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Genetics. Mar 2008; 178(3): 1251–1269.
PMCID: PMC2278109

Reduced Mismatch Repair of Heteroduplexes Reveals “Non”-interfering Crossing Over in Wild-Type Saccharomyces cerevisiae

Abstract

Using small palindromes to monitor meiotic double-strand-break-repair (DSBr) events, we demonstrate that two distinct classes of crossovers occur during meiosis in wild-type yeast. We found that crossovers accompanying 5:3 segregation of a palindrome show no conventional (i.e., positive) interference, while crossovers with 6:2 or normal 4:4 segregation for the same palindrome, in the same cross, do manifest interference. Our observations support the concept of a “non”-interference class and an interference class of meiotic double-strand-break-repair events, each with its own rules for mismatch repair of heteroduplexes. We further show that deletion of MSH4 reduces crossover tetrads with 6:2 or normal 4:4 segregation more than it does those with 5:3 segregation, consistent with Msh4p specifically promoting formation of crossovers in the interference class. Additionally, we present evidence that an ndj1 mutation causes a shift of noncrossovers to crossovers specifically within the “non”-interference class of DSBr events. We use these and other data in support of a model in which meiotic recombination occurs in two phases—one specializing in homolog pairing, the other in disjunction—and each producing both noncrossovers and crossovers.

IN yeast, deletion of the meiosis-specific gene MSH4, which, despite its name, is said to have no involvement in mismatch repair (Ross-Macdonald and Roeder 1994), usually leaves residual crossovers, and these crossovers have reduced interference (Novak et al. 2001). In Caenorhabditis elegans, however, which is characterized by strong crossover interference as well as by cis-acting “pairing centers” that promote synapsis of homologous chromosomes (Dernburg et al. 1998; MacQueen et al. 2005; Phillips and Dernburg 2006), deletion of him-14, a homolog of MSH4, eliminates essentially all crossing over while apparently leaving intact the ability to repair meiotic double-strand breaks (Zalevsky et al. 1999). On the basis of these data, Zalevsky et al. (1999) suggested that yeast, and other creatures lacking pairing centers, have two kinds of crossing over, one of which is Msh4 independent, has little or no crossover interference, and serves to establish effective pairing of homologous chromosomes.

Stahl et al. (2004) noted that the concept of two kinds of crossing over provides an explanation for the apparent correlation between the strength of interference and the fraction of crossovers that are Msh4 dependent in a given interval. Furthermore, Malkova et al. (2004), using a statistical analysis, which in the light of information presented here appears oversimplified, reported that the distribution of crossovers along the left arm of chromosome VII in wild-type yeast was better described by a two-kinds-of-crossover model than by the simple “counting model” for interference (Foss et al. 1993). More compelling support came from the phenotype of mms4 and mus81 deletions. Each of these mutations caused a reduction in crossing over but not in interference, while deletion of MMS4 along with deletion of MSH4's partner, MSH5, caused a further reduction in crossing over (De Los Santos et al. 2003). Apparently, the mms4 and mus81 mutations specifically reduce Msh4-independent crossing over. However, in otherwise wild-type strains, mms4/mus81 reductions in crossing over do not appear to reduce chromosome pairing nor do they reduce meiosis I disjunction (De Los Santos et al. 2001, 2003; and see Maloisel et al. 2004). These observations prompt a modification of the influential hypothesis of Zalevsky et al. (1999): instead of being dependent on Msh4-independent crossovers, chromosome pairing in yeast is dependent on a class of double-strand-break-repair (DSBr) events of which the crossovers happen to be relatively Msh4 independent. This framework of thought, similar to that adopted by Peoples-Holst and Burgess (2005), has guided our analysis.

To test the hypothesis of Stahl et al. (2004) that interfering and “non”-interfering crossovers should be distinguishable from each other in wild-type yeast, we measured interference in strains marked (near DSB hotspots at HIS4 on chromosome III and at ARG4 on chromosome VIII) with palindromes that make poorly repairable mismatches (PRMs) in heteroduplex DNA, often resulting in 5:3 segregation at the palindrome site. (Throughout, we designate an aberrant segregation as 5:3 or 6:2 without regard to which allele is present in excess.) In the event, our results refute particulars of the hypothesis—identifiable “resolution types” proved indifferent to Msh4—and our concept of ligated vs. unligated intermediates of canonical DSBr (Sun et al. 1991; popularly referred to as DSBR intermediates) proved useless. However, our results provide compelling evidence that wild-type yeast has distinct interference and “non”-interference classes of DSBr. [The quotation marks on “non”-interference reflect the observations that, in wild type, this class appears to yield crossovers with negative interference (see results) and that some msh4 strains show residual positive interference.]

Our observations include evidence that one class of conversions, those with 5:3 segregation at the palindrome site, is characterized by the absence of normal crossover interference. Furthermore, the crossover (and noncrossover) frequencies of 5:3 tetrads are seen to be relatively independent of Msh4 function, implying that there were few, if any, interfering, Msh4-dependent crossovers among tetrads that failed to undergo mismatch repair (MMR) of the marked heteroduplex. This conclusion prompts the deduction that interfering, Msh4-dependent crossovers essentially always undergo such MMR. This concept has provided a framework for dealing with all the observations reported here.

In yeast, most MMR is apparently directed by strand discontinuities. Strand discontinuities are notably present at two stages of DSBr: during the process of strand invasion (round one) and during or following any steps required to resolve recombination intermediates (round two; e.g., resolution of Holliday junctions). MMR at invasion (Haber et al. 1993) is deemed responsible for the observation that, in yeast, repair of mismatches yielding 6:2 conversions close to the DSB favors markers from the parent that does not suffer the initiating double-strand break but serves as jig and template for the repair of that break. [It was this that misled Szostak et al. (1983) to propose gap repair as the major conversion mechanism in yeast.] In yeast, this bias is apparent as well in the short-patch repair that is evident in MMR-compromised conditions (Coïc et al. 2000). Foss et al. (1999) presented evidence in support of the idea of a second opportunity for MMR, directed by cuts introduced at Holliday junction resolution.

Our data suggest rules for the repair of PRMs as well as for well repairable mismatches (WRMs) in the two classes of DSBr: (1) In the “non”-interference class, PRMs are subject to some repair, but only during the process of invasion; (2) in the interference class, PRMs are invariably repaired, but only as part of the process of the resolution of a joint-molecule intermediate; and (3) in both classes, WRMs close to the DSB are usually repaired at the invasion stage to yield 6:2 segregation of the marker. We will refer to this proposal as “the rules.” We offer the rules not as “eternal truth,” but as a guide for thinking about our results. As far as we know, they contradict no established observations from other investigations, although they seem to lead to views of meiosis that contradict some beliefs. As with all biological rules, nature may sometimes bend them.

