CHROMOSOME COILING IN RELATION TO MEIOSIS AND CROSSING OVER

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CHROMOSOME COILING I N RELATION TO MEIOSIS AND CROSSING OVER

KARL SAX

Arnold Arboretum, Harvard University

Received February 17, 1936

URING the past five years a considerable amount of evidence has

D

been obtained which strongly supports JANSSENS’ partial chias-

matypy theory of chiasma ’formation. This evidence includes (I) the meiotic configurations found in trivalents and quadrivalents (DARLINGTON

1930) ; (2) the frequency of figure-8 chromosomes in segmental interchange rings of Pisum (SANSOME 1933); (3) the relation between the failure of chiasma formation and absence of crossing over (DOBZHANSKY 1932), BEADLE 1933) ; (4) the relation between chiasma frequency and crossover frequency (BEADLE 1932, DARLINGTON 1934) ; (5) the similarity in effect of environment on chiasma frequency and crossover frequency (WHITE 1934) ; (6) the behavior of heteromorphic homologues (HUSKINS and SPIER 1934);

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the evidence for interference in both chiasma formation and crossing over (HALDANE 1931) ; (8) the negative correlation of frequencies for both chiasmata and crossing over in bivalents of the same cell (MATHER and LAMM 1935); (9) the types of chromatid associations a t meiosis (HEARNE and HUSKINS 1935); and (IO) the types of interlocking between non-homologous bivalents a t meiosis (HUSKINS and SMITH 193 5, MATHER

1935). Some of this evidence can not be considered as critical, because its

interpretation is based on unproved assumptions; but the cumulative value of the various lines of evidence does prove the validity of Janssens’ theory. The direct relation between chiasma formation and crossing over certainly facilitates cytogenetic studies and the analysis of the causal factors in crossing over, a feature not found in the hypothesis suggested by the author some years ago (SAX 1930).

Recent cytological studies of chromosome structure and behavior in mitosis and meiosis have indicated the factors which are responsible for the fundamental differences in the two types of division. Although the time of chromosome duplication is a disputed question, the general features of chromosome behavior seem to be fairly well established.

The chromonemata are in the form of minor spirals a t anaphase in mitosis. During the formation of the daughter nucleus the minor spirals begin to uncoil, but further uncoiling is inhibited as the chromosomes pass into the resting stage. At early prophase the coiled chromosomes begin to elongate and uncoil, but a t the same time the two chromatids in each chromosome begin to coil independently. By the time these relic coils are

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CHROMOSOME CQILING 325 largely eliminated, the new spirals are well established and continue to effect chromosome shortening until metaphase. The two chromatids of each chromosome are associated in the relic spiral, and, as the relic spiral is uncoiled, the two chromatids are twisted about each other (relatio.nal coiling, see fig. B). The amount of twisting is reduced as the chromatids contract, and a t metaphase few twists remain in the chromosomes of most species. The chromonemata of somatic chromosomes are always coiled. Before the relic coils of the previous division are straightened out, the new spirals are well established in each chromatid. There is a tendency for homologous chromosomes to pair in certain species, but intimate association is inhibited by their coiled structure during the entire mitotic cycle. The resting stage preceding meiosis shows the same type of chromosome structure. The tempo of the early prophase stage is slower than it is in mitosis, and the relic spirals are well straightened out before the daughter chromatids become differentiated and begin to form new minor coils. At this time the affinity between homologous chromosomes permits intimate pairing. The attraction is effective only when the chromosomes are relatively free from coils and before the chromatids of each homologue become differentiated and begin to coil independently. The chiasmata are formed, and the homologous chromosomes tend to repel each other. During this time the minor coils are developed, and during the later stages the major coils (plate I ) are superimposed on the minor coils. The reduction in chromosome length between pachytene and metaphase is about IO:I and may

be even greater in certain species. This contraction may be effected by a

linear contraction, or perhaps a “minimum” spiral, and by minor and major coiling. Major coils are not an essential feature of meiosis (O’MARA, unpublished) and apparently do not occur in all genera. The major coils do not prevent free separation of chromatids a t the first meiotic division. The interphase is so short that the minor spirals, and in some species even the major spirals, persist in the second meiotic division.

