Studies on the induction of translocations in mouse spermatogonia

Mutation Research Elsevier P u b l i s h i n g C o m p a n y , A m s t e r d a m P r i n t e d in T h e N e t h e r l a n d s

427

STUDIES ON T H E INDUCTION OF TRANSLOCATIONS IN MOUSE SPERMATOGONIA I. T H E E F F E C T OF DOSE-RATE A. G. S E A R L E , E. 17. E V A N S , C. E. F O R D AND B. J. W E S T w i t h A p p e n d i x b y D. G. P A P W O R T H Medical Research Council, Radiobiological Research Unit, Harwell, Didcol, Berhs. (Great Britain) (Received A u g u s t t 2 t h , 1968)

SUMMARY

The effect of dose-rate on the induction of reciprocal translocations in mouse A type spermatogonia by 600 R X- and ),-irradiation was studied by scoring multivalent configurations in descendant spermatocytes. With X-irradiation over a range of dose-rates from 0.8 to 913 R/rain there was no significant change in the frequency of affected spermatocytes, which averaged 12.8°/o . With ),-irradiation, however, there was a steady increase in frequency from 1.4% at 0.02 R/rain to 12.1°/o at 86 R/rain, the points fitting a straight line on a semi-log plot. At 0.08 R/rain the X-ray yield was twice that for 7-rays. Possible reasons for these differences are discussed. Frequencies of o, I, 2 translocations per spermatocyte did not fit a Poisson distribution since there were less then expected in the 1-class, but more in higher classes. This was probably a consequence of differential radiosensitivity of the irradiated spermatogonia, although preferential clonal proliferation may also be involved.

INTRODUCTION

After the discovery that reciprocal translocations could be induced by irradiation of mouse spermatogonia% 1°,13,~ as well as of post-meiotic germ-cell stages, PHILLIPS AND SEARLE15 investigated the effect of dose-rate on translocation yield, as measured by the frequency of semi-sterility in the F1 males. They found that the incidence of heritable semisterility following 1200 R chronic ),-irradiation of spermatogonia was significantly lower than that resulting from a fractionated dose of 1200 R acute X-irradiation given to males of the same hybrid stock in a previous experiment 13. They attributed this dose-rate effect to the restitution of chromosome breaks, with less opportunity for the formation of interchanges when the radiation dose is protracted. Since the development of an air-drying technique for meiotic preparation of mammalian testes 3 a more direct approach to the problem of chromosomal aberrations in pre-meiotic germ-cells has become feasible. Large random samples of spermaMutation Res., 6 (1968) 427-436

428

A.G. SEARLE et al.

tocytes in diakinesis or metaphase I can now be readily obtained from a single male mouse and confidently scored for the presence of multivalent configurations indicative of reciprocal translocation. The frequency of such configurations gives a better indication of the true frequency of induction of translocations in the pre-meiotic germcells being studied than is obtainable from a genetic analysis, since the time available for action of selective processes is shorter. Thus it was decided to use this cytological approach for a more detailed study of the effect of dose-rate. The chief aims were (a) to find the form of the response curves, for X- and y-irradiation, (b) to derive from this and from fractionation studies an estimate of the average length of time before restitution of breaks, (c) to compare this type of dose-rate phenomenon with that obtained for specific locus nmtations after irradiation of mouse spermatogonia. Some preliminary results of this experiment have been published in abstract form 2a. PLAN

OF EXPERIMENT

F 1 (C3H/HeH ~ × I o I / H ~) hybrid male mice of ages ranging between 6 and i i weeks were given doses of approx. 6oo R X-irradiation (HVL 1.2 mm Cu, 25o kVp) or 6°Co v-irradiation at 13 different intensities between o.o2 and 91o R/min (Table I). Irradiations were carried out in 4 groups, as shown in Table I, the groups being treated on different dates, as follows: I in May 1965 (April-June for the lowest intensity), I I in Sept.-Oct. 1965, I I I in Feb. 1966 and IV in Sept. 1966. Three mice were irradiated at each intensity except in group II, for which there were two. All exposures were continuous except for the one at o.o2 R/rain, which was given in 44 nightly exposures of 12 h. 12-14 weeks after the end of the irradiation period the mice were killed and meiotic preparations made by the air-drying method of EVANS et al. a. Totals of 800 (groups I and II) or 4oo (groups I I I and IV) spermatocytes per mouse were scored for the presence of multivalent configurations, with equal numbers of ceils from each testis except in one mouse given 91o R/min, where one testis had insufficient scorable cells. Full details of the scoring process are given elsewhere 1.

