Open Journal of Genetics, 2012, 2, 155-162 OJGen
http://dx.doi.org/10.4236/ojgen.2012.23020 Published Online September 2012 (http://www.SciRP.org/journal/ojgen/)
Further evidence for the theory that crossover interference
in Drosophila melanogaster is dependent on genetic rather
than physical distance between adjacent crossover points
Petter Portin
Laboratory of Genetics, Department of Biology, University of Turku, Turku, Finland
Received 19 May 2012; revised 28 June 2012; accepted 10 July 2012
ABSTRACT
Effect of heat shock on certain meiotic parameters in
Drosophila melanogaster was studied in the cv-v-f re-
gion of the X chromosome of females homozygous for
mus309 mutation, deficient in DNA double-strand
break repair, or being of wild type. The heat shock in
the wild females caused that the frequencies of the
single crossovers and all the map lengths decreased
while the frequency of the double crossovers and
crossover interference remained unchanged. In the
mus309 mutants all parameters remained unchanged
except that single crossovers in the cv-v interval were
less frequent, and that crossover interference dimin-
ished. Thus, heat shock seems have two separate ef-
fects; one being independent on the mus309 gene and
affecting the occurrence of crossing over itself, and
the other being dependent on the mus309 gene and
affecting some precondition of crossing over. This
precondition is probably the choice between two
routes of the repair of double-strand DNA breaks
known to be controlled by the mus309 gene. The re-
sults are in accordance with the genetic models of
interference in which interference depends on genetic
distance between the crossover points, but in contra-
diction with physical models where interference is
dependent on physical distance between the crossover
points.
Keywords: Chiasma; Chromosome; Map Length;
Meiosis
1. INTRODUCTION
1.1. General Introduction
Meiotic crossing over, the exchange of genetic material
between homologous chromosomes during the genera-
tion of gametes in animals and sexual spores in plants
and fungi leads to recombination of genes and formation
of chiasmata. A chiasma is a sufficient condition for the
segregation of homologous chromosomes, which leads to
the reduction of the chromosome number from diploid to
haploid.
An important phenomenon, which has recently gar-
nered much attention, associated with crossing over is
crossover interference, i.e. the fact that multiple cross-
overs in each pair of homologous chromosomes are less
frequent than would be expected on the basis of random
coincidence of single crossovers [1-3]. The phenomenon
of crossover interference is very likely responsible for
the occurrence of so called obligate crossovers, and thus
for the formation of obligate chiasmata.
The term “obligate crossover” refers to the fact that, in
most species, it is rare to find chromosomes that do not
undergo crossing over. For example, in Drosophila, there
is usually one chiasma per chromosome arm. The feature
of the obligate chiasma is biologically sensible because it
ensures the disjunction of homologous chromosomes.
1.2. Models of Crossover Interference and
the Purpose of the Present Study
In principle, there are two different categories of models
of crossover interference. The first of these categories of
models are called genetic models which assume that in-
terference depends on the genetic (i.e. linkage map) dis-
tance, measured in Morgans, between adjacent crossovers
[4]. To my knowledge, currently only one model, called
the “counting model”, falls into this category [4,5].
The second category of models, called physical mod-
els, hypothesize that crossover interference is dependent
on the physical distance (microns or base pairs) between
the adjacent crossovers. In general, these models, which
are many, suggest that some kind of physical signal trav -
els along the bivalent and determines the distribution of
crossovers.
Recently I presented evidence for the genetic models
of crossover interference in Drosophila melanogaster [6].

P. Portin / Open Journal of Genetics 2 (2012) 155-162 156
The aim of the present study was to get further evidence
for the theory that crossover interference is dependent on
genetic rather than physical distances between adjacent
crossover points. Crossing-over frequencies, crossover
interference, recombination frequencies and map dis-
tances were compared in the cv-v-f region of the X
chromosome of D. melanogaster in females bearing ei-
ther wild type 3rd chromosomes (control) or having the
DNA double-strand break repair deficient mus309D2/
mus309D3 mutant constitution in the 3rd chromosomes
(experiment), an d given a h eat shock of 24 hr in 35˚C, o r
being without a heat shock.