For DSBr events monitored by a PRM, the rules predict that round two MMR will often erase evidence of the event by restoring normal 4:4 segregation of the diagnostic marker. We tested this prediction by using a marker that makes frequent WRMs close to a DSB hotspot to screen for tetrads with a DSBr event. Within that class of tetrads, we tested whether the conversion frequency of a PRM, close by and on the opposite side of the DSB, would be lower than that of a WRM at the same site.

To pursue the attractive proposal of a connection between homolog pairing and the “non”-interference class of DSBr, we made use of PRMs to assess whether the DSBr phenotypes of the pairing mutant ndj1 (also known as tam1) are preferentially associated with one or the other of the two DSBr phases. Deletion of NDJ1 causes a delay in pairing of homologs (Chua and Roeder 1997; Conrad et al. 1997; Peoples-Holst and Burgess 2005), homolog nondisjunction (Chua and Roeder 1997; Conrad et al. 1997), and an apparent reduction in “noncrossovers,” i.e., conversions unaccompanied by crossing over (Wu and Burgess 2006), and in crossover interference without any reduction in crossing over (Chua and Roeder 1997). In fact, the published data of Chua and Roeder (1997) are compatible with a modest increase in crossing over for the ndj1 mutants, varying, perhaps, with the interval tested. Here we offer evidence of a specific ndj1-induced increase in crossovers that are “non”-interfering as deduced from their segregation pattern. We propose that this increase in crossovers contributes to the ndj1-induced decrease in interference reported by Chua and Roeder (1997).

We apply the rules to interpret the principal differences among our data, those of Mortimer and Fogel (1974) and Malkova et al. (2004), and those of Kitani (1978), who conducted a similar study in Sordaria fimicola, a filamentous fungus that frequently fails to correct mismatches. Together, these studies suggest (1) that “poor repairability” of mismatches used to identify a DSBr event allows identification of the “non”-interfering crossovers in wild-type yeast and Sordaria and (2) that Sordaria, like yeast, relies on a class of DSBr characterized by reduced interference and distinctive MMR to achieve normal homologous pairing.

MATERIALS AND METHODS

Strain construction:

Strains bearing markers that make PRMs at the ARG4 and HIS4 loci were constructed in two different backgrounds (Table 1). Markers were introduced by standard lithium acetate transformation using either DNA restriction fragments or PCR fragments primed by the oligonucleotides listed in Table 2. Both the PCR and restriction fragments were generated from plasmids described in Table 3.

TABLE 1
Yeast strains
TABLE 2
Oligonucleotides
TABLE 3
Plasmids

Previously characterized palindromic markers at HIS4 (Nag and Petes 1991) and at ARG4 (Gilbertson and Stahl 1996) were introduced by standard two-step transplacement (Ausubel et al. 1994). The haploid progenitors for the first background were F1225 and F1227, obtained from the laboratory of Jasper Rine (“Rine background”). The haploid progenitors for the second background were strains AS4 and AS13, obtained from the laboratory of Tom Petes (“Petes background”). Deletion of MSH4 was achieved in the Petes background via the loxP-Cre recombinase system and the bleomycin-resistance gene (Güldener et al. 1996), leaving a residual loxP site. The deletion reduced the frequency of tetrads with four viable spores from 0.76 to 0.67. The hygromycin-resistance gene was used to replace MSH4 in the Rine background, reducing four-spore-viable tetrads from 0.76 to 0.46.

YFS26 and YFS27 were constructed by transformation (Gietz et al. 1992) of F1209 or F1210 (Rine background) with a 2.2-kb fragment liberated by NotI from pYORC-YOL104C. YFS644 and YFS645 were made by deletion of TAM1 in YFS617 and YFS618 was made by replacement with the HPHMX4 ORF of pAG32 using primers FS280 and FS281. Confirmation of the insertion was made by PCR, using primers FS282 and FS283. YFS637 is a meiotic segregant of F1231. YFS638 and YFS639 were generated by transforming YFS637 with HindIII–EcoRI fragments of pLG56 (ARG4::HpaI-SalI) and pLG57 (ARG4::HpaI-lopC), respectively. For each strain, Arg+ transformants were screened by PCR with primers FS91 and FS92, and the presence of the correct ARG4 allele was verified by restriction analysis. The 398-nucleotide (nt) PCR fragment containing the silent ARG4::HpaI-SalI allele is labile to SalI digestion and resistant to HpaI and SpeI digestion. The 424-nt PCR fragment containing the silent ARG4::HpaI-lopC allele contains a SpeI site within the lopC palindrome.

The reported locations of the ARG4 and HIS4 double-strand-break sites (Nicolas et al. 1989; Fan et al. 1995) were assumed to apply to our strains.

Genetic analyses:

Data:

Data were tabulated and analyzed with the aid of the MacTetrad 6.9.1 program available from Gopher at merlot.wekj.jhu.edu. The high rates of conversion at HIS4 and ARG4, indicative of high rates of DSBs, inevitably led to multiple-event four-spore viable tetrads that could not be included in some analyses. Standard statistical analyses were conducted with the aid of the online calculators at VassarStats. Tetrad-specific statistical analyses were carried out with calculators at Stahl Lab Online Tools (http://molbio.uoregon.edu/~fstahl/). All P-values are reported without regard to the number of analyses performed.

Map lengths:

Map length (in centimorgans) for any interval, defined as 100 times the mean number of exchanges per meiosis, was calculated according to Perkins (1949). Map length can be calculated only when neither marker defining the interval undergoes conversion.

Interference:

In some analyses, the map length of an interval (Perkins 1949) was compared for populations that did, or did not, have a crossover in an adjacent interval. A significant difference in map length (two-tailed P < 0.05) due to the crossover in the adjacent interval conservatively indicates interference. Tests for significance of difference between two Perkins map lengths were conducted with the aid of Stahl Lab Online Tools. In Table 4, all such tests that indicated a significant difference in map lengths were confirmed by a Monte Carlo simulation as follows.

TABLE 4
MAT-KAN and HYG-KAN map distances among crossovers and noncrossovers in the adjacent KAN-HIS4-NAT interval in tetrads with 6:2, 5:3, or normal 4:4 segregation for HIS4

To determine whether two genetic distances were statistically distinguishable or not using a permutation test, we first pooled the parental ditypes (PDs), tetratypes (TTs), and nonparental ditypes from the two intervals. Then, for 1000 simulations, we randomly distributed the pooled types back into two randomized data sets, keeping the original total number of tetrads in each data set. The approximate P-value for this permutation test is the proportion of the 1000 randomized data sets with a standardized absolute difference in length, |X1X2|/(SE(X1X2)), that was at least as large as that observed in the original data.

In other analyses, interference was detected as a shortage of multiple exchanges as indicated by a nonparental ditype (NPD) ratio significantly less than unity (Papazian 1952). When wild-type interference is compared with interference in a mutant that has very different map lengths, m, an index of interference that is independent of map length (Stahl and Lande 1995), was determined using the m calculator at Stahl Lab Online Tools. Beginning with Foss et al. (1993) and McPeek and Speed (1995), this model has proven to be a useful description of interference.

