25
OFFICIAL ORGAN OF THE RADIATION RESEARCH SOCIETY RADIATION RESEARCH EDITOR-IN-CHIEF: DANIEL BILLEN Volume 83, 1980 ACADEMIC PRESS New York London Toronto Sydney San Francisco
OFFICIAL ORGAN OF THE RADIATION RESEARCH SOCIETY
RADIATION RESEARCH EDITOR-IN-CHIEF: DANIEL BILLEN
Volume 83, 1980
A C A D E M I C P R E S S New York London Toronto Sydney San Francisco
•• - i i f ii r_r_f ' Universitäts-
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München
Copyright © 1980 by Academic Press, Inc. All rights reserved
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MADE IN THE UNITED STATES OF AMERICA
RAD1A11UJN KÜ5fc,AKU*l
OFFICIAL ORGAN OF THE RADIATION RESEARCH SOCIETY
Editor-in-Chief: DANIEL BILLEN, University of Tennessee-Oak Ridge Graduate School of Biomedical Sciences, Biology Division, 0ak Ridge National Laboratory, P.O. Box Y,
Oak Ridge, Tennessee 37830 Managing Technical Editor: MARTHA EDINGTON, University of Tennessee-Oak Ridge Graduate
School of Biomedical Sciences, Biology Division, Oak Ridge National Laboratory, P.O. Box Y, Oak Ridge, Tennessee 37830
ASSOCIATE
H . I . ADLER, Oak Ridge National Laboratory J. W. BAUM, Brookhaven National Laboratory S. S. BOGGS, University of Pittsburgh J. M. BROWN, Stanford University S. S. DONALDSON, Stanford University J. D. EARLE, Mayo Clinic J. J. FISCHER. Yale University E. W. GERN ER, University of Arizona E. L. GILLETTE, Colorado State University R. H. HUEBNER, Argonne National Laboratory' J. W. HUNT, Ontario Cancer Institute, Toronto,
Canada
EDITORS S. LIPSKY, University of Minnesota S. OKADA, University of Tokyo, Japan N. L. OLEINICK, Case Western Reserve
University A. M. RAUTH, Ontario Cancer Institute,
Toronto, Canada M. C. SAUER, JR., Argonne National
Laboratory S. P. STEARNER, Argonne National Laboratory R. C. THOMPSON, Battelle, Pacific Northwest
Laboratories J. E. TURNER, Oak Ridge National Laboratory S. S. WALLACE, New York Medical College
OFFICERS OF THE SOCIETY President: WILLIAM C. DEWEY. Department of Radiology & Radiation Biology,
Colorado State University, Fort Collins, Colorado 80521 Vice President and President-Elect: ODDVAR F. NYGAARD, Department of Radiology,
Case Western Reserve University, Cleveland, Ohio 44106 Secretary-Treasurer: ROBERT B. PAINTER, Laboratory of Radiobiology,
University of California, San Francisco, California 94143 Editor-in-Chief: DANIEL BILLEN, University of Tennessee-Oak Ridge Graduate School
of Biomedical Sciences, Biology Division, Oak Ridge National Laboratory, P.O. Box Y, Oak Ridge, Tennessee 37830
Executive Director: RICHARD J. BURK, JR., 4720 Montgomery Lane, Suite 506, Bethesda, Maryland 20014
ANNUAL MEETINGS 1981: May 31-June 4, Minneapolis, Minnesota
1982: April 18-22, Salt Lake City, Utah
T i tus C . E v a n s , Edi tor- in-Chief V o l u m e s 1-50 O d d v a r F. Nygaa rd , Editor-in-Chief V o l u m e s 5 1 - 7 9
V O L U M E 83 , 1980
Counc i l o r s Radiat ion Resea r ch Society 1980-1981
PHYSICS M. Inokuti, Argonne National Laboratory H. J. Burki, University of California, Berkeley
BIOLOGY J. S. Rasey, University of Washington A. M. Rauth, Ontario Cancer Institute, Toronto, Canada
MEDICINE H. D. Suit, Massachusetts General Hospital J. A. Belli, Harvard Medical School
CHEMISTRY J. F. Ward, University of California, San Diego M. Z. Hoffman, Boston University
AT-LARGE L. A. Dethlefsen, University of Utah R. M. Sutherland, University of Rochester
CONTENTS OF VOLUME 83
N U M B E R 1, JULY 1 9 8 0 L. R. P A I N T E R , E. T. A R A K A W A , M. W . WILLIAMS, A N D J. C. ASHLEY. Optical Properties of
Polyethylene: Measurement and Applications 1 A. B O N I C E L , N. MARIAGGI, E. H U G H E S , A N D R. TEOULE. In Vitro y Irradiation of DNA:
Identification of Radioinduced Chemical Modifications of the Adenine Moiety 19 R. W . M A T T H E W S . The Radiation Chemistry of the Terephthalate Dosimeter 2 7 T. S. T E N F O R D E , S. B . CURTIS, K. E. CRABTREE, S. D. T E N F O R D E , W . A. SCHILLING,
J. H O W A R D , A N D J. T. L Y M A N . In Vivo Cell Survival and Volume Response Characteristics of Rat Rhabdomyosarcoma Tumors Irradiated in the Extended Peak Region of Carbon-and Neon-Ion Beams 4 2
BARBARA C. MILLAR, E. MARTIN F I E L D E N , A N D JENNIFER J. STEELE. Effect of Oxygen-Radiosensitizer Mixtures on the Radiation Response of Chinese Hamster Cells, Line V - 7 9 - 7 5 3 B , in Vitro. II. Determination of the Initial Yield of Single-Strand Breaks in the Cellular DNA Using a Rapid Lysis Technique 5 7
ROBERT P. L I B U R D Y . Radiofrequency Radiation Alters the Immune System. II. Modulation of in Vivo Lymphocyte Circulation 6 6
T. J. WRONSKI , J. M. S M I T H , A N D W . S. S. JEE. The Microdistribution and Retention of Injected 239Pu on Trabecular Bone Surfaces of the Beagle: Implications for the Induction of Osteosarcoma 7 4
GEORGE H. HARRISON A N D ELIZABETH K . BALCER-KUBICZEK. The Oxygen Enhancement Ratio for dim + (Be + Ta) and </(80) + (Ta + Be) Neutrons 9 0
R. P. HILL. Radiation-Induced Changes in the in Vivo Growth Rate of KHT Sarcoma Cells: Implications for the Comparison of Growth Delay and Cell Survival 9 9
W . STEVENS, F . W . BRUENGER, D. R. A T H E R T O N , J. M. S M I T H , A N D G. N. TAYLOR. The Distribution and Retention of Hexavalent 233U in the Beagle 1 0 9
