The distribution of genes in the second and third chromosomes of Drosophila melanogaster suggests that crossing-over may be influenced by the spindle fibre at least in neighboring regions. The disparity between the genetic and cytological maps of these chromosomes especially in the spindle fibre regions (Dobzhanzky 2,3) is consistent with such a view

Beadle, G. W.

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GENETICS: G. W. BEADLE
A POSSIBLE INFLUENCE OF THE SPINDLE FIBRE ON
CROSSING-OVER IN DROSOPHILA
By G. W. BEADLE'
WILLIAM G. KER'cZIOFF LABORATORIES OF THE B.OLOG:CAL. SCIENCES,
CALIFORNIA INSTITUTE OF TECHNOLOGY, PASADENA
Communicated December 19, 1931
The distribution of genes in the second and third chromosomes of
Drosophila melanogaster suggests that crossing-over may be influenced
by the spindle fibre at least in neighboring regions. The disparity be-
tween the genetic and cytological maps of these chromosomes especially
in the spindle fibre regions (Dobzhanzky2'3) is consistent with such a view.
Sturtevant4 suggests from studies of crossing-over in Drosophila stocks
homozygous for inverted sections of the autosomes that crossing-over in
a given region is a function of the material in that region rather than of
its position in the chromosome. He found no significant changes in
amount of crossing-over with change in position of a section of a chromo-
some with respect to the spindle fibre or the end of the chromosome.
Muller and Stone5 in a study of crossing-over in the case of a homozygous
inversion in the X-chromosome of Drosophila apparently found that the
regions in the inverted section gave normal crossing-over. However,
since in none of these cases of homozygous inversions did the inversion
include regions close to the spindle fibre, the possibility remains that the
spindle fibre influences crossing-over in regions close to it.
Dobzhansky6 studied crossing-over in a homozygous III-IV trans-
location in Drosophila (designated as translocation-c) and found' no
significant differences from normal controls. However, the regions which
.might have been expected to be influenced by the spindle fibre were not
studied. At the suggestion of Professor Dobzhansky, the Writer has
made additional studies of crossing-over in flies homozygous for this
translocation.- The results are reported in the present paper.
In the translocation stock under consideration a distal segment made
up of about three-fourths of the right limb of chromosome III (cytologi-
cally3) is broken off and attached to chromosome IV The break in chromo-
some III is close to and to the left of the curled gene (0.7 unit according
to Dobzhanky's data3 and somewhat closer according to results obtained
by the writer). Accordingly, in the homozygous translocation flies the
section of the third chromosome including curled and regions to the right
is closer to a spindle fibre (of the fourth chromosome) by a cytological
distance equal to about one-fourth the length of the right limb of chromo-
some III. Genetically this distance represents about 2 crossover units
(standard map7).
PROC. N. A. S.160
GENETICS: G. W. BEADLE
A stock of the homozygous translocation was made up carrying in one
of the translocated third chromosomes the genes roughoid (ru), hairy
(h), thread (th), scarlet (st), curled (cu), stripe (sr), sooty (e') and claret
(ca) and in the homolog the normal allelomorphs of these genes. The
constitution of this stock was therefore + +++ -+++ All of
ru h th st cu sr eS ca
the recessives were introduced, by crossing-over, from a normal stock.
The normal allelomorphs of ru, h, th, st, eS and ca were likewise introduced
from a normal stock. Females of the above-mentioned constitution were
used for a study of crossing-over by mating with homozygous translocation
males carrying the above-named recessives in both third chromosomes.
The control was made up by using the stocks which had been used in
introducing the desired genes into the translocation stock.
The standard map7 positions of the loci used are shown in figure 1.
S F
ru h tWI t cu sr eas ca
00 26.6 42.4440 7500 2O 70.7 Ob.o
TRANS-C
FIGURE 1
Standard map positions of the loci used. SF refers to the spindle fibre.
Crossover data from the homozygous translocation stock and. the
control are presented in table 1. These data together with the crossover