Msh4 crosses:

For crosses in the Rine background, diploids YFS621 and YFS636 (Figure 1) were streaked onto YEPD, grown for 2 days at 30°, patched onto YEPD, and incubated for 1 day at 30°. The patches were then replica printed to sporulation medium (Malkova et al. 2004) and incubated for 3 days at 30°. Asci were dissected onto 2× YEPD and incubated for 5 days at 30°. For crosses in the Petes background, diploids YFS707 and YFS713 (Figure 1) were streaked onto rich medium, grown for 2 days at 30° and then inoculated into 50 ml YEPD in a 500-ml flask and aerated at 300 rpm for 1 day at 30°. Cells were then diluted to an A600 of 2.5, washed once with water, and resuspended in a 250-ml flask in 25 ml sporulation medium with amino acids at 1/5 the standard concentrations for growth (Hillers and Stahl 1999). They were then incubated for 5 days at 18° with aeration at 300 rpm. Asci were collected, washed, and dissected on 2× YEPD plates (Hillers and Stahl 1999). After incubation for 5 days at 30°, the dissection plates were replica printed to determine segregation patterns. Our ability to score conversions correctly was confirmed by picking and replating an appropriate number of colonies that had been identified as 5:3 or 6:2 conversions.

Figure 1.
Diagrams of Rine background YFS621 (MSH4) and YFS636 (msh4) and Petes background YFS707 (MSH4) and YFS713 (msh4) diploids employed in the Msh4 studies (Tables 4–8).). The data from the diploid YFS621 were also used in the ...

PRM vs. WRM study:

Sporulation of YFS641 and YFS642 (Figure 2) was performed as in Gilbertson and Stahl (1996) except that diploid cells were grown for only 1 day on YEPD prior to replica printing onto sporulation medium. Tetrads were dissected onto 2× YEPD and then incubated at 30° for 5 days. The tetrads were then printed to plates containing standard arginine, leucine, and uracil omission media.

Figure 2.
Diagram of the Rine background diploids employed in the PRM vs. WRM study (Tables 9 and and10).10). ΔSalI is an arg4 marker that makes WRMs to the right of the DSB site. HpaI, at the left of the DSB site, is a native restriction site. ...

For screening tetrads by PCR, the tetrads were printed to fresh YEPD and incubated overnight (only) at 30°. Each entire colony was lifted with a plastic pipette tip and suspended directly into a 30-μl PCR reaction mix containing 300 μm dNTPs, 2.5 units TAQ polymerase (Promega, Madison, WI), 2 mm MgCl2, primers FS91 and FS92 at 640 pmol, all in Promega 1× reaction buffer. FS91 and FS92 amplify a fragment from −506 nt through −108 nt, upstream of the start of the ARG4 ORF. The resulting PCR reactions were screened for the respective silent ARG4 alleles by restriction digestion (as above) and electrophoresis. The ARG4::HpaI-lopC allele yields a 424-bp fragment readily distinguishable from both the wild-type ARG4 and ARG4::HpaI-SalI alleles (each 398 bp in length) by electrophoresis on 3% NuSieve GTG low-melting-point agarose gels run in 1× TBE buffer at room temperature. To ensure proper scoring of the ARG4::HpaI-SalI allele, PCR reactions were split in two. One aliquot was digested with SalI and the other with HpaI prior to gel electrophoresis. The reliability of detection of 5:3 conversions was confirmed by the procedure described in Hoffmann et al. (2005); all 41 reconstructed colonies tested positive for sectoring of the PRM.

The intended properties of the three markers closely bracketing the DSB site were confirmed by randomly testing tetrads from each of the two crosses. Of 100 tetrads, the silent marker making WRMs (Hpa1-Sal1) had nine 6:2 conversions and no 5:3 conversions, as did the arg4 marker. All conversions were co-conversions. Of 105 tetrads, the silent marker making PRMs (lopC) had five 6:2 conversions and seven 5:3 conversions. Of the five 6:2 conversions, three were accompanied by 6:2 conversion at ARG4. Of the seven 5:3 conversions, four were accompanied by 6:2 conversion at ARG4 (in one of these tetrads, the two conversions were in favor of different parents), and three were 4:4 at ARG4. In all cases, except the one noted, the two associated conversions were in favor of the same parent (i.e., co-conversions). In this set of 105 tetrads, the arg4 marker enjoyed nine 6:2 conversions and no 5:3 conversions.

Ndj1 study:

Diploid strains (Rine background) YFS40 and YFS41 (Figure 3) were streaked from the −70° freezer onto YEPD and grown for 3 days at 30°. Single colonies were then patched onto YEPD and incubated for 1–2 days at 30°. The patches were replica printed to YEPEG (Ausubel et al. 1994) for 2–3 days at 30° and then replica printed to KOAC (McCusker and Haber 1988) for 5 days at 25°. Tetrads were dissected to YEPD and grown for 5 days at 30°.

Figure 3.
Diagram of Rine background diploids used in the ndj1 study (Tables 11–13).). The palindrome marker HpaI-lopC in YFS40 (NDJ1) and YFS41 (ndj1) was not scored in this study. The YFS621 strain, also used in the ndj1 study, is diagrammed in ...

Diploid strains (Rine background) YFS621 (Figure 1) and YFS646 were streaked onto YEPD and grown for 2 days at 30°. YFS621 data are from the Msh4 study. Single colonies were then patched onto YEPD plates and incubated for 1 day at 30°. The patches were then replica printed to sporulation medium containing ampicillin (100 mg/liter) for 3 days at 30°. Tetrads were dissected on YEPD plates and grown for 5 days at 30°. The tetrad colonies were replica printed to the appropriate omission or antibiotic media to determine the phenotypes. The NDJ1 strains YFS40 and YFS621 yielded different ratios of 6:2/5:3 tetrads at ARG4 (P = 0.01). The conclusions that we draw from our analyses are insensitive to that ratio.

RESULTS

Experimental approach:

Our crosses were designed to yield a high rate of conversion (to facilitate data collection) with a large proportion of 5:3's (to detect heteroduplexes). For most of these crosses, full data sets have been deposited as supplemental material. For each of two loci (ARG4 and HIS4) in each of two strain backgrounds (“Rine” and “Petes”: Figure 1), we analyzed meiotic tetrads in which each DSB hotspot was marked with a small palindrome that makes PRMs (Nag et al. 1989) in heteroduplex DNA. The high rate of conversion resulted in numerous tetrads that had evidently enjoyed multiple events. These tetrads were necessarily excluded from some analyses. A DSBr event is recognizable as a gene conversion if either repair of the resulting mismatch failed (resulting in 5:3 segregation of the marker) or the mismatch was repaired in favor of the duplex that was invaded, as defined by the DSBR model (yielding 6:2 segregation). Repair of the mismatch in favor of the invading strand will restore normal 4:4 segregation of the marker, thereby erasing the incipient gene conversion. To allow us to detect crossing over, we bracketed each hotspot with two closely linked, conveniently scored insertions. In addition, the mating-type locus (MAT) in the Rine background and the inserted drug-resistance marker HYG in the Petes background defined intervals adjacent to the HIS4-containing interval to be used for assessing interference (Figure 1).

