume that two primary ionizations must o occur within a distance the order of 1 nm (10 A) or less. For example, see how such an assumption fits the observed cross section for cell killing (derived from the linear part of the survival curve) as a function of LET for x rays, protons, alphas, and heavier ions (Figure 2). The distance o d is roughly 0.3 nm (3 A); n is the number of primary ionizations per nanometer. The solid curve is given by: nd 2 K = Ko (1 - e" )

where KQ is the DNA saturation cross section (corrected for nuclear cross section). This curve has a definite square-of-LET region leading to a plateau at LET much in excess of 100 keV/ym, a behavior we associate with two primary ionizations (doublet) within the DNA molecule, probably one ionization in one base (genetic letter) and the other in an adjacent base. Each of these primary ionizations Is likely to have a close secondary ionization which may land in two more adjacent bases. Each of our two initiation events would then consist of four ionizations each within four adjacent code letters. Conceivably, this mechanism could produce a double strand break in each - 5 -

200 100 50 20 ON. i 10 oUJ CO 5 CO 2 CO . o i oc 1 ; ** 0.5 0.2 0.1 100 1000 10000 LETfteW/im)

FIG. 2.~Prelirainary comparison v2 the two lonization model with the Bevelac datalO for the cross section for cell killing. The curve corresponds to the^ probability of finding two primary ionizations, each within a distance of 3 A, normalized to a plateau value of 100 ym2. These data are relevant to our problem if Go cell killing at low dose rate is due to one unrejoined double strand break.

DNA molecule and could lead to an irreparable disruption of the information in one or two base-pairs in the visinity of the double break. The loss of two pairs of letters of the genetic code would make their correct repair highly improbable (one chance in sixteen), an error-prone repair. If the double break were not rejoined (say one chance in 10-40), then the cell would die. If SOS repair rejoined the double break, it would carry an intragenic mutation. With four positive charges in an array of mean spacing 3-5 angstroms (0.3 - 0.5 tun) we should develop a coulomb repulstion energy sufficient to break two sugar-phosphate backbone bonds plus the base-pair stacking energy: 6 repulsive charge pairs of 4 ev each. Such a mechanism appears to be the simplest approach to the initiation of cancer by radiation. It might have all the properties required to fit the dose dependence and the LET dependence of cancer initiation. Whether it will, in fact, under closer analysis act the way we describe is the question we are - 6 - presently addressing. The current work seeks to bridge the gap between the fundamental studies of alpha, beta and electron track structure and a realistic model of the process of cancer initiation. The Cross Section for Two Ionizatlons within One DNA Molecule — Doublet Model Now that we have the number of delta rays (ionizations) per unit distance along the tracks of alpha, beta, and delta rays down to fourth order (accompanying paper in this Symposium), we can calculate the probability of finding one ionization within a specified distance along each track. If n is the mean number of ionizations per micrometer, and d the specified distance o (we have chosen 3 A as a starting point), then the probability of finding no ionization within distance d, is by the Poisson Law, e . The probability of finding at least one ionization within d is 1 -e . The doublet model for initiation of one DNA molecule which we are testing. Figure 3, requires that o one ioniration fall within 3 A of one of the bases (A, G, C, or T) and that o another ionization from the same track fall within 3 A of an adjacent base. The cross section for this doublet ionization is ,, -nd.2 a = ao(l - e )

FIG. 3.—The Doublet Model of DNA disruption by one charged particle (alpha particle, beta particle, delta ray from alpha, or delta ray from beta), The double helix is drawn to scale with its two sugar-phosphate backbones and its ladder of pairs of letters of the genetic code. A single particle track is shown intersecting two DNA bases. Each of the two ionizations we postu- late must land within 3 A of a base. DNA The energetics of coulomb repulsion suggest that each of these ionizations must have a close secondary ionization in adjacent bases to get sufficient LETTER PAIR energy to break the double helix. - 7 -