KAZIMIERZ S U L E K , CHARLES J. SCHLÄGEL, WIESLAW WIKTOR-JEDRZECJAK, HENRY S. Ho, WILLIAM M. L E A C H , A F T A B A H M E D , A N D JAMES N. W O O D Y . Biologic Effects of Microwave Exposure. I. Threshold Conditions for the Induction of the Increase in Complement Receptor Positive (CR+) Mouse Spleen Cells following Exposure to 2 4 5 0 - M H z Microwaves 1 2 7
R. L. ULLRICH. Effects of Split Doses of X Rays or Neutrons on Lung Tumor Formation i n R F M M i c e 138
R. F. JOSTES, K. M. B U S H N E L L , AND W . C. D E W E Y . X-Ray Induction of 8-Azaguanine-Resistant Mutants in Synchronous Chinese Hamster Ovary Cells 1 4 6
ISABEL M. F I S E N N E , NORMAN C O H E N , JAMES W . N E T O N , A N D PAMELA PERRY. Fallout Plutonium in Human Tissues from New York City 162
PETER J. CONROY, ROBERT M. S U T H E R L A N D , A N D WILLIAM PASSALACQUA. Misonidazole Cytotoxicity in Vivo: A Comparison of Large Single Doses with Smaller Doses and Extended Contact of the Drug with Tumor Cells 1 6 9
BEVERLY S. C O H E N , MERRIL E I S E N B U D , A N D NAOMI H. HARLEY. Alpha Radioactivity in Cigarette Smoke 1 9 0
CORRESPONDENCE
J. B. ROBERTSON A N D M. R. RAJU. Sudden Reversion to Normal Radiosensitivity to the Effects of X Irradiation and Plutonium-238 a Particles by a Radioresistant Rat-Mouse Hybrid Cell Line 197
TOMMIE J. LAUGHLIN A N D J. HERBERT TAYLOR. The Effects of X Rays on DNA Synthesis in Synchronized Chinese Hamster Ovary Cells 2 0 5
WALTER A. H U N T A N D THOMAS K. D A L T O N . Reduction in Cyclic Nucleotide Levels in the Brain after a High Dose of Ionizing Radiation 2 1 0
N U M B E R 2, A U G U S T 1 9 8 0 EDITORIAL iii R. S. C A S W E L L , J. J. C O Y N E , A N D M. L. R A N D O L P H . Kerma Factors for Neutron Energies below
3 0 M e V W. 217 MARIA-ESTER B R A N D A N A N D PAUL M. D E L U C A , JR. A Detector for the Direct Measurement of
LET Distributions from Irradiation with Fast Neutrons 255 C. H O U E E - L E V I N , M. G A R D E S - A L B E R T , C. FERRADINI, A N D J. P U C H E A U L T . Radiolysis Study of
the Alloxan-Dialuric Acid Couple. I. The Reduction of Alloxan by eäti and COO" Radicals 270 J. M. N E L S O N , L. A. BRABY, A N D W. C. ROESCH. Rapid Repair of Ionizing Radiation Injury in
Chlamydomonas reinhardi 279 T. K. M A N D A L A N D S. N. CHATTERJEE. Ultraviolet- and Sunlight-Induced Lipid Peroxidation in
Liposomal Membrane 290 G U N N A R WESTMAN A N D S T E F A N L. M A R K L U N D . Diethyldithiocarbamate, a Superoxide
Dismutase Inhibitor, Decreases the Radioresistance of Chinese Hamster Cells 303 M U N E Y A S U U R A N O , LEO E. GERWECK, ROGER EPSTEIN, MARY C U N N I N G H A M , A N D HERMAN D.
S U I T . Response of a Spontaneous Murine Tumor to Hyperthermia: Factors Which Modify the Thermal Response in Vivo 312
ERIKA SALAJ-SMIC, DRAGO PETRANOVIC, MIRJANA PETRANOVIC, A N D ZELJKO TRGOVCEVIC. Relative Roles of uvrA and recA Genes in the Recovery of Escherichia coli and Phage A after Ultraviolet Irradiation 323
RICHARD L. W A R D . Mechanisms of Poliovirus Inactivation by the Direct and Indirect Effects of Ionizing Radiation 330
DIETMAR W. S I E M A N N A N D ROBERT M. S U T H E R L A N D . The Interaction between Adriamycin and Radiation in a Solid Murine Tumor 345
CORRESPONDENCE HARRIS S . TARGOVNIK A N D PALGHAT V. HARIHARAN. Excision Repair of 5,6-Dihydroxy-
dihydrothymine from the DNA of Micrococcus radiodurans ABSTRACTS OF TWENTY-EIGHTH A N N U A L MEETING OF THE RADIATION RESEARCH SOCIETY,
N E W O R L E A N S , LOUISIANA, 1-5 June, 1980 ERRATA
Volume 78, Number 3, June 1979: Douglas K. Craig, James F. Park, Gerald J. Powers, and Dennis L. Catt, "The Disposition of Americium-241 Oxide following Inhalation by Beagles," pp. 445-473 496
A D D E N D U M Volume 82, Number 3, June 1980: L. A. Dethlefsen: J. D. Ohlsen, and R. M. Riley, "The
Combined Effects of Hydroxyurea and X Irradiation on Murine Duodenal Mucosa and Host Survival," pp. 518-525 497
N U M B E R 3, SEPTEMBER 1980
ROSE A N N ROTH A N D ROBERT K A T Z . Heavy Ion Beam Model for Radiobiology 499 ALBRECHT M. KELLERER, Y U K - M I N G P. L A M , A N D H A R A L D H. ROSSI. Biophysical Studies with
Spatially Correlated Ions. 4. Analysis of Cell Survival Data for Diatomic Deuterium 511 JOHN CLARK SUTHERLAND A N D KATHLEEN PIETRUSZKA GRIFFIN. Monomerization of Pyrimidine
Dimers in DNA by Tryptophan-Containing Peptides: Wavelength Dependence 529 GEORG ILIAKIS. Effects of ß-Arabinofuranosyladenine on the Growth and Repair of Potentially
Lethal Damage in Ehrlich Ascites Tumor Cells 537 M. J. PEAK A N D J. G. PEAK. Protection by Glycerol against the Biological Actions of Near-
Ultraviolet Light 553 N. D E G A N I A N D D. PICKHOLTZ. Radiosensitivity of Different Tissues from Carrot Root at Differ
ent Phases of Growth in Culture 559
D . S. RAPPAPORT A N D J. M. B R O W N . A Study of the Mechanism by Which Localized Preinocula-tion Irradiation Enhances the Rate of Lymphatic Spread 566
TAKEHITO SASAKI , MASAHIKO Y A M A M O T O , A N D M A S A M U N E T A K E D A . Function of Parotid Gland following Irradiation and Its Relation to Biological Parameters 579