TABLE

I

DISTRIBUTION OF PRESUMPTIVE TRANSLOCATIONS IN PRIMARY ,KS S P E R M A T O G O N I A WITH 600 R AT DIFFERENT DOSE-RATES

SPERMATOCYTES

AFTER

Group T y p e of radiation

Dose-rate (R/rain)

N u m b e r of translocations o z 2 3 4

Total number in sample

11 I IV III 11 111

X X X X X X

91o 89 9. 8 9.7 5.0

1395 2[o9 lO41 [o38 1396 lOl 9

185 237 137 134 185 159

15 39 20 15 17 20

5 14 2 13 2 o

o I o o o 2

16oo 2400 12oo I2OO 16oo i2oo

i2.81 12.12 i3.25 13.5 ° 12.75 15.1o

IIl

X

2. 4

lO53

135

12

o

o

12oo

12.25

Ill IV IV I 1I 1

X ?, ~, 7 7 7

o.8o 83 11 0.86 0.09 0.02

lO71 1o55 [°77 228o 1553 2367

124 125 113 I16 47 33

5 19 9 4 o o

o 1 t o o o

o o o o o o

12oo 12oo 12oo 2400 16oo 2400

lO.7O 12.o8 lO.25 5.00 2.94 1.37

87

2VIutation Res., 6 ( 1 9 6 8 ) 4 2 7 - 4 3 6

IRRADIATION

Pe r cent cells with translocations

I N D U C T I O N O F T R A N S L O C A T I O N S IN M O U S E S P E R M A T O G O N I A . 1. TABLE

429

II

DEGREE

OF I N D E P E N D E N C E

OF T R A N S L O C A T I O N S IN S P E R M A T O C Y T E S

\VITH MORE THAN ONE

Translocalions/ spermatoeyte

W i t h no chromosomes shared

W i t h one shared

W i t h two shared

Total

2 3 4

i2o 15 l

55 21 2

2 o

175 38 3

RESULTS

T a b l e I shows t h e p o o l e d results for t h e b a t c h e s of mice i r r a d i a t e d at different d o s e - r a t e s over t h e 5oooo-fold range. I t can be seen t h a t up to 4 reciprocal t r a n s l o e a tions were d i a g n o s e d as being p r e s e n t in i n d i v i d u a l s p e r m a t o c y t e s , on t h e basis of t h e n u m b e r a n d t y p e of m u l t i v a l e n t configurations observed. I n those s p e r m a t o c y t e s carr y i n g m o r e t h a n one t r a n s l o c a t i o n (Table II) it was f r e q u e n t l y f o u n d t h a t t h e t r a n s locations d i d n o t involve i n d e p e n d e n t pairs of c h r o m o s o m e s b u t s h a r e d i or even 2 chromosomes, as shown b y the f o r m a t i o n of m u l t i v a l e n t configurations w i t h 6 (or V + I ) a n d 8 e l e m e n t s respectively. P r e s u m a b l y this is m a i n l y or e n t i r e l y the result of t h e 2.5:1 range of l e n g t h in the 20 pairs of m o u s e chromosome, w i t h t h e largest ones being m u c h m o r e likely to be i n v o l v e d in a t r a n s l o c a t i o n t h a n t h e smallest ones. L i n k a g e studies on mouse t r a n s l o c a t i o n s t e n d to confirm this. F o r each testis e x a m i n e d t h e d i s t r i b u t i o n of p r e s u m p t i v e t r a n s l o c a t i o n s was t e s t e d for goodness of fit to a Poisson d i s t r i b u t i o n . The m e t h o d s used a n d t h e results o b t a i n e d are given in t h e A p p e n d i x b y D. G. PAPWORTH. There were significant d e v i a t i o n s from e x p e c t a t i o n w i t h r e s p e c t to a n u m b e r of t h e X - r a y results, w i t h a general t e n d e n c y for a deficit of t r a n s l o c a t i o n s in the 1-class b u t a surplus in the higher classes. T h e possible m e a n i n g of this is discussed later. T h e r e was no significant overall h e t e r o g e n e i t y either b e t w e e n testes (ff = 46.44, d.f. = 36, P = o . i i ) or b e t w e e n mice (Z2 = 2o.51, d.f. ~ 23, P = o.61) in t h e frequencies of affected s p e r m a t o c y t e s following the i r r a d i a t i o n at different dose-rates. S t a n d a r d errors of t h e frequencies, shown in Fig. I, are therefore b a s e d on the usual 16