where aQ is the geometric cross section, which, when multiplied by the fluence of incident particles (alpha or beta), gives the number of times the stack of base-pairs is intersected by a particle track in the particular length of the DNA carrying the crucial information. We do not have independent knowledge of OQ, but when we compare the initiation cross section in one species of animal for particles of different LET, Og should be the same. Therefore, it is the relative cross section O7OQ, that is of most interest at present. (A 0/OQ value of unity would mean that the target was black.) We use the above formula for contribution to the total cross section of both the main track and all the delta ray tracks. To combine the contributions of the delta tracks, we integrate tr over each delta track length obtaining an associated volume similar to that used by Lea. The sum of the associated volumes per micron of primary particle track length gives total initiation cross section. The results for an incident beta particle are shown in Figure 4. The top curve is the total cross section, 00 indicates that both ionizations are on the main track 11 that both ionizations are on the first order delta tracks, 22 on the second order delta tracks, etc. In Figures 4 and 5, 23 have averaged each cross section over the entire residual range of the beta particle with a given initial energy, so these are track average cross sections (applicable to the in vivo case of a distributed source of particles with no collimation). Note that the doublet ionization occurs more frequently on the first, second, and third order delta rays than it does on the main track of a beta particle of more than 1 MeV. The whole of the main track (including its high LET ending) has a negligible effect on the cross section for a high energy beta emitter such as 90Sr. However, when the beta particle (electron) energy is 1 keV or less, as it is for soft x rays, 13 then the main track takes over and the delta ray contribution is small, The corresponding preliminary plot for an incident alpha particle (Figure 5) shows that the main track dominates for all energies up to roughly 10 MeV. If this Doublet Model is correct, then it appears that the delta rays are not very important in the direct disruption of DNA by natural alpha particles. - 8 -

O 01 0.1 1 10 100 1000 1O0O0 INITIAL BETA FWTICLE ENERQV IN KCV

FIG. 4.~Track average cross sections for the ionization doublet as a function of the initial beta particle energy. (This treats the beta spectrum as a line spectrum. Integration over the beta spectrum for a given nuclide has not yet been done). The curves labelled 00, 11, 22, 33, and 44 refer to doublets on the main track, first delta, second delta, third delta, and fourth delta, respectively.

1O* i i I il I 1 1 F 1O° R A to"1 T 1O-2 I 1O"3 H 1O"4 "lO"*

X 1O" G n io" A o 10 10"1 IO"1 II II 'I I 101 . INITIAL ALPHA PARTICLE ENERCV IN KCW

FIG. 5.—Track average cross sections for the ionization doublet as a function of initial alpha particle energy. The cross sections for each component have been averaged over the whole track of the slowing alpha particle. This graph is preliminary; it does not include Pagnamenta's improvements on the alphatree structure but is based merely on Rutherford's law. - 9 -

A summary of the results sc far is shown in Figure 6. Here the track average cross sections for the alpha and beta particle are plotted together versus initial particle energy. The delta ray contributions have been summed. In Figure 7 are shown the cross sections as a function of the instantaneous energy of the alpha or beta particle (not averaged over the track as in Figure 6. Figure 7 is the cross section to be used when the incident alpha or beta particles are monoenergetic as in track segment experiments.

Conclusions 1. Doublet Model Though refinements must still be made in these calculations, the Doublet Model (Figure 3) looks promising as a candidate for the low dose rate initial damage to DNA involved in cell killing, mutation, and a single cancer initiation. Note in Figure 6 that the track average cross section for beta particles (electrons) of 0.1 to 1 keV is about equal to that for high energy alpha 12 particles, as found by Goodhead for mutations in culture by ultrasoft x rays. Furthermore, in Figure 7, the ratio of the cross sections for 3.4 MeV alpha particles and for 2.2 MeV beta particles is about equal to the corresponding measured ratio in the cell killing cross sections given by M. M. Elking and 13 14 Gordon F. Whitmore (based on work of Barendsen et al.). ' 2. Twin Doublet Model Combining the Doublet Model with the two initiation model of Figure 1, introduced in the latter part of the Marshall-Groer paper, we obtain the Twin Doublet model of the initiation of cancer by ionizing radiation. Prelimi- nary comparison of its predictions for the ratio of the initiation cross sections derived by fitting the Marhsall-Groer model to 22SRa versus 90Sr in the osteosarcoma data for beagle dogs from the Radiobiology Laboratory at Salt Lake City, Utah, locks hopeful. 3. Twin Doublet Pair Model As pointed out above, the energetics of coulomb repulsion appear to require more than two positive charges left within the double helix. Preliminary trials suggest that a beta particle could not produce more than four such ioniza- tions and still fit data. We suggest 4 ionizations as the model of choice. PAHTICUr ENEROV IN KCU FIG. 6.—Summary graph. Track average cross section for the ionization doublet as a function of initial particle energy.