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3 2 6 KARL SAX

somes pair while still coiled in relic spirals. After the pairing of coiled homologues a t meiosis, the chromosomes elongate and produce a “relational” coiling at pachytene. Each chromosome now divides so that relational coiling exists in the chromatids of each homologue. The relational coiling of chromatids is in the same direction in each homologue, and the relational coiling of chromosomes is in the reverse direction (fig.

A).

The torsional strain induces chromatid breaks which reunite in such a way that crossing over is effected between two of the four chromatids a t any one locus. “The torsion which determines relational coiling is removed by crossing over and consequently must determine it.”

FIGURE A. Relational coiling of homologous chromosomes a t pachytene, according to DAR- LINGTON’S interpretation. The chromatids of each homologue are twisted about each other in

the same direction, while the chromosomes twist about each other in the opposite direction.

The theory is logical, but unfortunately most of the underlying assumptions are erroneous. If hypotheses are of more importance than facts

(DARLINGTON 1935c), further analysis should be unnecessary; but perhaps

a few cytological observations and an analysis of chromosome behavior will be of some value in correlating cytological and genetic behavior.

MINOR COILS AND RELATIONAL COILING I N SOMATIC CHROMOSOMES

The number of coils in somatic chromosomes can be observed only in species with relatively large chromosomes, and even in such species the direction of coiling can not be determined accurately. There does seem to be a tendency for the coiling to be in the same direction from the spindle fiber to the end of the chromosome. The number of minor spirals in a somatic chromosome is about 2-25 in Tradescantia (SAX and SAX 1935) and is

about 80 in Fritillaria (DARLINGTON 1935).

Since the direction of coiling in somatic chromosomes can not be determined directly, we must rely upon indirect evidence. This evidence is based on the assumption that the relational coiling of chromatids is determined by the minor coils, either as a result of uncoiling the relic coils

(DARLINGTON 1935) or by the formation of new coils in each chromatid a t prophase (HUSTED, unpublished).

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CHROMOSOME COILING 3 2 7

tional coiling could be observed and the direction of this coiling determined for all chromosomes (figs.

B

and

C).

R

I

FIGURE B. Somatic chromosomes of Trillium grandijwum showing relational coiling of chromatids. The five pairs of homologous chromosomes are numbered, and the direction of relational coiling is indicated. XSm.

Trillium gramdiflorum has five pairs of chromosomes: (I) with a nearly terminal fiber attachment, (2) fiber subterminal, ( 3 ) sub-median fiber and

short arms, (4) sub-median fiber and medium arms and ( 5 ) sub-median fiber and long arms (figs. B and C)

.

The corresponding arms of homologous chromosomes could be determined accurately for chromosomes

I,

11, and V, and with a fair degree of accuracy for chromosomes I11 and

IV.

The direction of twisting of the chromatids is easily determined a t late prophase or early metaphase.

The direction of relational coiling was obtained for all the chromosomes in each of twenty-five cells. The direction of twisting of chromatids in corresponding arms of homologous chromosomes is shown in table I.

The total number of chromosome arms with right-handed or clockwise spirals is 113, and with left-handed or counter clockwise twists, 118, while 219 arms showed no twisting of chromatids a t the stage of development examined. The homologous chromosomes show an approximately random distribution for direction of relational coiling. Where both of the terminal chromosomes showed relational coiling, the direction of twisting was the same in the two homologues in 9 cells and reversed in 9 cells. The total for all homologous arms was 16 with right-handed twists in both arms, 23

with left-handed twists in both arms, 36 with a right-handed twist in one homologue and a left-handed twist in the other homologue, and 150 pairs of arms which showed relational coiling in only one or in neither arm.

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3 2 8 KARL SAX

TABLE I

Direction of twisting (relational coiling) in sister chromatids for homologous arnzs of all chromo- somes in 2.5 somatic cells of Trillium. RR=relational coiling right in both homologues; RL or LR

=right-handed twists in one homologue and left in the other; LL=left-handed twists i n both homo- logues; O=no twist.

DIRECTION OF TWIST

___

CHROMOSOME

RR R L o R L R LL BO LO 00 n

long arm short arm short arm short arm

4 9

4 3

I 5

3 4

2 7

I 7

I

2 21 2 16 6 7 6 4 5

16 36 23 45 36 69 225

the direction was right in both arms of 9 chromosomes, left in both arms of 13 chromosomes, and right in one arm and left in the other arm of 24

W

FIGURE C. Somatic chromosomes of Vicia fuba. The direction of coiling is indicated in the long ‘‘M” chromosomes. The short chromosomes are so similar that homologues can not be identified, although the loose pairing may indicate homology. X 2000.