It was observed that the heat shock in the wild control
females caused that the frequencies of the single cross-
overs and all the map lengths decreased while the fre-
quency of the double crossovers and crossover interfer-
ence remained unchanged. In contrast to this, in the ex-
perimental mus309 mutant females all other meiotic pa-
rameters studied remained unchanged except that the
frequency of the single crossovers in the cv-v interval
decreased, and that crossover interference diminished.
Thus, it appears that the heat shock has two separate ef-
fects; one being independent on the mus309 gene and
affecting the occurrence of crossing over itself, and the
other being dependent on the mus309 gene and affecting
some precondition of crossing over. It is suggested that
this precondition of crossing over is the choice between
two routes of the repair of double-strand DNA breaks
known to be controlled by the mus309 gene. It should
also be noted that the effect of the heat shock in the mu-
tant females was generally speaking the opposition of its
effect in the wild type females. These results are in ac-
cordance with the genetic models, particularly the coun-
ting number model, of interference in which interference
depends on genetic distance between the adjacent cross-
over points, but the result is in contradiction with any
physical model of interference where interference is de-
pendent on physical distance between the adjacent
crossover points.
1.3. The mus309 Gene and Molecular Models
of Crossing Over
Molecular models of meiotic crossing over suggest that
crossing over is initiated by the formation of meio-
sis-specific double-strand breaks (DSBs) of DNA, cata-
lyzed eventually in all eukaryotes by the topoisomerase-
like Spo11 protein, encoded in Drosophila by the mei-
W68 gene [7], in co-operation with other enzymes. The
birth of DSBs is followed by formation of heteroduplex
DNA and rejoining of the ends created in the breakage
involving a single-end-invasion intermediate. Following
this, a physical structure called the displacement loop
will be formed. Subsequent DNA synthesis and second
end capture form a structure known as the double
Holliday junction (dHJ), which is then resolved to form
either crosso vers or non-crossovers [8,9].
Two alternative pathways for the repair of the DSBs
are known: the synthesis-dependent strand annealing
(SDSA) pathway and the double-strand-break repair
(DSBR) pathway. The former pathway leads exclusively
to non-crossover products and the latter to both crossover
and non-crossover products [10,11].
In D. melanogaster, the mus309 gene located on the
right arm of chromosome three (86F4) encodes, in a
manner similar to its orthologues in other organisms, a
RecQ helicase [12-15] and, accordingly, is involved in
DSB repair [10,11,16]. In particular, it is known that the
product of the mus309 gene is involved in the SDSA
pathway of the repair of the DSBs [17,18]. More spe-
cifically, in the mus309 mutants the SDSA pathway is
blocked, while the DSBR pathway remains functional
[19]. Thus, the mus309 gene seems to control the choice
made by the oocyte between the two alternative path-
ways of DSB repair. The same is also true for the Sgs1
gene, the mus309 orthologue of yeast [20]. Consequently,
if in mus309 mutants more DSBs are repaired as cross-
overs by the DSBR pathway, a change in the crossover/
non-crossover ratio can be expected, since fewer non-
crossovers are produced.
2. MATERIAL AND METHODS
2.1. Experimental Procedures
Crossing over frequency and interference in the X chro-
mosome in the regions between the crossveinless (cv, 1 -
13.7), vermilion (v, 1 - 33.0) and forked (f, 1 - 56.7)
markers in four different experimental procedures were
studied. In each procedure, six daily broods of progeny
were derived after a certain treatment of virgin females
before they were mated with males. The progeny was
collected as daily broods in order to get the best yield of
progeny flies. In the analysis of the results, however, the
materials of the broods were pooled. The females were
isolated and the treatment started not later than twelve
hours after their hatching from the pupa. In the control
crosses, cv v f/+ + +; +/+ females were crossed with cv v
f / Y males, and in the experimental crosses, cv v f/+ + + ;
mus309D2/mus309D3 females were crossed with cv v f/Y
males. The experimental females were derived from the
following preliminary cross: cv v f; mus309D3/TM6, Tb
females crossed with + + +/Y; mus309D2/TM6, Tb males
(Tb; Tubby 3 - 90.6) and identified on the basis of their
non-Tubby pheno type. The treat ments in bo th the contr ol
crosses and in the experimental crosses were as follows:
The virgin females were either given a heat shock of 24
hours in 35˚C  0.5˚C or they were kept in 25˚C  1˚C
for 24 hours.