5:3 crossovers lack positive interference:

To assess interference between DSBr events in the KAN-HIS4-NAT interval and crossovers in the adjacent MAT-KAN or HYG-KAN interval, we measured, for each segregation class as defined with respect to HIS4 conversion, the effect of a crossover or a noncrossover in the KAN-HIS4-NAT interval on the map length (centimorgans) of the MAT-KAN or HYG-KAN interval. A reduction or increase in the latter relative to those in the remaining population of classifiable tetrads indicates positive or negative interference, respectively. Table 4 shows that conversion crossovers, as a class, failed to manifest interference. [This behavior differs from that reported for WRMs by Mortimer and Fogel (1974) and Malkova et al. (2004); see Testing the rules in the discussion.] However, the 5:3 crossovers as a class are seen to differ from the 6:2 and 4:4 crossovers. Specifically, the 5:3 crossovers appear to manifest negative interference, whereas the 6:2 and 4:4 crossovers display positive interference.

We take these results to be a demonstration that wild-type yeast does have both interference and “non”-interference crossovers, which, by means of their different MMR properties, can be demonstrated without the involvement of recombination-disrupting mutations. According to the “two-pathway model” of Zalevsky et al. (1999), the 5:3 crossovers must have arisen from the Msh4-independent, “non”-interference class of DSBr. That view predicts that deletion of MSH4, which does reduce both crossing over (Table 5) and interference (Table 6) in most intervals of our strains, should reduce the frequency of 6:2 and 4:4 crossovers but not the frequency of crossovers with 5:3 segregation for the palindrome site.

TABLE 5
Map distances in MSH4 and msh4 strains
TABLE 6
Interference as m; NPD ratio; and observed PD/NPD/TT in MSH4 and msh4 strains

Deletion of MSH4 reduces primarily 4:4 and 6:2 crossovers:

We tested the above prediction (Table 7) with a set of diploids that are isogenic to those described, except for deletion of the MSH4 gene. Deletion of MSH4 had a minor effect on crossovers with 5:3 segregation at the palindrome site at HIS4 or ARG4 in the Petes background, but strongly reduced crossovers with 6:2 or 4:4 segregation.

TABLE 7
msh4-induced changes in percentage (and number) of crossovers and noncrossovers for intervals containing ARG4 or HIS4 among tetrads with 5:3, 6:2, or normal 4:4 segregation for the relevant palindrome site

In the Rine background, the msh4 mutants displayed an overall increase in conversion rates of the nonpalindrome markers (23.5/16.0 = 1.5-fold, Table 8), reflected in an increase (1.6-fold) in the (“Msh4 independent”) 5:3 conversions at ARG4 and HIS4 in Table 8. msh4-induced increases in conversion have been seen previously (Ross-Macdonald and Roeder 1994) but have been downplayed (Roeder 1997; Novak et al. 2001). Despite the increased conversion in the Rine strain, 6:2 crossover conversions were reduced significantly at ARG4 and were not increased at HIS4, in contrast with the 5:3 conversion crossovers (Table 7). Thus, the Rine data show the same kind of differential effect on the 6:2 vs. 5:3 crossovers as do the Petes data.

TABLE 8
Conversion frequencies in MSH4 and msh4 backgrounds for markers making WRMs or PRMs

The effect of msh4 on the frequencies of crossover tetrads with 5:3, 6:2, or 4:4 segregation of the palindrome sites is quantified for the Petes strains as the percentage of change (Table 7). For the two loci, the msh4-induced changes in frequency of 5:3 crossovers average −8%. In contrast, the average value for the 6:2 crossovers is −50% (P = 0.02) and for 4:4 crossovers is −55% (P < 0.0001).

These data argue that one class of crossovers, which often fails to repair a PRM, occurs with relatively little dependence on Msh4 and displays no positive interference in a MSH4 background; the other, which rarely, if ever, fails to enjoy such repair, is strongly Msh4 dependent and displays positive crossover interference.

msh4-induced increase in noncrossovers:

Table 8 shows that, in the Petes background, the combined frequencies of conversion for the markers with WRMs (all markers except those at HIS4 and ARG4) were unaffected by the msh4 mutation (26.2% vs. 26.3%), as expected. The expectation failed, however, for each of the markers making PRMs. At HIS4, 21.3% for MSH4 fell to 18.3% for msh4 (P = 0.02). At ARG4, the corresponding values are 8.9% vs. 7.0% (P = 0.02). The msh4-induced reductions in conversion for HIS4 and ARG4 (21.3 − 18.3 = 3.0 and 8.9 − 7.0 = 1.9 percentage points, respectively) are comparable to the msh4-induced reductions in 6:2 crossovers (Table 7) for HIS4 and ARG4 (1.8 and 1.9 percentage points, respectively). The lost 6:2 crossovers appear to be accommodated by increases in 4:4 noncrossovers, which were greater than the reductions in 4:4 crossovers; for HIS4 this net increase is 1.6 points, and for ARG4 the net increase is 1.8 points. Thus, these data (Tables 7 and and8)8) support our expectation of no net change in conversion frequency for markers making WRMs, but imply that the potential crossovers with 6:2 segregation for markers with PRMs were lost, not only as crossovers but also as conversions, as a result of the msh4 deletion.

The observation that the markers making WRMs suffered no msh4-induced reduction in conversion rates argues against msh4-induced, sister-chromatid-dependent DSBr as the cause of reduced conversion associated with PRMs.

The data for HIS4 in the Petes strain (Table 7) suggest that the modest loss of 5:3 crossovers is compensated by an increase in 5:3 noncrossovers.

Evidence for MMR-dependent restoration of 4:4 segregation for palindromic markers:

As described above, tetrads with 4:4 segregation at HIS4 or ARG4 enjoyed a net increase associated with deletion of MSH4 (Tables 7 and and8,8, Petes background), and this increase was in the noncrossover class. This invites the proposal that, in wild-type yeast as well, 4:4 noncrossovers are created by round two MMR. This proposal is in harmony with the rules (see Introduction) stating that products of the interference class are subject to MMR-dependent restoration of 4:4 segregation.