TABLE 1
CROSSOVER DATA FROM HOMOZYGOUS TRANSLOCATION-C FEMALES
ru h th st cu sre7 ca Xru h th si cu s7 e ca)
1 2 3 4 5 6 7 Xruhtstcsreca
AND A NORMAL CONTROL OF SIMILAR CONSTITUTION
(The class carrying the dominant allelomorph of ru is given first in each case)
CROSSOVERS TRANS- CROSSOVERS TRANS-
RBGION LOCATION CONTROL REGION LOCATION CONTROL
0 519 140 2,3 5 0 1
330 107 l0 0
1 5199 50 2,4 5168 1
255 57 131 0
2 5140 36 2,5 5 2 6
151 45 1 3 6
3 3 1 2,6 3 8
3 0 6 5
4 450 8 2,7 79 25
442 8 84 1 27
5 1 6 25 3,4 54 0
73 20 0 0
6 529 34 3,5 5 1 0
21 22 0 0
VOI,. 18, 1932 1161
GENETICS: G. W. BEADLE
TABLE I (Contisnued)
CItOSSOVERS
CONTROL RBGION
85 3,6
54
12 3, 7
7
0 4,5
1
2 4,6
5
6 4,7
9
9 5,6
9
33 5,7
36
3 2,4, 7
4
1 2,5, 7
1
1 2,6, 7
2
0 3,4,7
3
4 4, 5,7
4
0 4,6, 7
0
0 5,6,7
0
0 1,2,4, 7
1
1 1,2,5, 7
4
1 1,3,4,7
0
3 1,4,5,7
7
3 1,4,6,7
6
1 2,4,5,7
2
0 2,4,6,7
1
1,2,4,5,
Total
PR(
Tlt"S
LOCAT1ON
5269
213
45
25
1
2
5240
199
1
3
8
7
583
124
11
519
30
-t1
513
8
54
1
2
l4
8
7
118
102
5o
5ooo
51
3
56
9
CROSSOVBRS
RBGION
7
1,2
1,3
1,4
1, 5
1,6
1, 7
6, 7
1,2,4
1,2, 5
1,2,6
1,2, 7
1,3,4
1,4, 5
1,4,6
1,4, 7
1,5,6
1,5, 7
1,6,7
2,4,5
2,4, 6
oc. N. A. S.
CONTROL
0
0
0
1
1
1
3
2
8
5
0
1
12
10
2
1
5
8
0
0
.0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1019
TIANS-
LOCATION
2
5
7
56
4
25
5200
240
51
582
77OOO
3
53
7
52
0
5
1
5
13
16
5
1
o
1
2
0
50
11
52
0
7 5
1
5303
162
GENETICS: G. W. BEADLE
data from the heterozygous translocation flies (from Dobzhansky9) are
summarized in table 2. As compared with the control, crossing-over in
TABLE 2
SUMMARY OF CROSSOVER DATA FROM HOMOZYGOUS TRANSLOcATmON-c, HETEROZYGOUS
TRANSLOCATION-C (FROM DOBZHANSKY) AND NORMAL FLIES
PER CBNT CROSSING-OVER IN REGION NO. INDI-
BXPBRIMEBNT 1 2 3 4 5 6 7 VIDUALS
Homozygous
translocation 29.1 21.2 0.8 49.9 0.9 2.8 33.2 5303
Heterozygous
translocation 26.9 16.9 0.9 4.5 3.7 7.5 28.9 3185
Control 27.5 21.3 0.4 6.1 13.3 11.6 35.0 1019
flies carrying the translocation in homozygous form is reduced in the
cu-sr interval from 13.3 to 0.9 and in the sr-eS interval from 11.6 to 2.8
per cent. Other comparable regions show no differences. Crossing-over
in flies heterozygous for the translocation is also decreased as compared
with the controls in the cu-sr and sr-e' intervals. This decrease has been
explained by Dobzhansky8 on the basis of decreased frequency of synapsis.
The fourth chromosome to which a section of chromosome III is attached
presumably exerts a mutual attraction with its free homolog. Likewise,
the two sections of chromosome III and the homologous unbroken third
chromosome are attracted together. These counter-forces working on
the broken third chromosome would be expected to interfere with synapsis
and presumably also with crossing-over. This explanation obviously
cannot be applied to the homozygous translocation form. One must,
therefore, seek another explanation of the decrease.
Crosses were made to test the possibility that the observed decrease
in crossing-over might have been due to the presence of an extra fourth
chromosome. It is known from Dobzhansky's cytological work3 on
the original stock of the homozygous translocation that an extra fourth
chromosome is probably not necessary for the survival and fertility of
flies homozygous for the translocation. Crosses of homozygous trans-
location flies with flies carrying dominant eyeless in one-fourth chromo-
some and minute-IV in the other gave only two classes, eyeless and minute-
IV. A total of 22 flies homozygous for the translocation were so tested.
Since two normal allelomorphs suppress minute-IV this test indicates
that the homozygous translocation flies did not carry an extra fourth
chromosome. Two normal allelomorphs also suppress dominant eyeless
but since the extra fourth chromosome would have carried the recessive
eyeless-2 gene this test may not be valid. Crosses of 11 homozygous
translocation flies with haplo-IV gave normal and haplo-IV flies in varying
ratios but in two cases these were such (215 to 161 and 105 to 116) that
the translocation parent could hardly have carried an extra fourth chromo-
some. The fact that haplo-IV flies carrying the translocation survive
VOL. 18, 1932 163
GENETICS: G. W. BEADLE
and are fertile shows that the fourth chromosome to which the section of
chromosome III has been translocated does not carry a lethal. There