P. Portin / Open Journal of Genetics 2 (2012) 155-162 157
Both the mus309 alleles used carry mutational chan ges
that could potentially impair or abolish at least the heli-
case function of the MUS309 protein. In mus309D2, there
is a stop codon between the sequence motifs encoding
the third and fourth helicase motif of the protein.
mus309D3, for its part, has a glutamic acid to lysine sub-
stitution in the conserve d helicase II motif, in addition to
another amino acid substitution close to the C terminus
[21]. It has been demonstrated that the genotype mus-
309D2/mus309D3 is semi-sterile (Janos Szabad, personal
communication; see also [21-23]).
Because of the semi-sterility of the females, the mu-
tant-female crosses were carried out in cultures in which
three females were mated with 3 - 5 males, whereas the
control crosses were single-female cultures. The same
number (30) of crosses was made in both the control and
the mutant-female series. After the initial mating, the
parental flies were transferred without etherisation into
fresh culture bottles ev ery 24th hour for five consecu tive
days, and discarded after the six th day of egg laying. The
progeny, thus consisting of six daily broods in both the
experimental and control procedure, were raised in 25˚C
on a standard Drosophila medium consisting of semolina,
syrup, agar-agar and both dried and fresh yeast.
2.2. Calculation of the Frequency of the
True Single Crossovers
Some of the observed single crossovers in the cv-v and
v-f intervals actually result from meioses that have two
exchanges, one in each interval. Assuming no chromatid
interference, the three classes of double-exchange tetrads,
2-, 3- and 4-strand doubles, occur in a 1:2:1 ratio [24].
Therefore, the true frequency of single crossovers, i.e.
the number of single crossovers that resulted from meio-
ses with only one ex change in the cv-v-f region, was cal-
culated by subtracting the observed frequency of double
crossovers from those of each of the single crossover
classes.
2.3. Measurement of Interference
The coefficient of coincidence, C, was calculated ac-
cording to the following formula of Stevens [25], which
is a maximum likelihood equation

ˆ,
wn
cwxwy 
where w is the number of flies which were double cross-
overs, x and y are the numbers of flies which were single
crossovers for cv and v, and v and f, respectively, and n is
the total number of flies.
The variance of C was calculated according to the fol-
lowing formula, also given by Stevens [25]

2
12
ˆ,
ccacbcabcab
Vc nab

 


where a and b are the recombination frequencies of cv
and v, and v an d f, respectively. This is also a maximum
likelihood eq uation.
2.4. Statistical Methods
In the calculations of the variance of the coefficient of
coincidence, the formula of Stevens [25] given above
was used. Otherwise, the variance of binomial frequen-
cies, such as recombination frequencies, was calculated
according to the usual formula: s2 = pq/n, where n is the
total number of flies, p is the recombination frequency,
and q is 1 – p. The standard deviation (S.D.) of all the
binomial frequencies the coefficient of coincidence in-
cluded is the square root of their variances.
In the analysis of the significance of difference of the
coefficients of coincidence and other binomial frequen-
cies the two-tailed binomial t-test was employed.
3. RESULTS
The distribution of the progeny into differ ent phenotypic
classes in the control crosses is given in Table 1, and in
the experimental crosses in Table 2.
The effect of the heat shock on the phenomenon of
crossing over including crossover interference in the
control cross females is given in Table 3. It appears that
all the parameters studied except the frequency of double
crossovers and the coefficient of coincidence changed
due to the heat shock treatment. The frequencies of true
single crossovers decreased in both intervals studied. The
recombination frequencies, directly giving the genetic
map distances between the markers involved , firstly of cv
and v markers and secondly of v and f markers decreased,
and so did—of course—also the map distance of the cv
and f markers.
The respective figures derived from the experimental
crosses are given in Table 4. The measurement of the
parameters studied resulted in almost complete opposi-
tion of the parameters in the control crosses: All the pa-
rameters remained unaltered except that the frequency of
true single crossovers in the cv-v interval decreased and
the coefficient of coincidence increased, i.e. crossover
interference diminished. It should be noted that despite
the fact that interference diminished, the frequency of
double crossovers did not change at all. This must mean
that the distribution of single crossovers changed be-
coming denser due to the heat shock treatment.