To test whether repair of PRMs close to a DSB hotspot in fact does result in frequent 4:4 segregation for the palindrome site, we conducted two crosses in which the DSB hotspot at ARG4 was marked with an arg4 mutation that makes WRMs, resulting in a high frequency of 6:2 conversions. This arg4 marker, located a nominal 190 bp to the “right” of the DSB site (arg4::1691SalI, Figure 2), should signal all or most of the DSBr events at ARG4 that involved homologs. [We consider it likely that most of the conversions are a consequence of DSBs at the ARG4 hotspot. DSBr events originating from the DED81 break site, >2 kb distant to the left, would generally have resulted in normal 4:4 segregation rather than 6:2 segregation of the marker (Foss et al. 1999).] Markers on the left side of the ARG4 DSB site were designed to detect the influence of MMR. One of the crosses had a marker (ARG4::HpaI-lopC, Figure 2) that makes PRMs at a “silent” (nonauxotrophic) site a nominal 130 bp to the left of the DSB site, while the other had a marker (ARG4::HpaI-SalI, Figure 2) making WRMs at the silent site. The silent markers were scored by restriction analysis of PCR-amplified DNA, as described in materials and methods. It is an important feature of these constructs that the WRMs are close enough to the DSB site that they will usually be subject to invasion-directed repair and, consequently, unavailable for resolution-directed repair, which can result in restoration of normal 4:4 segregation (Foss et al. 1999; Hillers and Stahl 1999; Stahl and Hillers 2000). In both crosses, LEU2 and URA3 insertions bracketing the DSB site allowed us to detect crossing over associated with conversion at ARG4. To screen for conversion at ARG4 (6:2 in favor of either ARG4 or arg4; see materials and methods), we replicated the colonies from dissected tetrads to arginine-drop-out plates. The tetrads that exhibited a conversion event were then scored for the silent marker.

The data in Table 9 show that, in the cross with the PRMs at the silent site, tetrads with a conversion on the right side of the DSB often (25/49) lacked conversion on the left side of the DSB. In contrast, in the cross with WRMs on both sides of the DSB, tetrads with a conversion on the right side of the DSB usually (35/40) manifested conversion on the left side as well (see also Hoffmann et al. 2005). This degree of “two-sidedness” is higher than that noted in the pioneering article by Schultes and Szostak (1990), probably because their markers were farther from the DSB than the ones used here. Our data demonstrate that a major fraction of DSBr events indicated by conversion of a marker that makes WRMs fails to result in conversion for a marker that makes PRMs at the same site. At the same time, the ~12% of one-sided events observed in the WRM cross suggests some structurally lopsided DSBr events (e.g., Allers and Lichten 2001).

TABLE 9
Frequency of 4:4 segregation of the silent marker among tetrads with conversion for arg4

In >90% of the tetrads identified as conversions for the arg4 marker to the right of the DSB (Figure 2), both of the bracketing markers, LEU and URA, segregated 4:4, allowing each of these tetrads to be scored as either a crossover or a noncrossover. Table 10 shows that both crossovers and noncrossovers have a high rate of conversion (15/17 and 19/22, respectively) for the marker making WRMs at the silent site. In contrast, only 11/17 crossovers and 11/29 noncrossovers were converted for the silent marker making PRMs. The greater failure of conversion for noncrossovers than for crossovers was significant and in harmony with results reported by Gilbertson and Stahl (1996), Merker et al. (2003), and Jessop et al. (2005).

TABLE 10
Segregation of silent markers in crossover and noncrossover conversions of arg4

Phenotypes of the ndj1 mutant:

The identification of a “non”-interference class of DSBr, proposed to facilitate homologous pairing, prompted us to examine the phenotypes of the ndj1 mutant. This mutant, named after its meiosis I nondisjunction phenotype (Chua and Roeder 1997; Conrad et al. 1997; but see discussion and supplemental Figure S1), delays homolog pairing (Conrad et al. 1997), reduces interference (Chua and Roeder 1997), and reduces noncrossover frequency (Wu and Burgess 2006). The data in Chua and Roeder (1997) weakly suggest an increase in crossing over.

Map lengths:

To test whether an ndj1-induced increase in crossing over could be detected in our strains, we analyzed four-spore-viable tetrads from two sets of crosses in the Rine background (Figure 3). Table 11 indicates that the ndj1 mutants showed an increase over wild type in all five map-length measurements, with three of the individual measurements meeting the conventional level for statistical significance. More conspicuously than the data of Chua and Roeder (1997), our data imply that deletion of NDJ1 increases crossing over and may do so to a different degree in different intervals.

TABLE 11
PD/NPD/TT frequencies and map lengths in NDJ1 and ndj1 strains

Interference is decreased in our ndj1 mutant:

Table 12 shows that deletion of NDJ1 resulted in increased NPD ratios, compatible with the expected decrease in interference. While the increases for individual NPD measurements are not generally significant, all five measurements manifested the increase, while most showed significant residual interference (NPD ratio <1). For two measurements, the m-value (Stahl and Lande 1995) was decreased, strengthening the interpretation of decreased interference. These data are compatible with, but less robust than, the larger data set of Chua and Roeder (1997). Combined with the observed increases in crossing over, the data invite the hypothesis that deletion of NDJ1 increases the frequency specifically of “non”-interfering crossovers at the expense of noncrossovers. Our data and calculations (described above and in the appendix) suggest that noncrossovers in both the 5:3 and 6:2 classes are products primarily of the “non”-interference class of DSBr. Thus, the hypothesis predicts that an ndj1-induced shift from noncrossovers to crossovers should be most conspicuous in conversion tetrads.

TABLE 12
Interference as m; NPD ratio; and observed PD/NPD/TT in NDJ1 and ndj1 strains

NDJ1 deletion decreases noncrossover and increases crossover frequencies selectively in tetrads with a conversion event at a palindrome site:

The data presented in Table 13 fulfill the expectation that the ndj1 mutation causes a decrease in noncrossover frequency accompanied by an increase in crossovers in both the 5:3 and the 6:2 tetrads. For the 5:3 and 6:2 tetrads combined, the ndj1 mutation reduced the noncrossover frequency by values ranging from 23 to 45% (average 31%) and increased the crossovers by values ranging from 25 to 71% (average 47%). In contrast, the changes in noncrossovers in the 4:4 class ranged from −3.3 to +2.3% (average −0.8%) and the changes in the crossover class ranged from −8.1 to +7.3% (average +1.1%) with these deviations being, for the most part, statistically insignificant despite the large numbers of tetrads in these classes. These data support the prediction that the ndj1-induced shift from noncrossovers to crossovers will be concentrated in conversion tetrads and suggest (1) that, within the “non”-interference class, a shift of noncrossovers to crossovers contributes to the reduced interference phenotype of the ndj1 mutation and (2) that the 4:4 tetrads are selectively poor in “non”-interference class events.