D A V I D C . L. JONES, JOHN S. KREBS, D A N I E L P. SASMORE, A N D C H O MITOMA. Evaluation of Neonatal Squirrel Monkeys Receiving Tritiated Water throughout Gestation 592
JOHN L U N E C , W. A. CRAMP, A N D SHIRLEY HORNSEY. Neutron Irradiation of Bacteria in the Presence and Absence of Secondary Charged-Particle Equilibrium 607
J. G. SZEKELY, T. P. COOPS, A N D B. D. MORASH. Radiation-Induced Invagination of the Nuclear Envelope 621
PETER C. K E N G A N D K E N N E T H T. W H E E L E R . Radiation Response of Synchronized 9L Rat Brain Tumor Cells Separated by Centrifugal Elutriation 633
L Y L E A. DETHLEFSEN A N D REBA M . RILEY. Duodenal Crypt Survival and Crypt Cellular Recovery Kinetics following Combined Treatment with Adriamycin and X Irradiation . . . . 644
P. J. TROCHA A N D G. N. CATRAVAS. Variation in Cyclic Nucleotide Levels and Lysosomal Enzyme Activities in the Irradiated Rat 658
ERIC M . G O L D I N , A N N B. C O X , A N D JOHN T. L E T T . Correlation of Survival with the Restoration of DNA Structure in X-Irradiated L5178Y S/S Cells 668
E D W A R D L. A L P E N , P. POWERS-RISIUS, A N D M . M C D O N A L D . Survival of Intestinal Crypt Cells after Exposure to High Z, High-Energy Charged Particles 677
YOHICHI HASHIMOTO A N D MORIMASA W A D A . Comparative Study of the Sensitivity of Sporesand Amoebae of Dictyostelium discoideum to Ultraviolet Light 688
CHARLES R. G E A R D . Initial Changes in Cell Cycle Progression of Chinese Hamster V-79 Cells Induced by High-LET Charged Particles 696
P A U L R. S E E M A N , JAMES P. O K U N E W I C K , A N D BARBARA BROZOVICH. Rauscher Leukemia as a Model for Cancer Therapy Studies. I. Response to Acute and Fractionated Irradiation . . . 710
A D E L COURDI A N D E D M O N D PHILIPPE MALAISE. Effect of Size of Lymph Node Metastases on the Radiation Response: Influence of Misonidazole 723
CORRESPONDENCE M. ZAIDER A N D H. H. ROSSI. The Synergistic Effects of Different Radiations 732 ETHEL S. GILBERT A N D S I D N E Y MARKS. An Updated Analysis of Mortality of Workers in a
Nuclear Facility 740 OBITUARY 742
BOOK R E V I E W 744
A N N O U N C E M E N T 745
AUTHOR INDEX FOR V O L U M E 83 746
The Subject Index for Volume 83 will appear in the December 1980 issue as part of a cumulative index for the year 1980.
RADIATION RESEARCH 8 3 , 51 1-528 (1980)
Biophysical Studies with Spatially Correlated Ions
4. Analys is of Cel l Survival Data for Diatomic Deuter ium 1
ALBRECHT M . KELLERER, Y U K - M I N G P. L A M , * A N D H A R A L D H . ROSSI* Institut für Medizinische Strahlenkunde der Universität Würzburg, Würzburg, West Germany,
^Radiological Research Laboratory, Department of Radiology, Cancer Center/Institute of Cancer Research, Columbia University College of Physicians and Surgeons,
New York, New York 10032
KELLERER, A. M . , L A M , Y . M . P . , A N D ROSSI, H . H . Biophysical Studies with Spatially Correlated Ions. 4. Analysis of Cell Survival Data for Diatomic Deuterium. Radiat. Res. 8 3 , 511-528 (1980).
An analysis is given of previously reported results of experiments in which cells have been irradiated with pairs of ions of variable mean separation. These studies were motivated by the theory of dual radiation action and specifically by the postulate that the lesions responsible for cell impairment by ionizing radiation are formed by the combination of pairs of sublesions that are molecular alterations produced by individual energy transfers in the cell nucleus. It is concluded that the observations are consistent with dual radiation action, and the most striking finding is that there appears to be a bimodal distribution of interaction distances with maxima at less than 0.1 and more than 1 /xm. Single tracks cause primarily the lesions produced in short-range interactions but they also contribute, at least in late S phase, a relatively small proportion of the long-range interactions which are principally due to a two-track mechanism. The experiments suggest that the radiation-sensitive components of the cell are arranged in a highly nonuniform pattern which may take the form of floccules having diameters of less than 100 nm.
INTRODUCTION
This is Part 4 of a series of four papers which constitute an interim report on a number of experiments, still in progress, on the biological effect of spatially correlated deuteron ions with a linear energy transfer (LET) of about 33 keV//xm. The earlier papers (1-3) will be referred to as papers 1 through 3. The reader is advised to consult paper 1 for the motivation of experiment, paper 2 for the physical setup, and paper 3 for the experimental procedure in the assessment of the survival of V-79 Chinese hamster cells and for the results. The present paper deals with the scheme for analyzing these cell survival data and demonstrates it by application to the limited amount of data collected so far. The reader is urged to bear in mind that the data and their analysis and interpretation are preliminary, as more and better data are being accumulated.
1 The U. S. Government's right to retain a nonexclusive royalty-free license in and to the copyright covering this paper, for governmental purposes, is acknowledged.