is therefore no apparent reason why an extra fourth chromosome should
be necessary to flies carrying the translocation in homozygous form. The
above tests make it very improbable that the homozygous translocation
stocks carried an extra fourth chromosome or a fragment of one which
might have accounted for the observed decrease in crossing-over.
S F
ru Ch thst cu sr es ca
27.5 21.3 0.4 .1 X 133 11.635.0
29.1 21.2 o. 49.9 0.9 2i 33.1
SF S F
FIGURE 2
Comparison of crossing-over in control and in homozygous translocation-c. F~igures
represent observed percentages of crossing-over. SF refers to spindle fibres. The
fourth chromosome is designated IV.
The above data indicate that the decrease in crossing-over in the cu-sr
and sr-eS intervals in the translocation stock is due to these intervals
being closer to the spindle fibre (of the fourth chromosome) than in the
control by a distance equal approximately to one-fourth the length (cyto-
logically) of the right limb of chromosome III.
On the basis of the hypothesis of crossing-over recently presented by
Sax9 the spindle fibre should reduce crossing-over in its immediate neighbor-
hood. If the opening out of chromatids at diplotene is determined in
the reductional plane at the spindle fibre then interference with crossing-
over for a distance on both sides of the spindle fibre would be expected.
On the basis of the crossing-over hypothesis put forward by Janssens10
and recently supported by Darlington" or on the scheme of Belling'2
there is no apparent reason why the spindle fibre should interfere with
crossing-over.
Coincidence values across the break in chromosome III have been
calculated. They are as follows:
REGIONS COINIDENCE
1-6 0.76
2-6 0.90
1-7 0.94
2-7 1.01
As might have been expected there is no significant interference of crossing-
over between the two independent sections of chromosome III.
164 PROC. N. A. S.
MATHEMATICS: J. L. WALSH
Summary.-Crossing-over data from a homozygous III-IV translocation
in Drosphila melanogaster indicate that the spindle fibre interferes with
crossing-over in its immediate neighborhood.
Acknowledgments.-The writer is grateful to Professor T. Dobzhansky
who suggested the study here reported and furnished the original stock
carrying the translocation studied. Professor A. H. Sturtevant has made
many helpful suggestions for which the writer is thankful.
1 NATIONAL RESEARCH COUNCIL FELLOW in the Biological Sciences.
2 Dobzhansky, T., Genetics, 16, 629-658 (1931).
3 Dobzhansky, T., Ibid., 15, 347-399 (1930).
4 Sturtevant, A. H., Carnegie Inst. Wash. Pub., 421, 1-27 (1931).
6 Muller, H. J., and W. S. Stone, Anat. Rec., 47, 393-394 (1930).
6 Dobzhansky, T., Proc. Nat. Acad. Sci., 15, 633-638 (1929).
7 Morgan, T. H., C. B. Bridges, and A. H. Sturtevant, Bib. Genet., 2, 1-262 (1925).
8 Dobzhansky, T., Amer. Nat., 65, 214-232 (1931).
9 Sax, Karl, Journ. Arnold Arboretum, 11, 193-220 (1930).
10 Janssens, F. A., La Cellule, 25, 387-411 (1909).
1 Darlington, C. D., Proc. Roy. Soc., B107, 50-59 (1930).
12 Belling, J., Univ. Calif. Pub. Bot., 16, 311-338 (1931).
AN EXPANSION OF MEROMORPHIC FUNCTIONS
By J. L. WALSH
DEPARTMENT OF MATHEMATICS, HARVARD UNIVERSITY
Commmunicated January 9, 1932
It is the primary object of this note to exhibit a development in series
of an arbitrary meromorphic function, a development which represents
the function throughout its entire domain of definition, and which can
be chosen in an infinite variety of ways.
THEORE;M I. If f(z) is a meromorphic function of z (that is, analytic
except possibly for poles, at every finite point of the plane), if all the poles of
f(z) belong to the sequence a,, a2, a3, . . > 0, where every pole occurs a
number of times at least corresponding to its multiplicity, and if the numbers
13, 32, 13, *** are distinct from the a, and uniformly limited, then there
exists a unique expansion
f(z) = ao+ a, + a2 +X- °f1 (Z2- ai)(z- a2)
valid for all finite values of z other than the points ai. The series (1) con-
verges absolutely for all values of z other than the ai and uniformly in any
VOL. 18, 1932 165


A possible influence of the spindle fibre on crossing-over in Drosophila

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A possible influence of the spindle fibre on crossing-over in Drosophila

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