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CHROMOSOME COILING 329 1.3 for the short arms, while in the chromosomes with reversal in direction of twisting in the two arms, the average number of half twists was I . j for the long arms and 1.3 for the short arms. These observations indicate that the direction of twisting is approximately a t random for either arm of a chromosome and that there is no redistribution of coiling. If coiling is transferred from one arm to the other, there should be considerable reversal of coiling within a single arm, but such reversals are very rare and were observed in only two cases.

There are six pairs of chromosomes in Vicia fah, five pairs with nearly terminal fiber attachments and one pair with sub-median fiber attachment points. It is not possible to determine which of the ten short chromosomes are homologues, but the pair of long “M” chromosomes is easily identified, and the two arms can be distinguished easily because the shorter arm has a very clear secondary constriction. We have analyzed the direction of relational coiling in each of the two “M” chromosomes in sixty root tip cells. The results are shown in table 2.

TABLE 2

Direction of relational coiling of chromatids i n homologous arms of the “M” chromosomes of Vicia faba at early somatic metaphase.

RR LR OR RL LL RO LO 00 n

16 2 5 13 2 0 I 2 34 I 2 0

Direction of relational coiling in the two arms of single “M” chromosomes of Vicia

RR RL OR LR LL RO LO 00 n

9 1 8 6 41 33 13 I 2 0

The direction of twisting of chromatids about each other seems to be a t random for homologous arms, with 29 showing relational coiling in the same direction and 2 j showing relational coiling in opposite directions. The I 2 0 “M” chromosomes show relational coiling in 140 arms of which

77

were right and 63 left. I n single chromosomes the direction of relational coiling was the same in both arms of I j chromosomes and reversed in 18.

No case was observed where the direction of relational coiling was reversed in the long arm, but in the short arm the direction was reversed on either side of the secondary constriction in several chromosomes. The average number of half twists was found to be the same in the chromosomes with the same direction of relational coiling in both arms and those which had reversed coiling : I .

7

for the long arms and I . I for the short arms.

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330 KARL SAX

left in both homologues of six cells, and in reverse directions in the homologues of thirteen cells.

T H E MAJOR COILS I N T H E MEIOTIC CHROMOSOMES O F VICIA

The direction of coiling of major spirals has been determined in a number of species, but no adequate data are available for an analysis of coiling in relation to chiasmata. The meiotic chromosomes of Viciafaba have been used because the chiasma frequency is high, and in favorable preparations the direction of the major coils can be determined at all loci in some of the chromosomes. We have made and examined nearly a thousand preparations, but the technical difficulties have made it impossible to get very many data on major coils in this genus.

There are six pairs of chromosomes in Viciafaba, one long pair with sub- median fiber constrictions, and five shorter pairs with subterminal fiber constrictions. The average chiasma frequency in the material examined was 6.2 for the long “M” chromosomes and 3.0 for each of the five short chromosomes. There is a strong tendency for the chiasmata of the short chromosomes to be localized either near the spindle fiber or near the distal end, and the average number of clearly interstitial chiasmata is only 1.3 for these chromosomes.

The two chromatids of each chromosome are coiled together in a single spiral a t meiotic metaphase. There are about

15

major spirals in each of the long chromosomes and about 5 or 6 major spirals in each of the short chromosomes (plate I). The direction of coiling of a single spiral is seldom reversed between chiasmata, although reversals do occur in the loci con- taining the fiber attachment in the “M” chromosomes (figs. 2 and 4) and in some internodes of the short chromosomes (figs. I O and I I). The direction

of coiling seems to be a t random for corresponding segments of homologous

DESCRIPTION O F PLATE I

Camera lucida drawings of meiotic chromosomes of Vicia faba, showing major coils. From permanent smear preparations. X4000.

Figures 1-4. Bivalents with median fiber attachments. Major coiling is a t random for

homologues segments and for loci on either side of a chiasma. The direction of coiling may reverse a t the fiber attachment.