TABLE 13
ndj1-induced changes in percentage (and number) of crossovers and noncrossovers for intervals containing ARG4 or HIS4 among tetrads with 5:3, 6:2, or normal 4:4 segregation for the relevant palindrome site

DISCUSSION

We analyzed DSBr events at hotspots marked with small palindromes that make PRMs in heteroduplex DNA and compiled the results for tetrads segregating 5:3, 6:2, or 4:4 for the palindrome. Table 14 summarizes our conclusion that the 5:3 and 4:4 tetrads, for both crossover and noncrossover tetrads, have complementary features. Nonconversion (4:4) crossovers, which, as a class, are Msh4 dependent (Tables 5 and and7),7), display positive interference (Table 4) and promote Msh4-facilitated disjunction of homologs (Ross-Macdonald and Roeder 1994). Moreover, among 4:4 tetrads the absolute frequencies of both crossovers and noncrossovers were conspicuously affected by msh4 (Table 7), but only minimally by ndj1 (Table 13), a gene required for normal homolog pairing (Conrad et al. 1997). In contrast, among tetrads segregating 5:3 for the palindrome site, the crossovers lacked positive interference in wild-type meioses (Table 4). Among 5:3 tetrads, the frequencies of both crossovers and noncrossovers were conspicuously affected by ndj1 (Table 13), but only minimally by msh4 (Table 7, Petes).

TABLE 14
Properties of segregation classes for PRMs

Our results suggest that the 4:4 and 5:3 segregation classes represent two classes of meiotic DSBr, each with its own rules for repair of PRMs (see the Introduction) and each yielding both crossovers and noncrossovers. Tetrads segregating 6:2 appear to include crossovers from both classes (Table 7), but noncrossovers from the Msh4-independent class only (appendix).The data further suggest that the DSBr class represented by 5:3's promotes pairing but is not required for normal disjunction in wild-type crosses while the other, represented by 4:4's, promotes meiosis I disjunction and plays no conspicuous role in pairing. Henceforth, we shall refer to these two classes as “phases” of DSBr involved in “pairing” and “disjunction,” respectively.

Previously, the hypothesis of two DSBr classes in yeast relied on statistical analysis of interference and on inference based on the phenotypes of mutants that reduce crossing over. The demonstration that, in wild-type yeast, 5:3 segregants are identifiable as products of the pairing phase confirms the validity of the hypothesis.

We note that the interference data (Tables 4 and and6)6) and the msh4 data of Table 7 are variable with respect to strain and locus, as expected in the presence of two classes of DSBr that vary in relative frequency. The entries that fail to pass statistical tests of significance often come close to doing so and never manifest opposite trends.

Phenotypes of msh4 deletion:

The use of markers making PRMs revealed new msh4 phenotypes. Our data show, first, that among 5:3 tetrads crossover frequency is almost independent of Msh4 (Table 7, Petes) and that these Msh4-independent 5:3 crossovers lack positive interference (Table 4). This implies that inferences derived from studies involving 5:3 tetrads or heteroduplex DNA may apply only to the pairing phase of DSBr. Second, as anticipated from an Msh4-Msh5-dependent stabilization of Holliday junctions (Snowden et al. 2004 and see Ross-Macdonald and Roeder 1994), the tetrads segregating 4:4 for the palindrome show a msh4-induced decrease in crossovers accompanied by an increase in noncrossovers. However, among the 6:2 tetrads, the msh4-induced loss of crossovers is not accompanied by an increase in 6:2 noncrossovers. Instead, the 6:2 crossovers appear to have been transformed into 4:4 noncrossovers (Table 7, Petes). This suggests that whenever Msh4 is absent or unavailable a disjunction-phase DSB is repaired as a noncrossover with 4:4 segregation for the palindrome. The abundance in MSH4 crosses of tetrads with MMR-related 4:4 segregation of the palindrome site (Table 10) suggests that these products reflect the rules for MMR in the wild-type disjunction phase. Moreover, the overrepresentation of noncrossovers among the tetrads that appear to have MMR-dependent 4:4 segregation suggests that such noncrossovers result from a programmed, interference-related lack of access to Msh4 (Stahl et al. 2004). In Figure 4, we offer a scenario in which noncrossovers in the disjunction phase inevitably segregate 4:4 for a marker making PRMs. In the appendix, we support the view that all the visible (i.e., conversion) noncrossovers derive from the pairing phase.

Figure 4.
A model for noncrossover production via single-end invasion with synthesis-dependent strand-annealing (Haber 2000; Hunter and Kleckner 2001; Hoffmann and Borts 2004) in the disjunction phase of DSBr. Noncrossover products arise when the invasion is not ...

It was suggested to us, as an alternative interpretation of our data, that palindromes are prone to failing, in some situations, to enter a heteroduplex state. However, the observation (Hoffmann et al. 2005) that strains compromised for MMR by mlh1 or msh2 mutation give increased frequencies of one-sided conversions with point mutations challenges that view.

Phenotypes of ndj1 deletion:

Our data and those of Wu and Burgess (2006) show an ndj1-induced reduction in noncrossovers. In our experiments, but not in those of Wu and Burgess (2006), the reduction in noncrossovers is matched with an ndj1-induced increase in crossovers. The difference between these two sets of results may reflect strain or locus differences or differences inherent in the methods used for analysis. For example, Wu and Burgess (2006) looked for ndj1 phenotypes in DNA isolated from meiotic cells whereas we examined tetrads with four viable spores. Our ability to identify the classes of tetrads in which these phenotypes are concentrated secured our conclusions.

The ndj1 phenotypes observed in our crosses—reduction in noncrossovers, increase in crossovers—characterized the conversion tetrads in which the noncrossovers are assignable to the pairing phase (appendix). We propose that the observed ndj1-induced increase in crossovers represents an increase specifically in “non”-interfering, pairing-phase crossovers at the expense of pairing-phase noncrossovers. This increase, we propose, is responsible for the modest reduction in interference observed in our ndj1 mutants (Table 12). Chua and Roeder (1997) reported a more conspicuous reduction in interference and a weaker increase in crossing over. Their ndj1 strain differed as well in showing the classical nondisjunction phenotype of a conspicuous increase in two-spore viable tetrads (Chua and Roeder 1997), a phenotype not evident in our strain (supplemental Figure S1). Chua and Roeder (1997) also reported an increase in chromosomes that lacked crossing over (E0 tetrads), a reasonable phenotype for pairing-defective ndj1 mutants. We question the conventional interpretation (e.g., Trelles-Sticken et al. 2000) that the increased E0 class seen by Chua and Roeder (1997) is a result of diminished interference. It appears to us more likely that the increased E0 class in their strains arises from an occasional failure of effective pairing. Such pairing failures in the ndj1 strain of Chua and Roeder (1997) would account simultaneously for the greater reduction in interference and the smaller increases in crossing over by increasing the PD tetrads without imposing any changes in the frequencies of TTs and NPDs relative to each other. Pairing failures might also account for the lack of increase in crossover DNA in the studies of Wu and Burgess (2006).