Comparison of the meiotic parameters between the
genotypes studied in not-heat-shocked and in heat
shocked females are given in Tables 5 and 6 respectively.
As can be seen from the tables, all parameters except

P. Portin / Open Journal of Genetics 2 (2012) 155-162 158
Table 1. Results of the control crosses. Distribution of progeny from the crosses in which cv v f/+ + +; +/+ females without or after
a heat shock of 24 hr in 35˚C were crossed with cv v f/Y; +/+ males.
Number of progeny
Phenotype of the progeny + + + cv v f cv + + + v f cv v + + + f cv + f + v + Total number of flies
No heat shock 4690 4311 1197 1243 1499 1577 147 179 14,843
Heat shocked 2428 2383 566 570 700 753 70 67 7537
Table 2. Results of the experimental crosses. Distribution of progeny from the crosses in which cv v f/+ + +; mus309D2/mus309D3
females without or after a heat shock of 24 hr in 35˚C were crossed with cv v f/Y; +/+ males.
Number of progeny
Phenotype of the progeny + + + cv v f cv + + + v f cv v + + + f cv + f + v + Tota l n umber of flies
No heat shock 2545 2035 601 868 589 839 104 180 7761
Heat shocked 1661 1311 373 552 386 577 76 116 5054
Table 3. Effect of heat shock on crossing over in females being of wild type regarding the mus309 locus. Parameters measured from
the results of the crosses in which cv v f/+ + +; +/+ females without or after a heat shock of 24 hr in 35˚C were crossed with cv v f/ Y;
+/+ males.
Parameter No heat shock Heat shocked Significance of the differ ence
Total number of flies % ± S.D. 14,843 7532
Frequency of true single crossovers in the
cv-v interval % ± S.D. 14.24 ± 0.29 13.25 ± 0.39 t = 2.04; P = 0.04
Frequency of true single crossovers in the
v-f interval % ± S.D. 18.53 ± 0.32 17.46 ± 0.44 t = 1.96; P = 0.05
Frequency of double cro ssov ers % ± S.D. 2.20 ± 0.12 1.82 ± 0.15 t = 1.89; P = 0.06
Recombination frequency of the cv and v
markers % ± S.D. 18.64 ± 0.32 16.89 ± 0.43 t = 3.22; P = 0.0013
Recombination frequency of the v and f
markers % ± S.D. 22.92 ± 0.34 21.10 ± 0.47 t = 3.09; P = 0.0020
Map distance of the cv and f markers cM ± S.D. 41.55 ± 0.40 37.99 ± 0.56 t = 5.13; P = 0.0020
Coefficient of coincidence C ± S.D. 0.5142 ± 0.0253 0.5101 ± 0.0314 t = 0.58; P = 0.56
Table 4. Effect of heat shock on crossing over in mus309 mutant females. Parameters measured from the results of the crosses in
which cv v f/+ + +; mus309D2/mus309D3 females without or after a heat shock of 24 hr in 35˚C were crossed with cv v f/Y; +/+
males.
Parameter No heat shock Heat shocked Significance of the differ ence
Total number of flies % ± S.D. 7761 505 4
Frequency of true single crossovers in the
cv-v interval % ± S.D. 15.27 ± 0.41 14.54 ± 0.50 t = 3.69 P = 0.0002
Frequency of true single crossovers in the
v-f interval % ± S.D. 14.74 ± 0.40 15.26 ± 0.51 t = 1.40 P = 0.16
Frequency of double cro ssov ers % ± S.D. 3.66 ± 0.21 3.80 ± 0.27 t = 0.41 P = 0.68
Recombination frequency of the cv and v
markers % ± S.D. 22.59 ± 0.47 22.14 ± 0.58 t = 0.60 P = 0.55
Recombination frequency of the v and f
markers % ± S.D. 22.06 ± 0.47 22.85 ± 0.59 t = 1.05 P = 0.29
Map distance of the cv and f markers cM ± S.D. 44.65 ± 0.56 44.99 ± 0.49 t = 0.38 P = 0.70
Coefficient of coincidence C ± S.D. 0.7344 ± 0.0318 0.7508 ± 0.0447 t = 2. 0 7 P = 0.039

P. Portin / Open Journal of Genetics 2 (2012) 155-162 159
Table 5. Effect of the mus309 genotype on crossing over in females not given a heat shock. Comparison of parameters measured
from the results of the crosses in which cv v f/+ + +; +/+ (control) and cv v f/+ + +; mus309D2/mus309D3 (experimental) females not
given a heat shock were crossed with cv v f/Y; +/+ mal es.