Figures 5-7. Bivalents with sub-terminal fiber attachments Figures 8, 9. Anaphase chromosomes.

Figures IO, I I . Two “m” bivalents with reversal of coiling between chiasmata.

Figure x 2. Separation of homologues previously associated by two interstitial compensating chiasmata.

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SAX, CWOMOSOME COILINO PLATE I

L

R

I 5

L

R

k 6

1

3 7

-Y

f

&fz

I4 A

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CHROMOSOME COILING 3 3 1

chromosomes and for loci on either side of a chiasma. The theoretical and actual frequencies are shown in table 3.

TABLE 3

Vicia faba

Direction of coiling on either side of chiasmata; data f r o m both M and m chromosomes.

THEORETICAL ACTUAL

LLXLL or R R X R R 2

LLXRR or RRXLL 2

LRXLR or RLXRL 2

LRXRL or RLXLR 2

8

RLXRR or LRXLL etc.

16

-

2

I

3

8

16

2

-

As the chromosomes separate a t anaphase, the two chromatids of each chromosome arm separate so that the direction of the major spirals can be determined for each chromatid. We have been able to analyze direction of coiling a t anaphase only in the short chromosomes with the nearly terminal fiber attachments (figs. 8-16). The sister chromatids are coiled together in the same direction a t metaphase, and if no chiasmata were formed, the two chromatids of an anaphase chromosome should be coiled in the same direction a t all loci, with only an occasional double reversal. With random direction of coiling a t metaphase, the reversals in coiling of all anaphase chromatids should be twice the chiasma frequency. I n 2 7 anaphase chromosomes the direction of coiling of the two chromatids was the same at all loci in only 5 , and the total number of reversals was 3 2 . The reversals in

coiling are not so frequent as expected with a chiasma frequency of 3.0. Part of the discrepancy may be attributed to terminal chiasmata. The average number of interstitial chiasmata is 1.3, and the calculated number based on reversal in coiling is I . 2 .

Frequently the two chromatids of an anaphase chromosome coil in different directions a t all loci (figs. 9,13,16). Such configurations are the result of separating a bivalent which has a chiasma very near the spindle fiber and in which the homologues were coiled in opposite directions.

I n some cases the two homologues can separate without untangling their chromatids. Figure I 2 represents the separation of chromosomes previously associated by two compensating interstitial chiasmata. The association of the very short arms of the “m” chromosomes seems to be effected without chiasma formation (fig. 6). The fiber attachment points are occasionally stretched out from the chromonema, and in these cases they appear to be double (figs. 3 and 6).

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3 3 2 KARL SAX

(fig. 4). The short chromosome is locked in the “M” bivalent distal to the first chiasma from the fiber attachment.

INTERLOCKING O F CHROMATIDS

Whenever two or more chiasmata are formed on one side of the fiber attachment, there should be some interlocking of chromatids a t metaphase and early anaphase. I n V’icia fa b a there are usually two chiasmata distal to the fiber in the “m” chromosomes, and about three in each arm of

the “M” chromosomes. I n the

“M”

chromosomes chromatid interlocking

a b G

d e

f

FIGURE D. Bivalent chromosomes of Viciafuba a t first meiotic anaphase, showing chromatid locking in a, d, and e. A symmetrical (free) bivalent is shown in c.

could occur in either arm, but only in the single arms of the “m” chromosomes. I n 30 such arms chromatid interlocking was found in 5 cases, or about

17

percent. Chromatid interlocking is shown in figure D (a, d , and e) while a symmetrical “M” bivalent is shown in c. The proportions of these various configurations are of value in an analysis of the mechanism of crossing over.

CHROMOSOME STRUCTURE AND BEHAVIOR I N R E L A T I O N TO CROSSING OVER

The analysis of relational coiling of chromatids in somatic chromosomes of Vicia and Trillium provides indirect evidence that the direction of the minor coils is a t random for homologous chromosomes, that the direction of minor coiling in the two arms of a single chromosome is a t random, and that the direction of coiling is usually the same in any one arm of a somatic chromosome.