511
0033-7587/80/090511-18$02.00/0
512 KELLERER, LAM, AND ROSSI
D U A L RADIATION ACTION From the theory of dual radiation action it has been concluded that observed
cellular effects are due to cellular lesions that are the result of the combination of pairs of sublesions (4). The purpose of the present experiments is a critical examination of this conclusion and, in particular, a determination of the conditions for the combination of sublesions. In the earlier treatment it has, for simplicity, been assumed that sublesions are formed within certain spherical sites in the cell and that the combination probability of two sublesions is independent of their distance, provided both sublesions occur within the site. With this assumption it was concluded from a comparison of various effects produced by neutrons with those produced by sparsely ionizing radiations that combination of sublesions can take place over distances of the order of one or several micrometers. However, it is apparent that the combination probability of sublesions cannot, in reality, be independent of their separation. The site model is therefore an oversimplification, and a generalized formulation of dual radiation action has recently been given that takes into account a more complex geometry of the sensitive structures in the cell and a distance dependence of the combination probability of sublesions that are formed in these sensitive structures (5). This generalized formulation will in the following be applied to obtain conclusions concerning these two geometrical factors.
Energy transfers from ionizing radiations to the irradiated medium occur at discrete points which are termed transfer points.2 Two conditions have to be met if a pair of energy transfers is to produce sublesions which will then combine to create a lesion. First, the transfers have to occur in the sensitive structures in the cell where sublesions can be produced; these sensitive structures are postulated to extend over the entire nucleus, although only a portion of the nuclear volume, termed the matrix, can yield sublesions. Second, the energy transfers have to be close enough in distance that a pair of sublesions that may be produced can combine to form a lesion. Accordingly the probability p(x) that two energy transfers €x and e2 form sublesions that will produce a lesion depends on two functions s(x) and 8(x):
P(X) = — • ( 1 ) Airpx"
The function s(x) is termed the geometric proximity function and depends cnly on the configuration of the matrix. s(x)dx is the expected mass of the matrix n a spherical shell of radius x and thickness dx that is centered at a point randomly chosen in the matrix.3 The second function g{x) is the probability that sub-
2 An energy transfer is energy locally imparted to the medium; it is equal to the kinetic energy of the ionizing particle that undergoes an interaction at the transfer point minus the kinetic energy of any ionizing particle(s) emerging from the reaction. Changes of rest mass are here disregarded, if they cccur the definition is somewhat more complicated (6, 7).
3 s(.x)/47Tpx2 is equal to the quantity that has been called geometric reduction factor of a volurre by Berger (18 ) . It is equal to the probability that a point is in the matrix if it is separated by the distince .v from a random point in the matrix. In the earlier treatment (5) .v(.v) had been given the dimersion volume (instead of mass) divided by length. However, inclusion of the density p of the matrix simplifies some of the formulae.
MOLECULAR BEAM EXPERIMENT—ANALYSIS 513 lesions separated by the distance x do in fact combine. Equation (1) has been obtained earlier (5); it is here presented without derivation.
Experimental results will not usually provide information on the two functions s(x) and#(x) separately. Inferences can, however, be drawn that relate to their product, and it is therefore practical to introduce the function
y(x) determines, according to Eq. (1), the probability of two energy transfers separated by the distance x to produce a lesion. The normalization of the function is arbitrary as Eq. (1) contains a constant that cannot, in general, be determined experimentally. Nevertheless, the convention in Eq. (2) that gives y(x) the dimension of a reciprocal mass is practical [see Eq. (4)]. The evaluation of the function y{x) is the ultimate aim of this series of experiments.
If a medium is exposed to ionizing radiation one deals with a distribution of distances between transfer points. This (nonnormalized) distribution t(x), termed the energy proximity function, is defined in a manner analogous to that of s(x). However, the function relates not to the geometry of the matrix, but to the geometry of the charged particle tracks. t(x)dx is the expected energy imparted to a spherical shell of radius x and thickness dx that is centered at a transfer point which is randomly chosen. Only energy imparted due to the same particle and/or its secondaries and associated particles is considered in the definition of t(x).
With these definitions one obtains, as shown earlier (5), a formula for the total yield of lesions at the absorbed dose D:
k is a factor that can be related to various quantities. One of these is LET. However, it may be assumed that in these experiments A is independent of track separation. This is supported by data of Bird and Kliauga,4 who have found in track-segment experiments on V-79 cells that this coefficient shows no detectable variation between LET values 30 to 65 keV//xm.
The strategy of the molecular ion experiment is to change the function t(x) by exposing the cells to pairs of deuterons with different mean separations. Analysis of cell survival resulting with different mean separations will then provide information on the function y(x). In the studies carried out thus far only three different values of the mean deuteron separation have been utilized (5). However, it will be seen that even these limited results permit significant conclusions.
Recent studies (8) have shown that correlated ions also have higher effectiveness in the production of chromosome aberrations. However, this analysis is restricted to cell survival studies only.
6(D) = k{£D + D2), (3) with
(4)
' R. P. Bird and P. J. Kliauga, Irradiations with the track segment facility and the analysis of data. Annual Progress Report, Radiological Research Laboratory, Columbia University, Report No . COO-4733-2, July 1979, p. 162.
514 KELLERER, LAM, AND ROSSI S I N G L E I O N S P A I R E D IONS
V A C U U M
3 .5-10pm 3 .5-10 H m
M Y L A R M Y L A R
F O I L F O I L
FIG. 1. Schematic diagram of V-79 Chinese hamster cells plated on thin Mylar foils and irradiated by single deuterons and pairs of correlated deuterons. Deuterons of LET approximately 33 keVV/Lim traverse the cells, either as single ions or as pairs of ions originating from a single molecule. The average lateral separation between the two correlated deuterons depends on the Mylar thickness.
GENERAL FEATURES OF THE ANALYSIS In the experiments considered here, an event constitutes the passage of a single
deuteron, a single 3He ion, or a spatially correlated pair of deuterons through a cell. The last case results if, after breaking up in the supporting Mylar foil, the deuterons from a molecule pursue different paths through a cell nucleus, as illustrated in Fig. 1. If the distance between the two tracks at a depth midway through the cell nucleus is denoted by x, then the distribution in x is given by (2, 9)
d{x) = —e-*2lb\ (5) b where b, termed the mean separation at median cell depth, is the root mean square of x, and is dependent on, among other things, the thickness of the Mylar foil. The ion tracks in the cell nucleus can be treated as parallel straight lines, and the LET along them is considered constant (2). The assumptions are met with adequate accuracy. A further simplification arises from the fact that, at the energies selected, the lateral extension of the track can be disregarded in comparison even to the smallest mean separations of the paired ions {10). These considerations make it unnecessary to utilize the results of detailed calculations of t(x). For two parallel straight thin lines with constant LET (denoted by dashed lines in Fig. 1) the function tb(x) takes the form
th(-x) = 2L 2 1 + — b2 (6) (x2 - s2)m
L is the linear energy transfer. Its value is 33 keV//zm for the deuterons applied in the present experiment.