o . . . . x-rays

. . . . . r-~oy~

I

I

w b_

~8 ~J u [x

i t 0 0.01

0.I

I

DOSE

I0

I00

I000

R A T E (R//MIN)

F i g . I. F r e q u e n c i e s ( w i t h s t a n d a r d e r r o r s ) of s p e r m a t o c y t e s c a r r y i n g o n e o r m o r e t r a n s l o c a t i o n s , a s j u d g e d b y t h e o c c u r r e n c e of m u l t i v a l e n t c o n f i g u r a t i o n s , a f t e r 6 0 0 R X - o r ; M r r a d i a t i o n a t different dose-rates. Semi-log plot.

M u t a t i o n Res., 6 (1968) 4 2 7 - 4 3 6

43 °

A, G. SEARLEet al.

binomial formula [x/(pq/n)] except where individual differences between testes or between mice were significant at the 5 % level or higher.With these frequencies the standard errors have been increased by the appropriate heterogeneity factors 5. Fig. I shows that while the frequency of affected spermatocytes following v-irradiation rises fairly steadily with logarithmic increase in dose-rate there is little sign of any such effect following X-irradiation, although the lowest frequency of affected spermatocytes is at the lowest do:se-rate. The variance between the mean numbers of translocations per spermatocyte at the 8 X-ray dose-rates is not, in fact, significantly greater than the pooled variance between mice and between testes, the variance ratio being 1.64 for (7,59) degrees of freedom. Thus the X-ray data provided no significant evidence of a dependence on dose-rate of the frequency of affected spermatocytes. For the y-ray data, it was found by the method of maximum likelihood that there was no significant departure from linearity when the points shown in Fig. I were fitted to a straight line (Z32 = 6.63 and P = o.o85). Best estimates of intercept and slope were (6.12 -~ o . 2 7 ) . i o 2 and (2.9o ~ o.19). IO " respectively. Thus F -- 6.1 + 2.9 log10D, where F is the ~ frequency of affected spermatocytes and D is the doserate in R/min. Analysis of the data with respect to the numbers of translocations per spermatocyte was based on the assumption of a Poisson distribution. Taken as a whole, the data showed highly significant heterogeneity between testes (Z~ = 68.61, d.f. -- 36, P = o.ooo87) though not between mice. Other results agreed with those obtained for the proportions of affected spermatocytes, but less reliance was placed on the analysis based on numbers of translocations per spermatocyte because it was known that the distribution of o, I, 2, 3 ..... translocations per cell was in fact a poor fit to a Poisson distribution (see Appendix). DISCUSSION

An unexpected finding was the marked difference in the type of dose-rate response with X- and with v-irradiation. Only at the lowest point of the thousandfold range of X-ray intensities was there any suggestion of a change in translocation frequency, and the data as a whole showed no significant heterogeneity. With v-irradiation, however, there was a steady increase in translocation frequency with increase in the dose-rate, so that the points fitted a straight line on the semilog plot used. Thus at the lowest coinparable dose-rate (o.8-o. 9 R/rain) the translocation frequency with X-irradiation was twice that with v-irradiation (Table I), a difference which is clearly significant. At higher comparable dose-rates, however, the differences became less, although the X-ray frequency was higher than the T-ray one at each point of coinparison. An R B E of more than I for genetic effects of X- as against v-rays has also been found by a number of other workers~L though the figure has usually been less than 1.5. One relevant example is the finding of an R B E of 1.35 by CO.','GERat al. ~ for 25o kVp X-rays against 6°Co v-rays with respect to chromosomal exchange aberrations in Tradescantia. The reason for the higher effectiveness of X-rays probably resides in their higher track average L E T (2.6 keV/# compared with o.27 keV/# for 6°Coy-rays)L with an L E T range of o.4-36 keV/# for 2oo kVp X-rays compared with o.2-2 for 6°Co y-rays, according to JOHNS11, :YIutation Res., 6 (1968) 427-436

INDUCTION OF TRANSLOCATIONS IN MOUSE SPERMATOGONIA. f.