The direction of coiling of the major spirals a t meiosis has been analyzed in several genera. The paired chromosome arms may coil in the same direction or in opposite directions, apparently at random, in Tradescantia

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CHROMOSOME COILING 333

Rhoeo (SAX 1935) ; Trillium (MATSUURA 1935) ; Lilium (IWATA 1935) ; and in Vicia. The direction of coiling may change a t chiasmata and occasionally a t other loci (HUSKINS and SMITH 1935, MATSUURA 1935) and appears to change a t random a t chiasmata in Vicia. The major coils may reverse their direction of coiling a t the spindle attachment, but there is a strong tendency for the direction of coiling to be the same in both arms of a meiotic chromosome in Tradescantia and Rhoeo. DARLINGTON (1935) assumes that major coiling is in the same direction in homologous chromosomes of Fritillaria, and that the two arms of a single chromosome must coil in opposite directions; but he presents no data or references to support these assumptions, and in the few figures of meiotic chromosomes showing major coils, he fails to indicate the direction of coiling where i t is not in accord with his hypothesis (1935b, fig. I).

The random coiling in the two arms of a somatic chromosome proves that minor coilingis not caused by the rotation of the spindle fiber attachment point. I n fact the normal contraction of X-ray induced fragments with no fiber attachments shows that the spindle fiber has no causal effect on chromosome contraction (HUSKINS and HUNTER 1935, RILEY, O’MARA, HUSTED, unpublished). The relational coiling in homologous chromosomes is a t random in mitosis. The direction of major spirals is a t random, or nearly so, in homologous chromosomes. The direction of coiling of major spirals is not dependent on the direction of coiling of minor spirals, because the minor spirals usually coil in the same direction in any one chromosome arm, while the major spirals may change their direction a t a chiasma in the paired arms of homologous chromosomes.

All these observations are contrary to DARLINGTON’S assumptions, and most of them are not in accord with his recent hypothesis on the mechanism of crossing over. There is additional evidence which seems to invalidate this hypothesis.

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334 KARL SAX

torsional strain induced causes chromatid breaks with reunions in new associations.

There is little direct cytological evidence to support any one of these hypotheses, but we can test the different theories by comparing the theoretical chromatid relationships which must be produced with the configurations actually observed.

The only adequate data are those on the chromatid relationships of meiotic chromosomes of Melanoplus (HEARNE and HUSKINS 1935). I n the chromosomes with two chiasmata each, there are four types of chromatid relationships : free, chromosomes locked, chromatids locked, and continuous. These types are illustrated by diagrams in figure E. As the meiotic chromosomes begin to separate a t anaphase, it is difficult to distinguish the various types of configurations with the exception of chromatid interlocking. In 59 bivalents of Melanoplus there were 24 (40 percent) free,

7

(12 percent) with chromosomes locked, I O (17 percent) with chromatids

locked, and 18 (30 percent)continuous. In early anaphase chromosomes of Vicia 17 percent showed chromatid locking, and in Lilium (MATHER 1935) there was less than 17 percent of chromatid locking.

Where there are two chiasmata on the same side of the fiber attachment, we should expect to obtain the four types of bivalents shown in figure 5 . Configurations more complicated than simple chromatid locking are not found in Melanoplus and are rarely found even in species with higher chiasma frequencies. Any valid theory of crossing over should give the four types of bivalents observed.

Let us first examine the theory based on the suggestions of WILSON and MORGAN. The four chromatids lie parallel and twist together in one direction. The torsion causes a break in two non-sister chromatids and a sub- sequent reunion in a new association. If the torsion is in the same direction a t all loci, the greater stress may lie on either side of the chromatid breaks, so that, in effect, the rotation of broken chromatids will be a t random. The essential features of torsional strain, the chromatid breaks, types of crossover chromatids and chromatid relationships in the bivalents are shown in figure E and table 4. The application of this hypothesis produces 12.5 percent of free bivalents, 12.5 percent of chromosome locking, 25 percent of chromatid locking, and

50

percent of continuous association of chromatids.

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CHROMOSOME COILING 335

TABLE 4

Crossovers and types of bivalents resulting from two successive crossovers. Torsion of four parallel chromatids. See diagram in jigure E .