The function tb(x)IL is plotted in Fig. 2 versusxlb . The values resulting from Eq. (4) for different values of b will be denoted by %b. From Eq. (6) it follows that th(x) and consequently f ft differs by a factor of 2, for b = ^ and b = 0.
MOLECULAR BEAM EXPERIMENT—ANALYSIS 515 While t(x) is determined by the physical aspects of the irradiation, the values
£ in Eq. (3) are derived from the biological results. Cell survival curves are fitted to the expression
5 = e~€il)) = e~kl€D+I)2) (7) The objective of the analysis is then to determine the function y(x) that is
consistent with the observed values and the functions th(x) associated with the values of b employed in the experiment
-x
y{x)t,,U)dx = ( 8 ) This includes also the value b = oo, i.e., the case of random incidence of deuterons (breakup foil in place). Furthermore, an experiment with uncorrected 3He ions of linear energy transfer 65 keV/jum is included. This experiment serves as a substitute for the condition b = 0 which cannot be realized experimentally.
ANALYSIS OF THE EXPERIMENTAL DATA To determine the value jjb corresponding to a certain Mylar thickness it is neces
sary to assess the cell survival for a number of doses and then to fit the resulting surviving fractions to Eq. (7). Because of unavoidable fluctuations of cellular sensitivity between experiments the dose-effect curves for different values of b should ideally be performed simultaneously with the same suspension of cells ( / / ) . This would guarantee that the resulting parameters are comparable. However, because of the experimental limitations, it was impossible to irradiate with more than one dose and one Mylar thickness on the same day.
For this reason a method has been chosen which permits the determination of the difference between f ft and £x without the requirement to obtain full survival curves in one simultaneous experiment. The method consists in the determination of the values £b from observed survival ratios. According to Eq. (7) one has
In (SJSb) = £bkD - £x kD. (9) The values k and £x are obtained from the full survival curves for the unpaired deuterons and He ions and is then derived in a least-square fit including all observations for the mean separation h.
1 -
o I 1 1 1 1 1 1 1
0 2 4 6 8
x / b FIG. 2. The energy proximity function of a pair of correlated ions according to Eq. (6). The distance is
normalized to the mean lateral separation b of the ions.
516 KELLERER, LAM, AND ROSSI
T A B L E I Parameters Resulting from the Fit of the Expression In 5 = -tjkD - kD2 to the Survival Data3
Mylar thickness Late S phase GJS phase
(fjitn) btfxm (a/Gy-1) (a/Gy~l) - ( H e + ) 0 0.564 ± 0.027 0.762 ± 0.05
3.5 0.091 0.371 ± 0.042 0.448 ± 0.096 6.4 0.156 0.371 ± 0.041 0.434 ± 0.163
10 0.255 0.335 ± 0.044 0.436 00 0.278 ± 0.034 0.412 ± 0.066
k = (0.03 ± 0.0041) Gy-'2 k = (0.069 ± 0.012) Gy~2
a The corresponding values £ are plotted in Figs. 5, 8, and 9. The least-squares fit has been performed with one value k for the cells in late S phase and one value for GJS cells. The resulting curves are given in Figs. 2 and 4.
The results of the analysis are summarized in Table I. The statistical method is performed with the usual least-squares method (12) in terms of the parameters k and a = k£. Two cell ages, namely late S and G^S, and three foils of different thickness were studied, giving rise to six different combinations. The three thicknesses were 3.5, 6.4, and 10 /xm and yielded values of 0.091, 0.156, and 0.255 /im, respectively, for the mean separation b of correlated deuteron ions at median cell depth [taken to be 3 /im deep (2)] .
For each cell age, the survival data for uncorrected deuteron ions were actually pooled from more than one experiment performed on different days. This was done because these data fitted to Eq. (7) separately did not yield values a«, and k significantly different from one another. The analysis has been based on the assumption of one common value k for the uncorrected deuterons and the He ions. Figures 3 and 4 represent the data and their fit by the curves that correspond to the values given in Table 1. Essentially the same fit is obtained for late S cells if a common value k is not postulated. For G,/S cells an improved overall fit results in a larger value k for the 3He ions and accordingly in a ratio aja^ that is substantially smaller than 2 (see Appendix). However, this fit is poor for the low-dose points that determine a0 for the 3He ions. A direct fit to the low-dose points supports the value ao/aoc = 2. Further support for the ratio aja^ = 2 both for late S-phase and for G^S cells is given in recent track segment experiments with synchronized cells {13), where the initial slope of the survival curves increases by roughly a factor of 2 when the LET changes from 33 to 66 keV//zm. Earlier experiments on nonsyn-chronized cells5 (14) had led to essentially the same result.
For finite separations b the ratios £ö/£oc are considerably less than 2. This means that little combination of sublesions occurs between the two tracks of correlated ions even if their mean separation is only 0.09 /xm. For Gj/S cells the statistical
5 P. W. Todd, Reversible and Irreversible Effects of Ionizing Radiations on the Reproductive Integrity of Mammalian Cells Cultured in Vitro. Thesis, University of California, Lawrence Rad. Lab., UCRL 11614 (1964).
MOLECULAR BEAM E X P E R I M E N T — A N A L Y S I S 517
A B S O R B E D D O S E D/Gy
FIG . 3. Survival curves for late S-phase cells irradiated either with uncorrelated deuterons or 3He ions of twice the LET, as indicated in the diagram. The solid curves through the data are fits corresponding to the parameters in Table I.
uncertainties are too large to permit the conclusion that the ratios are significantly larger than 1. For late S cells a one-sided / test shows that taken together the three values £ft for finite b exceed £«, with significance level 96%. That there is a real increase of the effect for the correlated particles agrees with the conclusions drawn from the more detailed presentation of the data {3).
From the simple site model and the value £ of roughly 10 Gy for uncorrelated deuterons one would have inferred combination distances of the order of 1 /xm, and one would have further concluded that combination of sublesions from two deuteron tracks would be very likely if these were separated by distances of the order of 0.1 ^m. However, the data show that there is, in fact, relatively small interaction between the tracks of correlated ions and one must therefore ask
A B S O R B E D D O S E D/Gy
FIG 4. Survival curves for G,/S-phase cells irradiated either with uncorrelated deuterons or 3He ions of twice the LET, as indicated in the diagram. The solid curves through the data are fits corresponding to the parameters in Table I.