Our evidence for the noncrossover-promoting role of NDJ1 may reflect a selective advantage of noncrossover over crossover resolution in the pairing phase of DSBr, as previously suggested by Smithies and Powers (1986) and Carpenter (1987). One may speculate that a reduction or delay in the DSB-dependent phase of chromosome pairing increases crossing over by reducing the effectiveness of an unidentified process that favors noncrossover resolution in the pairing pathway, designed to prevent translocations caused by ectopic alliances. Rockmill et al. (1995) remarked that short chromosomes are slow to pair. Thus, the higher densities of “non”-interfering crossovers associated with shorter chromosomes (Kaback et al. 1999; Stahl et al. 2004; but see Turney et al. 2004) and with deletion of NDJ1 may be a common consequence of slow pairing.

Noncrossovers in two phases:

Börner et al. (2004) describe a view in which an “early” noncrossover pathway of DSBr (which also produces some, presumably noninterfering, crossovers) is the only source of noncrossovers. This view implies that these “early” noncrossovers had been programmed to be resolved as such by the interference apparatus. Börner et al.'s (2004) description of a “noncrossover pathway” yielding both noncrossovers and some noninterfering crossovers fits our “pairing phase.” However, our experiments with PRMs suggest (1) that neither the crossovers nor the noncrossovers in this phase were affected by the interference apparatus and (2) that the disjunction phase, as well as the pairing phase, generates both noncrossovers and crossovers. Specifically, both crossovers and noncrossovers in the pairing phase, represented by the 5:3 tetrads, are responsive to the pairing-promoting Ndj1 function but not appreciably so to the interference-promoting Msh4 function. Conversely, noncrossovers as well as crossovers in the disjunction phase, represented by the 4:4 tetrads, are characterized by their greater responsiveness to Msh4 than to Ndj1 (Table 14).

Further support for the concept of two kinds of meiotic noncrossovers comes from a study of crossover homeostasis (Martini et al. 2006). Those authors suggested that some, but not all, DSBs ordinarily destined to give rise to noncrossovers gave rise to interfering crossovers under conditions of DSB shortage, leading them to propose that some DSBs may be unavailable for homeostasis. We suggest that the unavailable DSBs are, in fact, precursors to the noncrossover products of the pairing phase, while the incipient noncrossovers available for crossover homeostasis belong to the disjunction phase.

Unless DSBr events are monitored with a marker making WRMs, as in Table 10, the use of PRMs allows no distinction between 4:4 MMR-related noncrossover tetrads and 4:4 tetrads lacking a DSBr event. This problem may account for the view, adopted, for example, by Börner et al. (2004), Bishop and Zickler (2004), and Wu and Burgess (2006), that the pathway that generates interfering crossovers fails to generate noncrossovers. We do not dispute the view that double-Holliday-junction intermediates give rise only to interfering crossovers as suggested by Allers and Lichten (2001). However, as indicated above, we propose that the intermediates destined by the interference apparatus to be resolved as noncrossovers generate only 4:4 (i.e., invisible) disjunction-phase noncrossovers when monitored with a PRM (see Figure 4), while the observed 5:3 noncrossovers (or heteroduplex DNA restriction fragments) are all products of the pairing phase. Implied in this proposal is the notion that the interference apparatus operates after DSB-dependent pairing has been initiated.

Negative interference between pairing-phase conversions and disjunction-phase crossovers?

In wild-type (MSH4) crosses of the Rine strain (Table 4), events in the pairing phase of DSBr manifested (an almost statistically significant) negative interference. The map length of the MAT-KAN interval in the total data is 36.7 ± 1.2 cM, while the value for the combined 5:3 and 6:2 noncrossovers is 50.0 ± 8.6 cM and that for the 5:3 crossovers is 52.7 ± 14.7 cM. The MAT-KAN map length for those crossover and noncrossover data combined is 50.9 ± 7.6 cM. We can test whether this indication of negative interference arises from above-average cell-wide rates of crossing over in these selected tetrads. For the Rine strain, among the tetrads with 5:3 segregation, plus the noncrossover tetrads with 6:2 segregation for the palindrome site at HIS4 (on chromosome III), the LEU-URA interval (on chromosome VIII) is 12.1 ± 1.9 cM as compared with 12.6 ± 0.5 cM among total tetrads. For the Petes strain, the analogous values for the TRP-URA interval are 18.9 ± 1.5 cM and 17.5 ± 0.6 cM, respectively. Thus, the negative interference that seems to characterize DSBr events in the pairing pathway is localized to the chromosome on which the event occurs.

Data for the HYG-KAN interval (Petes background) are too few to stand on their own but manifest leanings of the same sort. In brief, the combined 5:3 crossovers and conversion noncrossovers in the KAN-NAT interval have a HYG-KAN distance of 6.1 ± 1.6 cM, as compared with the HYG-KAN map length in the unselected data of 4.9 ± 0.3 cM.

Because the Perkins (1949) formula underestimates longer distances, we suspect the apparent negative interference is not a reflection of statistical inadequacy of the data. Since negative interference has not been reported for msh4 mutant crosses, we propose that the negative interference observed in our MSH4 crosses occurred between disjunction phase crossovers and pairing-phase conversion events.

If the negative interference is localized to the vicinity of pairing-phase events, which seems likely, it might have a corollary in cytological observations. Connections between homologs, called “axial associations” (Rockmill et al. 1995), may be visible manifestations of DSBr events of the pairing phase. These associations appear to correlate spatially with concentrations of recombination proteins whose activities are associated with crossing over in the disjunction phase (reviewed in Bishop and Zickler 2004). The possibility of physical association between events in the two phases is further supported by the studies of Tsubouchi et al. (2006). Negative interference between conversion noncrossovers and nearby crossovers might also account for recombination events in which a conversion is separated from its apparently “associated” crossover by a stretch of unconverted markers (e.g., Symington and Petes 1988; Jessop et al. 2005). Such negative interference could also account for trans events associated with crossovers as reported by Hoffmann and Borts (2005).

Testing the rules:

Jessop et al. (2005) reported a large fraction of one-sided conversions—conversions for a marker making PRMs on one side of a DSB accompanied by 4:4 segregation at a PRM that is 300 bp on the other side. The one-sided 6:2 tetrads obeyed the rules very nicely: junction-directed MMR fully converted one mismatch while, apparently, restoring the other (see below). However, some one-sidedness was seen for 5:3 conversions, too (and see Gilbertson and Stahl 1996). Such events, by virtue of their manifest 5:3 segregation of one marker, belong to the pairing phase, which, according to the rules, is not subject to restoration. Reconciliation between these data and the rules may lie in the possibility that these tetrads as well as our MMR-independent “one-sided” conversions, such as the 5/40 observed with two WRMs (Table 14), derive predominantly from the pairing phase and reveal structural lopsidedness unique to that phase, perhaps of the sort described by Allers and Lichten (2001).