4 compensating TORSION

A A’

B B

A A

B B‘

A A‘

B B ,

1-2

‘-3

1-2

1-3

1-2

‘-3

1-3

CROSSOVER CHROMATIDS

TYPE OF’ BIVALENT

_______ ~~

z non-crossover

z compensating

z non-crossover

z compensating

4 non-compensating

Chromatid lock Free

Chromatid lock Chromosome lock Continuous Continuous Continuous Continuous

t ‘ t

1 3

f ‘

FIGURE E. Pachytene association of chromatids before crossing over, with torsional strains and points of crossing-over indicated. Below are the four types of bivalents produced by the torsion, and the only types observed cytologically in Melanoplus.

A). The configurations produced in these various theories are shown in table 5 .

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3 3 6 KARL SAX

TABLE 5

The conjgurations fiodiued by different theories of crossing over i n chromosomes with two chiasmata distal to thejber.

HYPOTKESIS

TYPES OF BIVALENTS I N PERCENT

COMPLEX LOCK CONTINUOUS

FREE CHROMOSOME CHROMATID

LOCK LOCK

~ I _ ~ _ _ _ _ _ _ _____________ _

WILSON-MORGAN 12% 12% 25 50 0

BELLING random 25 I 8% 6% 25 25

BELLING same 0 0 50 5 0 0

DARLINGTON 0 0 25 50 25

OBSERVED

Melanoplus Lilium Vicia

Melanoplus. However, the theoretical and observed frequencies of the other classes do not deviate so greatly, considering the number of observations and the difficulties in interpreting the chromatid relationships. The percentage of chromatid interlocking in Melanoplus, Lilium, and Vicia is considerably less than the theoretical expectation, but observations based on anaphase figures would fail to detect all the chromatid locking.

This torsion hypothesis will produce no chromosome locking and does produce complex interlocking if twists occur in sister-chromatids or if sister strand crossing over occurs between the two chiasmata.

If BELLING’S and DARLINGTON’S theories have been interpreted cor- rectly, i t appears that neither one is valid. If the homologous chromosomes are twisted a t random at early pachytene, BELLING’S theory would be expected to produce very few chromatid locks, and 2 5 percent of co,mplex interlocking. If relational coiling is in the same direction a t all loci of the paired chromosome arms, as seems probable, we should expect only chromatid locking and continuous associations of chromatids. BELLING’S theory is also difficult to reconcile with the many observations that the chromosomes split a t least one cell generation in advance of division.

The application of DARLINGTON’S theory gives neither of the first two classes of bivalents and does produce complex interlocking. The cytological evidence also shows that most of DARLINGTON’S “observations” regarding relational coiling are incorrect.

The torsion theory based on the suggestions of WILSON and MORGAN seems to be most nearly in accord with the cytological observations. This theory demands the following cytological interpretation. The chromosomes

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CHROMOSOME COILING 337 of the chromatids in each chromosome. The homologous chromosomes pair so that all four chromatids are approximately parallel, or a t least tend to lie in the same relative quadrant a t all loci. The formation of minor or sub- minor coils is now initiated, and all four chromatids coil in the same direction. The torsion induced by the initiation of the new coiling causes a relational coiling of all four chromatids. This relational coiling produces crossing over a t late pachytene or a t early diplotene. Much of the relational coiling of the homologues may persist during diplotene, but further contraction of the chromosomes, effected by major and minor coils, eliminates relational coiling a t the later stages. The uncoiling of the homologous chromosomes will lead to no complex associations so long as there is no inde- pendent relational coiling of the chromatids of each chromosome.

This cytological interpretation of crossing over does not appear to be irreconcilable with the cytological evidence. It is difficult, however, to imagine the mechanism which would produce the precise crossing over demanded by the genetic evidence, and limit it to homologous chromatids, but this difficulty is inherent in any torsion theory of crossing over.

SUMMARY

During somatic prophase the two chromatids of each chromosome are twisted about each other. This relational coiling of chromatids has been analyzed in the somatic chromosomes of Trillium grandijorum and

Vicia

faba. The direction of relational coiling is approximately a t random for corresponding arms of homologous chromosomes and for the two arms of a single chromosome. I n any one chromosome arm the direction of relational coiling is rarely reversed. There is no evidence that relational coiling is transferred from one arm to the other arm of the same chromosome. It

is believed that relational coiling is conditioned by the nature of the minor coils in the somatic chromosomes, so that a study of relational coiling permits an indirect analysis of minor coiling.