Parameter Control Experiment Significance of the difference
Total number of flies % ± S.D. 14,843 7761
Frequency of true single crossovers in the
cv-v interval % ± S.D. 15.27 ± 0.41 14.54 ± 0.50 t = 2.06 P = 0.0394
Frequency of true single crossovers in the
v-f interval % ± S.D. 14.74 ± 0.40 15.26 ± 0.51 t = 7.10 P < 0.0001
Frequency of double crossovers % ± S.D. 3.66 ± 0.21 3.80 ± 0.27 t = 6.34 P < 0.0001
Recombination frequency of the cv and v
markers % ± S.D. 22.59 ± 0.47 22.14 ± 0.58 t = 6.98 P < 0.0001
Recombination frequency of the v and f
markers % ± S.D. 22.06 ± 0.47 22.85 ± 0.59 t = 1.45 P = 0.1471
Map distance of the cv and f markers cM ± S.D. 44.65 ± 0.56 44.99 ± 0.49 t = 4.43 P < 0.0001
Coefficient of coincidence C ± S.D. 0.7344 ± 0.0318 0.7508 ± 0.0447 t = 31.78 P < 0.0001
Table 6. Effect of the mus309 genotype on crossing over in heat shocked females. Comparison of parameters measured from the
results of the crosses in which cv v f/+ + +; + / + (control) and cv v f/+ + +; mus309D2/mus309D3 (experimental) females which had
received a heat shock of 35˚C, 24 h were crossed with cv v f/Y; +/+ male s.
Parameter Control Experiment Significance of the difference
Total number of flies % ± S.D. 7532 5054
Frequency of true single crossovers in the
cv-v interval % ± S.D. 13.25 ± 0.39 14.54 ± 0.50 t = 2.06 P = 0.0394
Frequency of true single crossovers in the
v-f interval % ± S.D. 17.46 ± 0.44 15.26 ± 0.51 t = 3.26 P = 0.0011
Frequency of double crossovers % ± S.D. 1.82 ± 0.15 3.80 ± 0.27 t = 6.13 P < 0.0001
Recombination frequency of the cv and v
markers % ± S.D. 16.89 ± 0.43 22.14 ± 0.58 t = 7.37 P < 0.0001
Recombination frequency of the v and f
markers % ± S.D. 21.10 ± 0.47 22.85 ± 0.59 t = 2.33 P = 0.0198
Map distance of the cv and f markers cM ± S.D. 37.99 ± 0.56 44.99 ± 0.49 t = 7.84 P < 0.0001
Coefficient of coincidence C ± S.D. 0.5101 ± 0.0314 0.7508 ± 0.0447 t = 27.08 P < 0.0001
the frequency of recombination of v and f markers in the
not-heat-shocked females were different in both sets of
data. It should specifically be observed that in both series
the frequency of double crossovers and the coefficient of
coincidence were higher in the mus309 mutant females
than in the wild type females. These data ind icate that in
both series the density of crossovers increased due to the
effect of the mus309 mutation.
4. DISCUSSION
4.1. The mus309 Gene Controls the Choice
Made by the Oocyte of the Route of
Double Holliday Junction Repair
The first six broods after the initiation of egg laying of
virgin females, i.e. the broods constituting the material of
this study represent oocytes which, for the most part at
least, were in the prophase stage of m e i osi s during the heat
shock treatment, and had mainly passed the stage of DNA
replication during the premeiotic interphase [26-29]. DSB
formation occurs only during the earlier stages of meiotic
prophase and initiates at a specific time after premeiotic
DNA replication [29]. Crossing over in D. melanogaster
for its part is known to occur duri ng t he pach y tene stage of
the meiotic prophase [29,30], and the progenies in the 3rd
brood represent this stage of meiosis [28] .