431

The marked difference between the dose-rate dependence of the y-ray response and virtual independence of the X-ray response might be connected with (i) a saturation effect with X-irradiation (ii) a high proportion of the X-ray-induced translocations, but not of the y-ray-induced ones, being the result of 1-track rather than 2track events (iii) different intensities of germinal selection with the two radiations, giving rise to secondary differences in transloeation frequency even where the initial responses in A type spermatogonia are similar. One line of evidence on this last point could be obtained from comparisons of the extent of spermatogonial killing after X- and y-irradiation at the same dose-rates. Such information does not seem to be available at present, but OAKBERG AND CLARK14 found no significant differences in survival of type A spermatogonia after 600 R X-irradiation at 86 and 9.3 R/rain and 600 R v-irradiation at 0.8 R/rain. So there is no evidence to suggest that the intensities of germinal selection are very different in the two series, insofar as these intensities are related to cell-killing. As far as surviving cells are concerned, long-continued germinal selection would lead to a progressive change in translocation frequency with increasing length of time after irradiation. We have tested this point in other experiments on X-irradiated mice 4 and found no evidence for it. If there was a saturation effect with X-rays at the 600 R level, so that no greater response was possible at high intensity than at low, then one would expect to see some signs of it where the dose rather than the dose-rate was varied. LI~ONARD AND DEKNUDT12 reported a linear response for translocation induction in mouse A type spermatogonia with acute X-irradiation (IOO R/rain) at doses between o and 600 R, the 600 R point being close to the straight line of best fit. In a similar experimenO we have found that 800 R acute X-irradiation (9° R/min) gave a frequency of 16. 5 ~2.2 o/ /o for spermatocytes carrying translocations, which is higher than any of the frequeneies obtained with 600 R in the present experiment. However, comparison with lower doses indicated that there was some flattening of the dose-response curve at the 8oo R level. Thus the evidence available supports the idea that the maximum frequency of affected spermatocytes results from acute irradiation with more than 600 R, so that expression of a dose-rate effect should still be possible at the 600 R level. There remains the possibility that the kinetics of translocation induction in spermatogonia is different for the 2 types of radiation and that this difference remains unobscured to the spermatocyte stage at least. The idea that translocation induction in spermatogonia may be mainly a one-track process with X-irradiation is supported by LI~ONARD AND DEKNUDT'S12 finding that the dose-response is linear. A doseresponse curve for translocation induction by acute y-irradiation has not yet been constructed, so its linearity or otherwise must remain a matter for conjecture at present. It is clear that further experiments will be necessary before the true interpretation of these results becomes apparent. These should include (i) a dose-response curve for acute y-irradiation (ii) acute y-irradiation at a dose-rate of about iooo R/rain, to see if the linear relationship continues to hold (iii) attempts to give Xirradiation at an even lower dose-rate (iv) fractionation studies. These effects of radiation quality and dose-rate on translocation induction in spermatogonia can be compared with those obtained for specific locus mutations in the same germ-eells17-19, 21. The overall magnitude of the dose-rate effect is larger with translocation induction, since the proportion of affected spermatocytes at the Mutation Res., 6 (1968) 427-436

432

A.G. SEARLE et al.