At meiosis major spirals are superimposed on the minor coils, a t least in a number of plant species. The direction of coiling of these major spirals can be observed directly. I n the various species which have been studied, the direction of coiling is approximately a t random for homologous chromosomes. I n Viciufuba the direction of coiling of major spirals is a t random on either side of a chiasma. Occasionally i t may be reversed a t other loci. The direction of coiling of major spirals is not necessarily dependent upon the direction of coiling of the minor spirals.

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338 KARL SAX

WILSON and MORGAN in 1920 seems to be most nearly in accord with the cytological observations.

LITERATURE CITED

BEADLE, G. W., 1932 The relation of crossing over to chromosome association in Zea-Euchlaena hybrids. Genetics 17: 481-501.

1933 Further studies of asynaptic maize. Cytologia 4: 269-287. 413.

B. 107: 50-59.

1934 The origin and behavior of chiasmata. VII. Zea Mays. Z. i. A. V. 67: 96-1 14. 1935a The time, place and action of crossing over. J. Genet. 31: 185-212.

1935b The internal mechanics of the chromosomes. Proc. Roy. Soc. B 118: 33-96.

1 9 3 5 ~ The old terminology and the new analysis of chromosome behavior. Ann. Bot. 49: BELLING, J., 1933 Crossing-over and gene rearrangement in flowering plants. Genetics 18: 388- DARLINGTON, C. D., 1930 A cytological demonstration of genetic crossing-over. Proc. Roy. Soc.

579-586.

DOBZHANSKY, T., 1932 Studies in chromosome conjugation. Z. i. A. V. 60: 235-286. HALDANE, J. B. S., 1931 The cytological basis of genetical interference. Cytologia 3: 54-65.

HEARNE, E. M. and C. L. HUSKINS, 193 j Chromosome pairing in Melanoplus femur-rubrum.

HUSKINS, C. L. and A. W. S. HUNTER, 1935 The effects of X-radiation on chromosomes in the HUSKINS, C. L. and S. G. SMITH, 1935 Meiotic chromosome structure in Trillizm erectum L. Ann HUSKINS, C. L. and J. D. SPIER, 1934 The segregation of heteromorphic homologous chromosomes IWATA, J., 1935 Chromosome structure in Lilium. Mem. Call. Sci. Kyoto B. IO: 275-288.

MATHER, K., 1935 Meiosis in Lilium. Cytologia 6: 3 54-380.

MATHER, K. and R. LAMM, 193 j The negative correlation of chiasma frequencies. Hereditas 20: MATSUURA, H., 193 j Chromosome studies on Trillium Kamtschaticum. 11. J. Sci. Hokkaido Imp.

Cytologia 6: 123-147.

microspores of Trillium erectum L. Proc. Roy. Soc. London 117: 22-23. Bot. 49: 119-1 50.

in pollen mother cells of Triticum vulgare. Cytologia 5 : 269-277.

65-70.

Univ. " 1 : ZZZ-Z<O. ""

-

MORGAN, T. H., 1919 The physical basis of heredity. pp. 305. J. B. Lippincott Co., Philadelphia. NEBEL, B., 1932 Chromosome structure in Tradescantia. 11. 2. Zellf. mik. An. 16: 285-304. SANSOME, E. R., 1933 Segmental interchange in Pisum. 11. Cytologia 5 : I 5-30.

SAX, H. J. and K. SAX, 1935 Chromosome structure and behavior in mitosis and meiosis. J. Arnold

SAX, KARL, 1930 Chromosome structure and the mechanism of crossing over. J. Arnold Arb. 11: 193 j Chromosome structure in the meiotic chromosomes of Rhoeo discolor Hance. J. Arnold Arb. 16: 216-222.

SAX, KARL and L. M. HUMPHREY, 1934 Structure of meiotic chromosomes in microsporogenesis of Tradescantia. Bot. Gaz. 96: 353-362.

SHINKE, U., 1934 Spiral structure of chromosomes in meiosis in Sagittaria Aglnaski. Mem. Call. Sci. Kyoto Imp. Univ. 9 : 367-392.

WHITE, M. J. D., 1934 The influence of temperature on chiasma frequency. J. Genet. 29: 203-31 j.

WILSON, E. B. and T. H. MORGAN, 1920 Chiasmatypeand crossing over. Amer. Nat. 54: 193-219. Arb. 16: 423-439.