Modulating Crossover Frequency and Interference for Obligate Crossovers in Saccharomyces cerevisiae Meiosis

Meiotic crossover frequencies show wide variation among organisms. But most organisms maintain at least one crossover per homolog pair (obligate crossover). In Saccharomyces cerevisiae, previous studies have shown crossover frequencies are reduced in the mismatch repair related mutant mlh3Δ and enhanced in a meiotic checkpoint mutant pch2Δ by up to twofold at specific chromosomal loci, but both mutants maintain high spore viability. We analyzed meiotic recombination events genome-wide in mlh3Δ, pch2Δ, and mlh3Δ pch2Δ mutants to test the effect of variation in crossover frequency on obligate crossovers. mlh3Δ showed ∼30% genome-wide reduction in crossovers (64 crossovers per meiosis) and loss of the obligate crossover, but nonexchange chromosomes were efficiently segregated. pch2Δ showed ∼50% genome-wide increase in crossover frequency (137 crossovers per meiosis), elevated noncrossovers as well as loss of chromosome size dependent double-strand break formation. Meiotic defects associated with pch2∆ did not cause significant increase in nonexchange chromosome frequency. Crossovers were restored to wild-type frequency in the double mutant mlh3Δ pch2Δ (100 crossovers per meiosis), but obligate crossovers were compromised. Genetic interference was reduced in mlh3Δ, pch2Δ, and mlh3Δ pch2Δ. Triple mutant analysis of mlh3Δ pch2Δ with other resolvase mutants showed that most of the crossovers in mlh3Δ pch2Δ are made through the Mus81-Mms4 pathway. These results are consistent with a requirement for increased crossover frequencies in the absence of genetic interference for obligate crossovers. In conclusion, these data suggest crossover frequencies and the strength of genetic interference in an organism are mutually optimized to ensure obligate crossovers.

accessory proteins (reviewed in Neale and Keeney 2006). The frequency and distribution of crossovers on chromosomes is a tightly regulated process. Four known aspects of this regulation are crossover interference, obligate crossovers, crossover homeostasis, and crossover invariance. Crossover interference regulates the spatial patterning of crossovers, where the presence of a crossover prevents the formation of a second crossover in its vicinity. As a consequence, an even distribution of crossovers is ensured, and closely spaced crossovers are less frequently observed than expected from a random distribution (Berchowitz and Copenhaver 2010). An obligate crossover per homolog pair facilitates disjunction. The obligate crossover is not a specific type of crossover, but refers to the observation that process(es) that generate most of the crossovers result in at least one crossover per homolog pair (Barchi et al. 2008). The obligate crossovers are ensured in different organisms with different crossover frequencies. For example, organisms that have strong genetic interference like Caenorhabditis elegans, Drosophila, Arabidopsis, mouse, and humans ensure obligate crossovers, although the number of crossovers per bivalent pair is low ($1-2) (Copenhaver et al. 2002;Hillers and Villeneuve 2003;Berchowitz and Copenhaver 2010;Libuda et al. 2013). But organisms with weaker interference, like S. cerevisiae, make $90 crossovers, or $6 times the number of bivalent pairs (16), to ensure an obligate event. Crossover homeostasis ensures that the number of crossovers is maintained (at the expense of noncrossovers) when the DSB precursors become limiting (Martini et al. 2006). This crossover buffering mechanism is also seen when the DSBs are increased (Cole et al. 2012). Crossover invariance is another mechanism that maintains the number of crossovers in organisms that lack interference. This phenomenon refers to the observation that, in Schizosaccharomyces pombe, the ratio of intersister to interhomolog repair is modulated in response to variations in DSB intensity to ensure uniform crossover distribution (Hyppa and Smith 2010). Recent studies suggest crossover interference, obligate crossovers, and crossover homeostasis are the outcomes of a single crossover patterning process regulated by the "mechanical stress relief" of chromosomes (Wang et al. 2015;Zickler and Kleckner 2016). As per this model, crossover interference and homeostasis are linked processes. But the designation of an obligate crossover is not dependent on either interference or homeostasis (Zhang et al. 2014;Wang et al. 2015).
It is not clear why organisms have vastly different crossover frequencies and how this is related to ensuring an obligate crossover. In this study, we address the relationship of obligate crossovers with crossover frequency using mlh3D and pch2D mutants. In S. cerevisiae, both these mutants have very different crossover frequencies but show high spore viability. At specific chromosomal loci, mlh3D shows up to a 50% reduction in crossover frequency but with good spore viability ranging from 72% and up to 92% depending on the strain background (Nishant et al. 2008;Cotton et al. 2010;Sonntag Brown et al. 2013). Pch2 is an evolutionarily conserved hexameric ring AAA+ ATPase protein that has roles in meiotic checkpoint signaling triggered by unrepaired DSBs, remodeling the chromosome axis at the future crossover sites and interhomolog bias (San-Segundo and Roeder 1999;Borner et al. 2008;Ho and Burgess 2011;Zanders et al. 2011;Chen et al. 2014). pch2D mutants are observed to make 50% more crossovers than wild type at specific loci, and also have good viability (95%) (Zanders and Alani 2009; but see Joshi et al. 2009). The mlh3D and pch2D mutants are therefore useful to test the effect of a wide range of crossover frequencies on obligate crossovers. It is important to note that pleiotropic effects of pch2D could affect the interpretation of changes in crossover frequencies on the obligate crossover.
We performed genome-wide mapping of meiotic recombination events in mlh3D, pch2D and mlh3D pch2D using the S288c/YJM789 hybrid. Crossovers in all three mutants, mlh3D (64 crossovers per meiosis on average), pch2D (137 crossovers per meiosis on average) and mlh3D pch2D (100 crossovers per meiosis on average) showed reduced genetic interference. Noncrossovers were not affected in mlh3D, but increased in pch2D and mlh3D pch2D. Crossover and noncrossover data suggest loss of chromosome size dependent DSB formation in pch2D mutants. mlh3D pch2D showed uniform crossover density on all chromosomes consistent with loss of genetic interference. Nonexchange chromosomes were abundant in mlh3Δ (47% of meioses), but efficiently segregated. pch2D (7%) had a reduced percentage of meioses with nonexchange chromosomes, showing that high crossover frequencies can promote crossover assurance in the absence of genetic interference. Even though the mlh3D pch2D mutant made as many crossovers as wild type, 20% of meioses showed nonexchange chromosomes, consistent with noninterfering crossovers being inefficient in promoting crossover assurance.