highest dose-rate of y-rays used is about nine times that at the lowest. This compares with a ratio of 3.2 for acute X-versus chronic v-radiation at the same dose-rates for specific locus mutation induction. No direct comparison of the relative effectiveness of X- and y-radiation at the same dose-rates has been made for specific locus mutation induction, but RUSSELLe~ al. 2l found no significant difference in nmtation frequencies obtained from 600 R 6°Co v-irradiation at 24 R/inin and the same dose of X-rays given at 80-90 R/rain, though the actual X versus V ratio was 0.78. This agrees with our findings at similar dose-rate levels. However, RUSSELLiv also found that the specific locus mutation frequency after 600 R X-irradiation at 9 R/lnin was significantly below that at 9 ° R/rain, while that at o.S R/rain v-irradiation was no higher than at lower dose-rates down to o.ooi R/rain. Both these results are in marked contrast to the translocation findings. Thus it seems probable that there are different mechanisms for these two dose-rate effects found after spermatogonial irradiation. As the Appendix shows, results frequently diverged from those expected on a Poisson distribution. Frequencies in the 1-class were less than expected and in the higher classes were more than expected, the deviation from Poisson thus tending to increase the variance. Thus the type of divergence differs from that obtained by ATWOOD and WOLFF24 for chromosome exchanges in Tradescantia microst)ores, V i c i a and barley seed, where there were more than expected of the 1-class and less of the 2-class. However, it should be remembered that in our material the treated A type spermatogonia must have undergone a large number of mitotic divisions during the I2 14 weeks between irradiation and examination during the subsequent ist meiotic division. Thus the divergence from a Poisson distribution may have arisen during that period and thus be a secondary effect. One factor which might lead to the type of divergence we found would be selection for or against particular translocation-carrying germ-cell lineages, during the period of mitotic multiplication. Preferential clonal proliferation occurs in irradiated normal tissues of the mouse*, ~ and has been demonstrated in some neoplastic cell populationsL but very little is known about the situation in immature germ-cells of mammals. Identification of clones at meiosis presents problems in the mouse, since chromosomes are all acrocentric and do not differ greatly in length. However, the relative lengths of the 4 segments in the quadrivalent help to distinguish translocations from each other and should permit recognition of clones. Those involving an X-autosome translocation can be recognised more easily, but no translocation involving the sex chromosomes was found in the present experiment. A clone of cells can be diagnosed with confidence where a group of spermatocytes, each containing several multivalent configurations of similar type, is found in one testis only of an irradiated mouse. This is especially so if large configurations are formed, e.g. rings or chains of 6 or 8 chromosomes, as happens when the saine chronmsome is involved in more than one translocation (Table II). Probable clones in our material which were identified by this method are given in Table III. There seems little doubt that some of these represent examples of preferential clonal proliferation. One example is the cluster of 13 among 2oo spermatocytes sampled from one testis, which was induced by 6oo R X-irradiation at 9.8 R/min. OAKBERG AND CLARKI4 found 8.6 o/,.o survival of A type spermatogonia after 6oo R at 0 R/min. Since the total number of type A gonia in the mature mouse testis probably lies between 5"IO5 and io 6 (E. F. OAKBERG, personal communication) the actual Mutation Res., 6 0968) 427-43(~

433

INDUCTION OF TRANSLOCATIONS IN MOUSE SPERMATOGONIA. 1. TABLE III CONSTITUTIONS OF PROBABLE CLONES OF SPERMATOCYTES WITH DERIVED FROM X - I R R A D I A T E D SPERMATOGONIA

MULTIPLE

TRANSLOCATIONS,

Dose-rate ( R /rain)

Total in clone

Arrangements found, with numbers oj each type in brackets

4.96 9-7 9.8 89

2 2 ~3 7

I ring V I @ 2 chain IV (I), I chain V I + I chain IV i 1 ring lV (1) t ring V I I I (I), I chain V I I I (t) 3 ring IV (5), 2 ring IV + I chain IV (5), 1 ring IV i 2 chain IV (3) I ring V I + I ring IV (I), I ring VI ~I chain IV (3), i chain V I + I chain IV (3)

numbers surviving such a radiation regime m a y well be around 50000. So such a large cluster can hardly have occurred by chance. RUSSELL AND RUSSELL2° found only 4 clusters of 2 each among i i i specific locus nmtations recovered following 6oo R acute X-irradiation to spermatogonia, where the average number of offspring examined per male was probably at least IOO. Thus it is possible that the divergence from a Poisson distribution is largely due to a tendency for spermatogonia carrying more than one translocation to show preferential clonal proliferation. This possibility clearly needs further study and analysis. It seems more likely, however, that the main cause is differential radi(~sensitivity. The tendency, described in the Appendix, for the distributions to diverge from a Poisson in the direction of a negative binomial is indicative of heterogeneity in the irradiated gonia with respect to genetic sensitivity. If so, this is probably connected with differential radiosensitivity during the gonial cell cycle, for which thele is good evidence from fractionation experiments TM. Alternatively the heterogeneity m a y be between different sub-populations of A type spermatogonia. Only further studies can discriminate between these and other possibilities. ACKNOWLEDGEMENTS