It is convincingly established that those meiotic mu-
tants of D. melanogaster affecting crossing over which
also affect interference involve preconditions of cr ossing
over, whereas those mutants that affect crossing over
without affecting interference involve the crossing over
event itself [31]. Consequently, the genes involved are
called precondition genes and exchange genes, respec-
tively.
This was theoretically shown by Sandler et al. [32] as
follows: Let a be the probability of the fulfillment of

P. Portin / Open Journal of Genetics 2 (2012) 155-162 160
preconditions of crossing over in one region and only in
that region in a three-point crossing-over experiment. Let
b be th e probability of fulfillmen t of the same in another
region and only in that region. Let d be the probability of
the fulfillment of the preconditions in both region s at the
same time, and x the probability of exchange, given the
preconditions. From this it follows that the coefficient of
coincidence, C, is

2
dxd
C
x
adxbd adbd

 
Since C is independent of x, if a mutant that acts on
crossing over also affects interference, it must influence
the preconditions of crossing over. If, however, interfer-
ence remains unaltered, the target of the effect is the ex-
change itself.
What in this respect is true for meiotic mutants is, of
course, also true for other factors that affect crossing
over, such as the heat shock treatment in the present
study.
Heat shock in the control females affected the crossing
over frequencies but interference remained unaltered
(Table 3). Thus, taking the foregoing into acco unt, it can
without doubt be concluded that heat shock in the control
females affected the event of crossing over itself.
In contrast to this, heat shock in the experimental fe-
males affected both the crossing over frequencies and
interference (Table 4). Thus, heat shock in the presence
of the mus309 mutation affected some precondition of
crossing over, and therefore mus309 belongs to the class
of mutations that Baker and Carpenter [33] referred to as
the “precondition mutants”, meaning that they act prior
to the time when crossovers are actually generated. This
conclusion is strongly supported by the fact that inter-
ference decreased in the experimental mus309 mutant
females as compared to the control females in both the
non-heat-shock-treated and heat shocked females (Ta-
bles 5 and 6).
Thus, it appears that the heat shock has two separate
effects; one being independent on the mus309 gene and
affecting the occurrence of crossing over itself, and the
other being dependent on the mus309 gene and affecting
some precondition of crossing over.
As indicated in the introduction, the precondition of
crossing over, which the mus309 gene product affects, is
the repair of DSBs—a necessary condition for crossing
over. In particular, it is known that the MUS309 protein
is involved in the SDSA pathway of the repair of the
DSBs. Specifically, it is also known that in the mus309
mutants the SDSA pathway is blocked, while the DSBR
pathway remains functional [19].
As also indicated in th e intro duction , of these p athways
the SDSA pathway leads exclusively to non-crossover
end products of the repairing process while the DSBR
pathway leads to both non-crossover and crossover end
products. Therefore, in the mus309 mu tant female s mor e
DSBs are expected to be repaired as crossovers than in
the wild type females. In other words, map lengths
should be increased in the mus309 mutants as compared
to the wild type females. This is precisely what was ob-
served in the present study (Tables 5 and 6). Moreover,
it should also be noted that, as indicated in the results,
the data show that in both the non-heat-shock-treated and
the heat shocked females the density of crossovers in-
creased due to the effect of the mus309 mutation. The
same result was obtained in the mus309 mutant females
where the distribution of single crossovers became
denser due to the effect of the heat shock. These two
results show that in the mus309 mutant females more
DSBs than in the wild type females are repaired as
crossovers instead of non-crossovers.
Consequently, it is suggested that actually the precon-
dition of crossing over which the mus309 gene affects
seems to be the choice between the two routes of the
DSB, or more precisely double Holliday junction, repair.
4.2. Testing the Models of Crossover
Interference
This part of the discussion is mutatis mutandis similar
with the respective discussion of an analogous series of
experiments conducted by the present author where the
effect of temperature on crossing over and crossover
interference in mus309 mutants of D. melanogaster was
investigated [6]. The results of these two studies recip-
rocally support each others.