518 KELLERER, LAM, A N D ROSSI
t i ' i i t d : 0 . 9 pm ^ L A T E S C E L L S
1 5
d --1.1pm J
10
t 1 Gy
5 - -
0 a
15
t /Gy
5
i . i i
d = 1.15 pm
. > l 1 '
G 1 / S C E L L S
-
d = 1.5 u m | |
. > l 1 '
G 1 / S C E L L S
I j :
b i i i i -
.001 .01 .1 1 10
M E A N SE PAR A T I O N b / p m
FIG. 5. The ratio £ of the linear and the quadratic coefficient in the survival curves as a function of mean separation b of the correlated deuterons. The values for the uncorrelated deuterons are given on the right-hand border of the diagrams, the values for tracks are given on the left border of the diagram. The standard deviations correspond to the uncertainty of the coefficient a of the linear term. A joint value of k is used for all curves (see Table I). The curves represent the theoretical values £ that result from the simple site model [Eqs. (8) and (10)]. With these equations no agreement with the data can be achieved.
whether this refutes the basic tenets of dual radiation action or whether a function y(x) exists that is consistent with the data.
INTERPRETATION OF THE RESULTS In Figs. 5a and b the values for the cells in late S phase and in G,/S are given
as solid dots together with standard deviations. Figure 5 includes, on the right border, the value for uncorrelated deuterons.
In addition the value is given for uncorrelated 3He ions with LET = 65 keW/xm; this point is plotted at the left border of the diagram. The dose-effect relations for the deuterons and the 3He ions are, as stated, fitted with the same k value of 0.030 Gy"2 for late S cells and 0.069 Gy~2 for G,/S cells.
The site model in its conventional form (sublesions uniformly produced within a sphere of diameter d and interaction probability independent of separation) corresponds, as has been shown (5), to the following function y(x):
r U ) = f l - i l + ^ ) / ^ l for x s d . (10) { 2d Id3)/ 6
MOLECULAR BEAM EXPERIMENT—ANALYSIS 519 Integrating Eq. (8) with this function y(x) as shown in Fig. 6 one obtains the curves
in Fig. 5 for the specified site diameters. All the resulting curves show the expected increase of £ by a factor of 2, as b decreases from large values to values that are small compared to d. It is readily apparent that the experimental data are not in agreement with the computed curves for any selected site diameter. According to the site model the observed values fx correspond to a site diameter of 0.9 and 1.15 ixm for late S and for G,/S cells; this is also in agreement with the values f0 for 3He ions. However, the values %h for the paired deuterons would in all cases have to be considerably larger than the values actually observed. The site model is therefore inconsistent with the data and other functions y(x) have to be examined.
In the present experiment only three different mean separations of the paired deuterons were applied, and it may be expected that there are various functions y(x) that may lead to equal agreement with the observed values £b. In particular this appears likely if one admits the possibility that the probability of two transfers to produce a lesion had a complicated nonmonotonous dependence on distance. While such a possibility cannot in principle be excluded, there is little evidence to support it. For the present analysis it will therefore be assumed that y(x) is a smooth and monotonically decreasing function of distance. With this constraint one can ask for that function y(x) that fulfills the least-squares condition:
y(x)tf)(x)dx - gb minimum (11)
(summation over all five points in Fig. 5a or b). By numerical optimization with the additional constraint that y(x) be a convex
function (from above) in the logarithmic plot the function y(x) depicted in Figs. 7a and b as broken lines have been obtained for late S and G^S cells. The numerical procedure that has been utilized is the method of the generalized reduced gradient (15) in the computer version of Abadie (16). The resulting functions y(x) are de-
10
.01 -
.001 I—i 1—i—' ' I'' • ' — .01 .1 1 10
D I S T A N C E x/pm
FIG. 6 . The functions y{x) that correspond to the site model [see Eq. (10)]. The resulting curves for £ are given in Fig. 5 . The function y(x) has the dimension of reciprocal mass: the unit picogram (pg) is used because it leads to convenient numerical values and also because with density p = 1, it corresponds to 1 /u.m'5.
520 KELLERER, LAM, A N D ROSSI 1 0 0 I — 1 — i — i 1 — i — i 1 — \ — i 1 — I 1 0 0 I—' ' — i — 1 1 — i — 1 1 — r
D I S T A N C E x/pm D I S T A N C E x/pm
FIG. 7. The functions y(.v) that lead to the best fit [see Eq. (11)] of the experimental data. The broken lines provide the best fit if one considers only curves that are convex (from above) in the logarithmic representation. A somewhat improved fit is obtained with the solid lines that do not meet this constraint. The fit obtained with these functions y{x) is represented in Fig. 8.
picted in Figs. 8a and b by the broken lines. These lines are consistent with the observed values & within the statistical errors of the observations.
It is apparent that no statements can be made on the actual form of the function y(x) at very small distances. The main result is therefore the strikingly wide range of interaction distances. According to the functions y(x) the probability of two energy transfers to form a lesion extends up to several micrometers; however, its value must be several orders of magnitude larger if the transfers occur at a separation of the order of 10 nm. This steep increase of the interaction function at small distances follows from the limited interaction between correlated tracks. However, it must be noted that the small but finite interaction probabilities at large distances are equally real. They follow from the presence of a substantial quadratic component in absorbed dose, i.e., from the low absolute values of Sufficient agreement with the experimental data can be achieved only with functions that reach up to a limit of at least 2 ^tm. If the upper limit is chosen to be 1 ^tm, no function y(x) exists that leads to even an approximate agreement with the experimental data. This means that no model based exclusively on short-range combination of sublesions is consistent with the observation of a substantial shoulder of the survival curve that is due to the interaction of independent particle tracks. This statement applies regardless of the geometry of the sensitive matrix in the cell and regardless of the form of the distance dependence for the combination of sublesions.
The precise form of y(x) may differ from that given by the broken lines in Figs. 7a and b. Thus one obtains a somewhat improved fit to the data and somewha: dif-
MOLECULAR BEAM EXPERIMENT—ANALYSIS 521
ferent functions y(x) if one abandons the constraint of convexity and requires merely that y(x) is a smooth monotonic function. With this relaxed constraint one obtains the solid curves in Figs. 7a and b for y(x) and the fit to the data that is indicated by the solid curves in Figs. 8a and b.