We are very grateful to Dr. A. L. BATCHELOR and Mr. M. J. CORP for looldng after the dosimetric side of the experiment, and to Mr. D. G. PAPWORTH for considerable help with the statistical analysis. REFERENCES I ASWOOD-SMITH, M. J., E. P. EVANS AND A. G. SEARLE, The effect of h y p o t h e r m i a on the induc-

tion of c h r o m o s o m a l m u t a t i o n s b y acute X-irradiation of mice, Mutation Res., 2 (1965) 544-551 . 2 CONGER, A. D., M. g. RANDOLPH, C. E. SHEPPARD AND H. J. LUIPPOLD, Q u a n t i t a t i v e relation of R B E in Tradescantia and average L E T of g a m m a - r a y s , X - r a y s and 1.3-, 2.5- and i4. i-Mev fast neutrons, Radiation Res., 9 (1958) 525 5473 EVANS, E. P., G. BRECKON AND C. E. FORD, An air-drying m e t h o d for meiotic p r e p a r a t i o n s from m a m m a l i a n testes, Cytogenetics, 3 (1964) 289-294. 4 EVANS, E. P., C. E. FORD, A. G. SEARLE AND B. J. WEST, U n p u b l i s h e d information. 5 FINNEV, D. J., Statistical Methods in Biological Assay, Griffin, London, 1964 (2nd ed.). 6 FORD, C. E., Selection pressure in m a m m a l i a n cell populations, Syrup. Intern. Soc. Cell Biol., 3 (1964) 27-45. 7 FORD, C. E., AND C. M. CLARKE, Cytogenetic evidence of clonal proliferation in p r i m a r y reticular neoplasms, Can. Cancer Conf., 5 (1963) 129-146. 8 FORD, C. E., P. L. T. ILBERY AND J. F. LOUTIT, F u r t h e r cytological observations on radiation chimeras, J. Cell. Comp. Physiol., 5 o, Suppl. I (1957) I O 9 - I 2 I . 9 GRIFFEN, A. B., Occurrence of c h r o m o s o m a l aberrations in p r e s p e r m a t o c y t i c cells of irradiated male mice, Proc. Natl. Acad. Sci. (U.S.), 44 (I958) 691-694.

Mutation Res., 6 (1968) 427-436

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A.G. SEARLE et al.

IO (;RIFFEN, A. B., The occurrence of chronlosonlal aberrations in prespermatocytic cells of irra-

11 12

13 14

15 16 i7 ~8 19

diated male mice, II. Cytological studies of sterile and semi-sterile F 1 individuals, in W. D. CARLSON AND F. X. GASSNER (Eds.), E~ects of Ionizing Radiation on the Reproductive System, Pergamon, Oxford, 1964, pp. 175-188. JOHNS, H. E., The Physics of Radiology, Thomas, Springfield, 1961 (2nd ed.). L~;ONARD, A., AND G. DEKNUDT, Relation between the X-ray dose and the rate of chromosome rearrangements in spermatogonia of mice, Radiation Res., 32 (1967) 35-41. LYON, M. F., R. J. S. PHILLIPS AND A. G. SEARLE, The overall rates of dominant and recessive lethal and visible mutation induced by spermatogonial X-irradiation of mice, Genel. Res., 5 (i964) 448 467 • OAKBERG, E. F., AND E. CLARK, Effect of dose and dose rate on radiation damage to mouse spermatogonia and oocytes as nleasured by cell survival, J. Cell. Comp. Physiol., 58, Suppl. I (196I) 173-182. PHILLIPS, R. J. s., AND A. G. SEARLE, The effect of dose-rate on the yield of translocations and dominant lethals following spermatogonial irradiation of mice, Genet. Res., 5 (1964) 468-472. RBE COMMITTEE, Report to the international Commissions on Radiological Protection and on Radiological Units and Measurements, Health Physics, 9 (1963) 357-384. RUSSELL, W. L., The effect of radiation dose-rate and fractionation on mutation in mice, in F. H. SOBELS (Ed.), Repairf)'om Genetic Radiation Damage, Pergamon, Oxford, 1963, pp. 2o52I 7. RUSSELL, \V. L., The nature of the dose-rate effect of radiation on mutation in mice, Jap..]. Genet., 4° , Suppl. (1965) 128-i4o. RUSSELL, W. L., AND E. M. KELLY, Radiation dose rate and mutation frequency, ,Science, I28