The rules, proposed to account for the observed relationships among conversion, interference, and mismatch repair in yeast, are applicable to previously puzzling data reported for Sordaria. Kitani (1978) conducted tetrad analyses, similar to ours, in S. fimicola, all of whose mismatches appear poorly repairable. Like ours, Kitani's data demonstrated that 5:3 crossovers lacked (positive) interference. Unlike ours, however, Kitani's 6:2 crossovers also lacked interference. A conspicuous difference between yeast and Sordaria lies in the patterns of non-Mendelian segregation: Sordaria has a relatively high ratio of aberrant 4:4 tetrads (tetrads with two spores bearing an unrepaired mismatch at the same site) to 5:3 tetrads as compared to that for yeast markers that make PRMs (reviewed in Meselson and Radding 1975). This difference suggests a difference in the structure of the bimolecular intermediates in the two species. As shown in Figure 1 of Stahl and Foss (2008, this issue), Sordaria's relative abundance of aberrant 4:4 tetrads, which lack interference (Kitani 1978), implies that heteroduplex regions in Sordaria's pairing phase are predominantly symmetric (heteroduplex on both participating chromatids), whereas those in yeast are predominantly asymmetric (heteroduplex on only one of the two participating chromatids). If disjunction-phase intermediates differ similarly, the rules predict that, in yeast crossovers, junction-directed MMR will lead either to restoration of 4:4 segregation or to 6:2 conversion, depending on which pair of strands, whose cutting results in resolution of a given junction, directs the repair. In our experiments, where the distances between the PRMs and either junction are almost equivalent (and, perhaps, irrelevant), one pair of strands is as likely to direct the MMR as the other pair. Hence, according to the rules, the disjunction-phase crossovers with 6:2 segregation should represent 50% of all interfering crossovers. As pointed out above, the predominance of “one-sided” 6:2 crossovers observed by Jessop et al. (2005) could be the result of restoration on one side of the DSB occurring hand in hand with MMR to 6:2 on the other. If Sordaria, on the other hand, has predominantly symmetric heteroduplex in its disjunction phase, junction-directed repair of PRMs will lead to restoration only (Stahl and Hillers 2000), regardless of which resolved junction directs the repair. Thus, Kitani's (1978) observation that, in Sordaria, interference can be detected only among normal 4:4 tetrads is in complete harmony with the rules. In our data, on the other hand, the lack of interference in the 6:2 pairing-phase crossovers was masked by the interference of the 6:2 disjunction-phase crossovers derived by MMR from asymmetric heteroduplex. Kitani's 1978 article is discussed further by Stahl and Foss (2008, this issue).

The rules also account for the differences between our data and those reported by Mortimer and Fogel (1974) and Malkova et al. (2004) with respect to interference among conversion crossovers. These authors used WRMs, allowing them to register most or all nearby DSBr events as 6:2 conversions. They showed that, unlike our combined 5:3 and 6:2 conversion crossovers (Table 4), their conversion crossovers manifest interference. The rules suggest that the use of PRMs in our experiments caused about half of the potential interfering conversion crossovers to be lost as conversions, as a result of MMR-related restoration to 4:4 segregation. In our experiments, this loss of interfering conversion crossovers allowed the negative interference of the 5:3 crossovers and the positive interference of the remaining interfering 6:2 crossovers to cancel out when we combined those two types.

The counting model for interference:

The counting model for interference (Foss et al. 1993), designed to describe the interference phase of DSBr, predicts that the region between two close crossovers will be enriched for noncrossover conversions. That a test of this prediction (Foss and Stahl 1995) gave a contrary result may have been due, in part, to the presence of pairing-phase crossovers, not governed by the usual rules of interference. Our proposal that PRMs in noncrossovers from the disjunction phase are repaired to invisibility (4:4 segregation) suggests that an additional factor may have been in play: Foss and Stahl (1995) may have detected an enrichment of invisible, disjunction-phase noncrossover events occurring at the expense of visible, pairing-phase ones. Such interference between noncrossovers, occurring at a limited number of sites in a short interval, might account for the observed decrease in visible noncrossovers in the interval between crossovers, where the counting model predicted an increase.

We offer this commutation for the counting model notwithstanding the assertion by Martini et al. (2006, p. 294) that their data represent “strong evidence against a ‘counting’ model,” referring to the model of Foss et al. (1993). That assertion was made without acknowledging the previously offered (Stahl et al. 2004) explicit reconciliation between the counting model and data showing that interference is maintained even as a shortage of DSBs results in the homeostatic loss of noncrossovers in favor of crossovers. The reconciliation proposed that the elements counted, rather than being DSBs, were precursors to DSBs.

Acknowledgments

Elizabeth Housworth generously designed and conducted the Monte Carlo tests for interference. Dan Graham kindly refurbished the website Stahl Lab Online Tools, much of which was originally constructed by J.S. and Blake Carper. Dan Graham (ude.nogerou@dmaharg) has offered to answer technical questions regarding the site. Tom Petes, Greg Copenhaver, and David Thaler provided valuable comments on a draft of the manuscript. We are grateful to A. Villeneuve and several conscientious, more-or-less anonymous referees for their patience and their insightful suggestions and corrections. The work was supported in part by National Science Foundation grant MCB-0109809 to the University of Oregon.

APPENDIX: ON THE ORIGIN OF CONVERSION NONCROSSOVERS

Table 7 shows that the crossovers and noncrossovers with 5:3 conversion (for ARG4 or HIS4) were minimally sensitive to the absence of Msh4. This indicates that the 5:3 tetrads include primarily products of the “non”-interference class. Tetrads with 6:2 conversion, on the other hand, included both Msh4-dependent, interfering crossovers and Msh4-independent crossovers, as well as noncrossovers. To determine whether these 6:2 noncrossovers also included products from both classes, we assumed that MMR in the “non”-interference class operates indiscriminately on incipient crossovers and noncrossovers. This assumption is consistent with the rules, which allow only limited, invasion-directed MMR in the “non”-interference class (at which stage crossovers and noncrossovers are assumed to be not yet differentiated).

The assumption that the degree of MMR in the “non”-interference class (invasion directed, leading to 6:2) should be the same for crossovers and noncrossovers may be stated as follows: Within the “non”-interference class, the fraction of 6:2 noncrossovers among total conversion noncrossovers should equal the fraction of 6:2 crossovers among total conversion crossovers. The number of “non”-interfering conversion crossovers may be measured directly as the number of Msh4-independent crossovers. For the noncrossover conversions, on the other hand, contributions from the “non”-interference class cannot be distinguished from those of the interference class. If, however, all of the observed conversion noncrossovers had come from the “non”-interference class, we could write (6:2 noncrossovers)/(5:3 + 6:2 noncrossovers) = (Msh4-independent 6:2 crossovers)/(5:3 crossovers + Msh4-independent 6:2 crossovers). Table A1 indicates that the equality is upheld, supporting the hypothesis that all the conversion noncrossovers are products of the “non”-interference DSBr class (see Figure 4). This conclusion is congruent with the observation (Table 4) that 6:2 noncrossovers, like the 5:3 noncrossovers (and crossovers), appear to manifest negative interference.

TABLE A1
Origin of conversion noncrossovers

Notes

This article is dedicated to the memory of David R. Stadler.

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