The statistical uncertainty of the data is too large to permit the statement that the solid lines in Fig. 7 are valid rather than the broken lines. Nevertheless it is of interest to note that these functions are similar to functions y(x) that would result if DNA were the target and if it were distributed randomly over an extended region of diameter d (several micrometers) in the nucleus of the cell in floccules that have smaller diameters 8 (up to 100 nm). For spherical floccules randomly distributed in a spherical site of diameter d one would obtain the function
y U ) ~ ( l -q){\ - — + —)+q.(\ - i l + i l ) . (12) A H \ 28 283 j H \ 2d 2dV
q is the product of the fraction of the larger volume filled with floccules of sensitive material and a factor that accounts for a possible reduction of the combination probability of sublesions from different floccules compared to that in the same D N A floccule. The first term extends to x = 8, the other term to x = d.
I /G
I i Gy
1 ' 1
Gl / S C E L L S
b i . i
M E A N S E P A R A T I O N b / u m
FIG. 8. The same representation of the experimental results as in Fig. 5. The solid curves represent the theoretical values that result from the functions y(x) that have been obtained by numerical op-timizauon and that are represented by the solid curves in Fig. 7. The broken lines correspond to the broker curves in Fig. 7 that provide the best fit if one admits only functions y(x) that are convex (from above) in the logarithmic plot of Fig. 7.
522 KELLERER, LAM, A N D ROSSI
\ 15
10
5
0
15
10
0 .001 .01 .1 1 10
M E A N S E P AR A T I O N b / p m F I G . 9. The same representation of the experimental results as in Figs. 5 and 8. The curves are the
theoretical values that result if small spherical targets of diameter 8 are randomly distributed in a larger spherical site of diameter d [see Eq. (12)]. Both the solid and the broken curves are consistent with the data; the possibility of values 8 much less than 0.1 /xm can therefore not be rejected.
Figures 9a and b show fits that are obtained with functions y(x) corresponding to Eq. (15). Due to the statistical uncertainties of the data, different values of 8 and d can lead to acceptable fits. All fits are somewhat inferior to that obtained with the functions y(x) from Fig. 7, and, in fact, no full agreement would be expected as the model is clearly a simplification. Nevertheless acceptable agreement is obtained if clusters of diameter 6 = 0.15 fim in a larger domain of diameter 2.2 /xm are assumed for late S cells, and if clusters of diameter 8 = 0.1 /xm in a larger domain of 4 /jlhi diameter are assumed for G,/S cells. However, it is also found that the possibility of much smaller clusters (diameter 8 ~ 0.01 /xm) in the larger domains cannot be rejected, especially in the case of GJS cells where the interaction of correlated tracks is not established with statistical significance. Further data would be necessary to decide this point; it would also be necessary to account for 8-ray structure, if a rigorous analysis at small values x were attempted.
One must therefore conclude that the precise form of the functions y(x) cannot be given with certainty. However, the essential finding is valid, the interaction function y(x) declines sharply at small separations, there is interaction between correlated tracks at least for late S cells, and there must be long-range interactions between independent tracks.
I > i " ' 1 S =.1 pm
• d = i p m
S =.01 urn"'" - ̂
G 1 / S C E L L S
d = i p m 1
b i i I i •
MOLECULAR BEAM EXPERIMENT—ANALYSIS 523 CONCLUSIONS
The data presently available from the experiment are limited and are subject to considerable statistical uncertainties. Nevertheless, two definite conclusions are possible. First, the ratio of the linear to the quadratic component in the survival curves of late S-phase cells is of the order of 10 Gy for the uncorrected deuterons and of the order of 20 Gy for the helium ions that have twice the stopping power and can therefore be assumed to be roughly equivalent to two coinciding deuteron tracks. For G^S cells the values are smaller (5.5 and 11 Gy). Second, with correlated deuterons only a small increase of the effect occurs even if the mean lateral separation of these correlated deuterons is as small as 0.1 /xm. Various functions y(x) can be considered that represent the effectiveness of a pair of energy transfers to create sublesions which then in turn interact to form a lesion. However, no function y(x) leads to values f as low as 10 or 20 Gy for the deuterons or the helium ions if it does not extend to distances x of roughly 1 /im. On the other hand, it is found that even a separation of 0.1 /xm of two correlated tracks leads to a substantial loss of intertrack interactions; two tracks separated by 0.1 /xm are considerably less effective than the helium ion that represents two coinciding tracks. This implies that the function y(x) must decline sharply at distances less than 0.1 /xm. The actual numerical analysis has resulted in estimated curves y(x) that show this property of declining sharply with distance x while reaching out, with small probability, to large combination distances.
D I S T A N C E x / ( j m
FIG. 10. Distributions of initial separations of combining sublesions for the cells in late S phase and in G,/S. In each case distributions are given separately for the linear (intratrack) and the quadratic (intertrack) terms. The distributions are per unit log-interval so that equal areas correspond to equal frequences. The ordinate is given in arbitrary units, but the relative contribution of the intratrack and the intertrack mechanism is correctly represented for single deuterons (L = 32 keW/xm) at an absorbed dose L of 1 0 Gy. The intratrack term is proportional to LD, the intertrack term to D2. The solid and the broken curves correspond to the solid and the broken curves in Fig. 7.
524 KELLERER, LAM, A N D ROSSI
D I S T A N C E x / p m
FIG. 1 1 . Distributions of initial separations of combining sublesions that correspond to a random distribution of spherical targets of diameter S in a larger region d. The distributions for the intratrack component are, in this diagram, given by solid lines, the distributions for the intertrack mechanism by broken lines. The curves correspond to the same functions y{x) that lead to the solid lines in Fig. 9 . The representation is analogous to that in Fig. 10.
For a linear track of stopping power L one has at a distance x to x + dx from an energy transfer an expected energy transfer from the same track equal to 2 Ldx. The expected energy transfer from unrelated tracks is 47rpx 2 Ddx. Using these values and the function y(x) one concludes that the frequency of //7/ratrack combinations at different separations x is proportional to y(x)LD, while the frequency of intertrack combinations is proportional to 4-irpx2y(x)D2. The functions in Fig. 7 then lead to the frequency distributions in initial separation of interacting transfers that are represented in Figs. 10a and b for late S-phase cells and for G^S cells. These functions contain the additional factor x that accounts for the logarithmic scale and preserves the areas under the curves. The intratrack term is proportional to the area under the left-hand peaks; the intertrack term is proportional to the area under the right-hand peaks. The relative contribution of the linear intratrack term and the quadratic intertrack term is correctly represented for single deuterons (L = 32 keV/Ltm) at an absorbed dose D of 10 Gy.