(1958) 1546 1550. 2O RUSSELL, W. L., AND L. B. RUSSELL, The g e n e t i c a n d p h e n o t y p i c c h a r a c t e r i s t i c s of r a d i a t i o n -

induced mutations in mice, Radiation Res., Suppl. i (1959) 296-3o 5. 21 RUSSELL, \~/. L., L. B. RUSSELL AND E. M. KELLY, Dependence of mutation rate on radiation intensity, in A. A. BUZATTI-TRAVERSO(Fd.), Immediate and Low-Level Effects of Ionizing Radiations, Taylor and Francis, London. 196o, pp. 3II 32o. 22 St~ARLE, A. G., Genetic effects of spermatogonial X-irradiation on productivity of F~ female mice, ~lutalion Res., 1 (1964) 99-1o8. 2 3 SEARLE, A. G., E. P. EVANS AND C. [*',. FORD,The effect of dose-rate on transloeation induction by spermatogonial irradiation of mice, .4bslv. / / I Intern. Congr. Radiation Research, 1966, p. 199. 24 VqOLFF, S., Interpretation of induced chromosome breakage and rejoining, Radiation Res., Suppl. I (1959) 4.53 462. APPENDIX TESTS FOR POISSON DISTRIBUTIONS SPERMATOCYTES

OF TRANSLOCATIONS

BETWEEN

1). (;. I'AP\V()RTH S i n c e t h e o b s e r v e d n u m b e r s of s p e r m a t o c y t e s h a v i n g 2 t r a n s l o c a t i o n s or m o r e a r e m o s t l y s m a l l , t h e u s u a l l a r g e - s a m p l e t e s t s of s i g n i f i c a n c e (e.g. f f g o o d n e s s - o f - f i t t e s t , d i s p e r s i o n t e s t ) a r e u n r e l i a b l e 4. E x a c t t e s t s w e r e t h e r e f o r e c a r r i e d o u t . T h e m e t h o d u s e d w a s t h a t d e s c r i b e d b y FISHER 1. Five statistics were chosen to test the goodness-of-fit. (I) T h e e x a c t p r o b a b i l i t y of t h e o b s e r v e d a n d all less l i k e l y d i s t r i b u t i o n s . T h i s is n o t r e c o m m e n d e d b y FISHER. (2) T h e P e a r s o n g o o d n e s s - o f - f i t c h i - s q u a r e , i.e. Z'(O E)'2/E. (3) T h e i n d e x of d i s p e r s i o n . T h i s is t h e r a t i o v a r i a n c e / m e a n for a g i v e n d i s t r i b u t i o n (N.B. for a P o i s s o n d i s t r i b u t i o n , v a r i a n c e = m e a n ) . I t t e s t s w h e t h e r tile v a r i a n c e of t h e o b s e r v e d d i s t r i b u t i o n is s i g n i f i c a n t l y g r e a t e r t h a n t h a t t o b e e x p e c t e d for a P o i s s o n d i s t r i b u t i o n . A s FISHER p o i n t s o u t , t h i s t e s t is r a t h e r i n s e n s i t i v e o w i n g t o g r o u p i n g , i.e. d i f f e r e n t d i s t r i b u t i o n s m a y h a v e t h e s a m e i n d e x of d i s p e r s i o n .

Blulation Res., 6 (I968) 427 436

INDUCTION OF TRANSLOCATIONS IN MOUSE SPERMATOGONIA. 1.

435

(4) The likelihood ratio criterion for goodness-of-fit. Essentially this is the logarithnfic difference in likelihood between the most likely Poisson distribution and the most likely (unrestricted) multinomial distribution giving rise to the observed class frequencies. This statistic is especially recommended b y FISHER. (5) The likelihood ratio criterion for dispersion. This criterion is used by RAO AND CHAKRAVARTI 4, who point out that it is more sensitive to over-dispersion than the index of dispersion, since, unlike the latter, it is not grouped. The calculations were performed on an I.C.T. ATLAS computer. SUMMARY OF RESULTS AND CONCLUSION

