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DNA Molecule 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 i 20 ON. 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.
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