As mentioned in the introduction, models of crossover
interference can, in principle, be divided into two differ-
ent categories. The first category of models, called ge-
netic models [4], assumes that interference is dependent
on genetic (i.e. linkage map) distance (Morgans) between
adjacent crossovers. To my knowledge, currently only
one model, called the “counting model”, [4,5] falls into
this category.
The central feature of the counting model is that re-
combinational intermediates (C’s) have two fates—they
can be resolved with crossing over (Cx) or without (Co).
The C’s are distributed at random with respect to each
other, and interference results from constraints on the
resolution of C’s. The basic constraint is that each pair of
neighboring Cx’s must have a certain number, m, of Co’s
between them, as if the meiocyte was able to “count”
recombination events.
The second category of models, which may be called
physical models, hypothesizes that crossover interference
is dependent on physical distance (microns or base pairs)
between the adjacent crossovers. In general, these mod-
els suggest that some kind of physical signal travels

P. Portin / Open Journal of Genetics 2 (2012) 155-162 161
along the bivalent and determines the distribution of
crossovers. One of the models belonging to this category,
the reaction-diffusion model [34], is quantitative while
the other models are qualitative.
According to the reaction-diffusion model, a “random
walking” precursor becomes immobilized and matures
into a crossover point. The interference is caused by a
pair-annihilation of the random walkers, called the A
particles, due to their collision together, or by annihila-
tion of a random walker due to its collision with an im-
mobilized point. This model has two parameters—the
initial density of the random walkers, α, and the rate, h,
of their processing into crossover points. It is logical to
conclude that interference decreases if the α value in-
creases and/or h decreases [34].
It is also quite logical to assume that if the mus309
mutations affect the balance by which the double Hol-
liday junctions will be resolved as crossovers instead of
non-crossovers the m value of the counting model should
decrease, and consequently interference should diminish,
in the mus309 mutants. The results of the present study
are consistent with this idea. It is, therefore, very prob-
able that the mus309 mutation affects the Drosophila
counting number, thus being the first mutation of this
kind identified. Consequently, the results of the present
study support the view that crossover interference in
Drosophila is tightly tied to genetic distance.
In contrast, however, the results of the present study
are not compatible with the reaction-diffusion model.
According to this model, interference depends on two
factors only, viz. the initial density of crossover precur-
sors, i.e. DSBs, and the rate of their processing into
crossovers. Therefore, it is hard to conceive, in terms of
the reaction-diffusion model, how the number of cross-
overs, i.e. the map distances, would change due to the
effect of temperature but their distances, i.e. interference,
would not, as the initial density of DSBs does not chang e.
This seems, however, to be the case in the results of the
control crosses of the present study. Namely, because the
coefficient of coincidence, C, did not change due to the
heat shock treatment, it can be concluded that the initial
density of the DSBs, i.e. the α value did not increase.
Therefore, it cannot be assumed that the α value in the
experimental crosses would change either.
Thus, if the reaction-diffusion model is correct, h in
the experimental crosses should decrease due to the heat
shock treatment. This means that the coefficient of coin-
cidence, C, should decrease. In fact, however, C in-
creased.
The results are also in contradiction with any model of
crossover interference based on physical distance on the
following grounds: The map distances in the experimen-
tal and control females are different, and re act diff erently
to heat shock, the map distances in the experimental
crosses being not heat shock sens itive while the distances
in the control crosses are heat shock sensitive. However,
the crossover interference is independent of the heat
shock in the control crosses, while in the experimental
crosses interference is dependent on the heat shock. As
explained above, this observation supports the models of
interference based on genetic distance. On the other hand,
the results are in contradiction with the models based on
physical distance. In fact, if interference was dependent
on physical distance, how could it change due to heat
shock when bo th the genetic map distances and, naturally,
the physical distances remain unchanged?
5. ACKNOWLEDGEMENTS
Thanks are given to Professor Janos Szabad (Szeged, Hungary) for
introducing me to the mus309 gene, and the generous donation of the
mutant stocks which, however, are also available from different stock
centers. Skilful technical assistance by Mirja Rantanen, M.Sc. is grate-
fully acknowledged.
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