The distributions found in each testis of the 36 irradiated mice were analysed separately. The significance levels associated with the 5 chosen statistics were generally in close agreement, indicating that the tests are satisfactorily consistent. Of the 72 distributions tested, 17 (or nearly 24%) show a significant deviation from a Poisson distribution at the 5 % level or higher. The results m a y be summarized as follows. (I) No distribution in which at most I translocation per spermatocyte was observed deviates significantly from a Poisson distribution. (2) Of the 38 distributions in which sperlnatocytes with 2 translocations (but not more) were observed, 6 (or nearly 16°,/o) deviate significantly from a Poisson distribution. (3) Of the I I distributions in which spermatocytes with 3 or more translocations were observed, all deviate significantly from a Poisson distribution, some at high levels of significance. (4) Of the 17 distributions which deviate significantly from a Poisson distribution, all have a variance greater than the mean. This would suggest that, when deviation from a Poisson distribution occurs, the deviation is of such a kind as to inflate the variance, i.e. to increase the frequencies in higher classes at the expense of those in lower classes. TA BLI:. I SIGNIFICANCE OF DEVIATIONS FROM EXPECTATION IN I-CLA.~S

Dose-rate (R/min)

Mouse

Testis

Observed frequency in z-class

Expected frequency in 1-class

Significance of deficiency u P

17 18 16

19 .8o 2o.6o 21.39

1.46 1.3o 2.60

o.o72 o.o97 0.0047

11 83 83

(;,) (;,) (F)

C A I3

2 i 2

83

(~')

C

2

22

3o.21

2.81

0.0025

(X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray) (X-ray)

B C B A A B C A A B B A B

1 I i 1 2 1 2 I 2 I 2 2 I

26 20 47 16 21 16 22 4° 47 4° 34 33 45

36.71 28.82 51.o3 45.16

3.02 3.16 1.14 6.72

o.oo13 0.00079 o.13 very small o.ool 4 o.ooooo89 o.15 0.0026 0.0026 0.0045 very small 0.026 0.0052

5.0 5.0 9.7 9.8 9.8 87 87 89 89 89 89 913 913

29.52

2.98

27.39 24.46 49.54 58.20 48.80 71.4o 39-47 54.66

4.29 I.O 4 2.79 2.79 2.61 7.63 1.94 2.56

Mutation Res., 6 (I968) 427 436

436

a. 6. SEARLE et al.

(5) Similarly, of the 17 d i s t r i b u t i o n s which deviate significantly from a Poisson d i s t r i b u t i o n , all have frequencies in the 1-class which are less t h a n expectation, i.e. there are fewer s p e r m a t o c y t e s t h a n expected h a v i n g just one translocation. Tests on these were carried out using results of RAO AND CHAKRAVARTI 4, section 3. As shown in Table I, this deficiency is statistically significant (at the 5 ~o level) in 13 of the 17 cases. F u r t h e r m o r e , this deficiency is also p r e s e n t in m a n y of the d i s t r i b u t i o n s which do not deviate significantly from a Poisson d i s t r i b u t i o n . These o b s e r v a t i o n s strongly suggest t h a t the i n d u c t i o n of translocations in s p e r m a t o g o n i a is n o n - r a n d o m , at least when the rate of i n d u c t i o n is high. D i s t r i b u t i o n s like these, which deviate from a Poisson d i s t r i b u t i o n in the direction of overdispersion, can often be fitted satisfactorily b y a n e g a t i v e b i n o m i a l d i s t r i b u t i o n which in this c o n t e x t could be i n t e r p r e t e d as a v a r i a t i o n from s p e r m a t o g o n i u m to spermatog o n i u m in the degree of s u s c e p t i b i l i t y to t r a n s l o c a t i o n 2& tlI£FERENCES I FISHER, R. A., Tile significance of deviations from expectations in a Poisson series, Biometrics, 6 (1950)

17-24 .

2 GREENWOOD, M., AND G. U. YULE, An inquiry into the nature of frequency-distributions of multiple happenings, etc., J. Ro3,. Star. Soc., 83 (1920) 255. 3 KIMBALL, A. VV., Approximate confidence intervals for specific locus mutation rates, diner. Naluralist, 9° (i956) 369-376. 4 Rao, C. R., AND I. M. CHAKRAVARTI,Some small sample tests of significance for a Poisson distribution, Biometrics, 12 (1956) 264-282. ~alutalion Res., 6 (1968) 427-436