10 10= PARTICLE EMEROV IH KEV

Fig. 7.—Summary graph of the doublet cross sections themselves as a function of instantaneous particle energy.

Returning to Figure 2, we can now explain the entire shape of the behavior of cross section versus LET, including the linear region of low LET. In our results, whether the initiation cross section goes as LET^ or just as LET depends upon whether the doublet ionizations which contribute most of the cross section lie directly on the main track or whether they lie on the delta rays, respectively. The latter case goes directly with LET even with the ionization doublet because the causative factor is a single primary ionization. This is the case for electrons of energy greater than a few KeV (Figures 6,7) for which the main track contribution to the doublet is no longer significant. - 11 -

References 1. J. H. Marshall and P. G. Groer, A theory of the induction of bone cancer by alpha radiation, Radiat. Res. 71, 149-192 (1977). 2. J. H. Marshall and P. G. Groer, A possible low-lying linear component in the induction of bone cancer by alpha radiation. Energy and Health, Proc. of a SIMS Conf., N. Breslow and A. Whittemore, Eds., Alta, Utah, June 1978, pp. 39-60. 3. R. E. Rowland, A. F. Stehney, and K. F. Lucas, Jr., Dose-response relationships to female radium dial workers, Radiat. Res. 715, 368-383 (1978) 4. R. D* Evans, Radium in man. Health Pbys, 27. 497-S3.rt <1374). 5. C. S. Serio, C. B. Henning, and E. L. Lloyd, Mytogenic stimulation of peripheral lymphocytes in radium cases, RER Annual Report: ANL-79-65, p. 143, Intl. J. Radiat. Biol. (In press). 6. J. D. Watson, The molecular biology of the gene, W. A. Benjamin, Inc., Reading, Mass., 1980. 7. J. M. Brown, The shape of the dose-response curve for radiation carcino- genesis: Extrapolation to low doses, Radiat. Res. 71, 34-50 (1977). 8. A. M. Kellerer and H. A. Rossi, The theory of dral radiation action. Current Topics in Radiation Research Quarterly 8, 85-158 (1972). 9. R. Cox, J. Thacker, D. T. Goodhead, andR. J. Munson, Mutation and inactivation of mammalian cells by various ionizing radiations. Nature 267, 425-427 (1977) 10. T.C.H. Yang, E. Blakely, A. Chatterjee, G. Welch, and C. A. Tobias, Response of cultured mammalian cells to accelerated krypton particles, COSPAR Life Sciences and Space Research, Volume XV, R. Holmquist and A. C. Stickland, Eds., Pergamon Press, Oxford, pp. 169-174 (1977); also data in P. W. Todd, Ph.D. Thesis UCRL-11614, University of California (1964). 11. D. E. Lea, Actions of radiation on living cells, University Press, Cambridge (1947) 12. D. T. Goodhead, Inactivation and mutation of cultured mammalian cells by aluminum characteristic ultrasoft x rays. III. Implications for the theory of dual radiation action, Int. Radiat. Biol. 32, 43-70 (1977). 13. M. M. Elkind and G. F. Whitmore, The radiobiology of cultured mammalian cells, Gordon and Breach, New York, p. 219 (1967). 14. G. W. Barendsen, H. M. D. Walter, J. F. Fowler, and D. K. Bewley, Effects of different ionizing radiation on -human cells in tissue culture. III. Experiments with cyclotron-accelerated alpha particles and deuterons, Radiat. Res. 18, 106-119 (1963).