The striking conclusion from Fig. 10 is the large difference in combination distances for the intratrack and the intertrack effect. Combination of sublesions within particle tracks appears to take place predominantly at distances below 0.1 ju-m, while the combination of sublesions from different particle tracks must be almost exclusively due to interactions in the micrometer range.
The possibility has been considered that the sensitive matrix in the cell consists of floccules of DNA distributed over a larger region in the cell nucleus. If this is so, one would have to conclude that the linear intratrack term involves mainly
MOLECULAR BEAM EXPERIMENT—ANALYSIS 525 single floccules, while the quadratic intertrack term involves mostly two D N A floccules. Figure 11 can illustrate this. This figure is analogous to Fig. 10. However, it corresponds to the solid lines in the fit that is represented in Fig. 9 and that results from the assumption of small spherical targets distributed over larger domains. This figure is given in addition to Fig. 10 to emphasize again the point that the exact dependence of the combination probability of sublesions on distance cannot be deduced from the present experiment, while the substantial difference of interaction distances for the intratrack and the intertrack mechanism is well established.
It is of interest to note that in recent experiments with the radioprotector DMSO Chapman et al. (17) have shown characteristic differences in the dose-modifying factors that apply to the linear and the quadratic component in the survival curve. The linear component appears to be more strongly affected than the quadratic component. This could be linked to the fact that the intratract effect is initiated simultaneously by the same particle track, while the sublesions involved in the quadratic effect are produced with a certain temporal separation. However, the authors have considered the additional possibility that their results reflect smaller interaction distances for the linear, one-particle effect and larger interaction distances for the quadratic, two-particle effect. This assumption is in line with the conclusions of the present analysis.
Although the "distance model" was considered in the original publication (4), the simpler "site model'' has frequently been employed. The results of the molecular ion experiment show that the concept of dual radiation action, i .e. , the pair-wise interaction of sublesions, cannot be applied to cell survival in the form of the site model, but they are consistent with the generalized formulation of the distance model (5).
An alternate explanation of the kinetics of cellular radiation effects in general is based on the concept of dose-dependent repair. This concept has been invoked to account for the presence of the shoulder of the survival curve. If the initial damage required highly localized energy transfer it certainly would be expected that even slight separations between tracks result in substantial increase of survival. It might also be argued that the capacity for repair of the damage produced by a single track is somewhat impaired by the presence of another track that is separated by distances of the order of 100 nm or even more; this could explain the degree of synergism that has been found for the correlated ions, and a general dose-dependent decrease of repair capacity could finally account for the observed nonlinear component in the dose-effect relations. However, there is at present no formulation of the concepts that permits a quantitative explanation. Furthermore, the repair model does not account for the second order kinetics of cellular inactivation and of various other cellular effects which is clearly indicated by the dependence of RBE on radiation quality and on absorbed dose (4).
APPENDIX: DETERMINATION OF THE SURVIVAL CURVE PARAMETERS
In the present experiments it has not been possible to obtain full survival curves simultaneously. Even for the uncorrected deuterons and the 3He ions it has been necessary to utilize data obtained in successive experiments. This, together with
526 KELLERER, LAM, A N D ROSSI 1. r * v
< .01 f-
. 0 0 1
.0 0 0 1
G 1 / S C E L L S
3 3 k e V / p m
G1 / S C E L L S .1 r \-
\ 3 H e " '•' 65 keV/pm
01 r \
i . 0 0 1 p
> i
Z> t n i
. 0 0 0 1 — — — • —
0 2 U 6 8 10
A B S O R B E D D O S E D/Gy
FIG. 12. The same survival data as in Fig. 4 fitted to linear-quadratic relations with different coefficients ß. The least-squares fit is obtained with a = 0 . 4 7 Gy - 1 and ß = 0 . 0 5 7 Gy"2 for the deuterons, and a = 0 . 6 1 Gy"' and ß = 0 . 1 1 G y - 2 for the 3He ions. The broken curve segment in the plot for deuterons indicates the inadequacy of the least-squares fit in this dose range.
some of the constraints of the irradiation setup, leads to fluctuations in the survival curves that exceed those attainable under optimal conditions. The statistical analysis of the survival curves in Figs. 3 and 4 may therefore be of limited validity. This is particularly true for the GJS data that show considerable fluctuations.
For these reasons, it is uncertain whether individual fits to the survival curves can lead to reliable conclusions on a possible dependence of the coefficient k on LET. It may nevertheless be helpful to consider the numerical results that are obtained by such individual fits.
For late S cells it is found that the individual fits lead to values k (0.028 and 0.034 Gy"2) similar to the joint value of 0.03 Gy"2. The values of a (0.26 and 0.54 Gy"1) are also close to the values obtained in the joint fit (0.28 and 0.56 Gy"1). All values are consistent with the values quoted in the earlier article (3) that was based on nearly the same set of data points.
For Gj/S cells the results are less consistent. A separate fit (see Fig. 12) leads to values k (0.057 and 0.11 Gy"2) that differ widely from the value k = 0.069 Gy"2 from the joint fit. The values of a (0.47 and 0.61 Gy - 1 ) deviate correspondingly from the values (0.41 and 0.76 Gy"1) of the joint fit.
MOLECULAR BEAM EXPERIMENT—ANALYSIS 5 2 7
A comparison of the curves in Figs. 3 and 4 with those in Fig. 12 and a consideration of the large fluctuations in the data points make it very uncertain whether the results of the separate fits are reliable. In particular, there is in Fig. 12 substantial disagreement of the fit with the low-dose points for the 3 3 keV//xm deuterons. As shown by the broken curve segment, the low-dose points indicate a much smaller value of the initial slope. For this reason a joint k, even for Gj/S cells, has not been rejected in the analysis, and the data in Table I have been used. It must, however, be noted that this introduces an element of uncertainty into the analysis that would require improved experimental data for G^S cells.
ACKNOWLEDGMENTS This investigation was supported by Contract DE-AS02-78EV04733 from the Department of Energy
and by Grant CA 12536 to the Radiological Research Laboratory/Department of Radiology, and by Grant CA 13696 to the Cancer Center/Institute of Cancer Research, awarded by the National Cancer Institute, DHEW. RECEIVED: August 2 4 , 1 9 7 9 ; REVISED: April 17 , 1 9 8 0
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