Tetrad analysis
Diploids were sporulated following the zero growth mating protocol (Argueso et al. 2003). Haploid strains were mixed together on synthetic complete media. After incubation for 4 hr at 30°, the resulting diploids were patched on sporulation media. After 2 d of incubation at 30°, tetrads were dissected on synthetic complete medium using a Zeiss dissection microscope. The dissected tetrads were grown for 2 d, after which they were replica plated to various selective media. The replica plates were scored after 1 d of incubation. Marker segregation was analyzed using the recombination analysis software RANA (Argueso et al. 2004).

Analysis of Rad51 foci
Slides were stained with rabbit anti-Rad51 antibody (1:500) (a gift from Dr. Akira Shinohara), incubated overnight at 4°, followed by 2 hr incubation with secondary antibody anti-rabbit TRITC (1:1500) (Jackson ImmunoResearch). Immunofluorescence images of Rad51 foci were captured using 100· oil immersion objective on a Leica SP5 confocal microscope. Images were captured at 0.25 mm interval Z sections. Maximum intensity images were produced by projecting the optical sections (Z stacks). For each time point 100 images were analyzed in three independent experiments. Image analysis and 3D deconvolution was done using Leica Application Suite (LAS) Advanced Fluorescence (AF) Lite 2.8.0 software.
DNA extraction and whole genome sequencing of meiotic spores Spore colonies from the four spore viable tetrads of mlh3Δ, pch2Δ, and mlh3Δ pch2Δ were grown overnight at 30°in 4 ml YPD broth. DNA was isolated from the culture using PrepEase DNA isolation kit (Affymetrix). Whole genome sequencing on Illumina platform was performed at Fasteris, Switzerland, as well as at the European Molecular Biology Laboratory (EMBL) Genomics Core Facilities (GeneCore), Heidelberg, Germany.

Annotation of recombination events
The raw reads were demultiplexed using the NGS QC Toolkit (version 2.3.3, http://www.nipgr.res.in/ngsqctoolkit.html), and processed for quality control (QC) using the trimmomatic tool (Version 0.36, http://www.usadellab.org/cms/index.php?page=trimmomatic) (Bolger et al. 2014). These QC filtered high quality reads were then mapped to the S. cerevisiae genome (version R64-1-1, 2011) using bowtie 2 (version 2.2.6) (Langmead and Salzberg 2012). Only uniquely mapped reads were considered for variant calling using Picard tools. Local realignment around indels was performed to reduce misalignment. Genotyping was done using GATK (UnifiedGenotyper, version 3.4-46) (McKenna et al. 2010;DePristo et al. 2011). From the alignment, an average of 59,215 SNPs was genotyped. Recombination events, such as crossovers, noncrossovers (type 0 gene conversions exhibiting 1:3 or 3:1 segregation of SNP markers), crossover independent gene conversions (type 0, 2, 3, and 4 gene conversions), and crossover associated gene conversions were annotated using the CrossOver program (v6.3) of the ReCombine program suite (v2.1) (Anderson et al. 2011). Parameters used for the CrossOver program were as described previously in Krishnaprasad et al. (2015). Custom R scripts were used to convert vcf files to segregation files (input file for the CrossOver program), to generate plots from the CrossOver program output and to perform various statistical tests. Detection of copy number variation was performed as described in Krishnaprasad et al. (2015).

Interference analysis
Interference analysis using the one pathway gamma model was performed as described previously (McPeek and Speed 1995;Krishnaprasad et al. 2015). For the two pathway analysis of interference, crossover distances between each crossover per chromosome was calculated for each tetrad, and converted to centimorgans. A gamma mixture model was fitted using an EM algorithm similar to that in the R package mixtools (Benaglia et al. 2009). The number of mixture components was fixed at two and the shape parameter for one of the components (Class II crossovers) was fixed at one. For the Coefficient of Coincidence (CoC) analysis, the genome was partitioned into 25 kb bins. The frequency of crossover events in each bin was calculated along with the expected and observed frequencies of double crossovers in all pairs of bins. The CoC (observed crossover frequency/expected crossover frequency) was analyzed for all bin pairs (with nonzero expected frequency) separated by a given interval (in kilobase) and averaged. Chi-square test was used to measure the statistical significance of observed and expected double crossover frequencies between wild type and the mutants.

Data availability
All strains listed in Table S1 are available upon request. Sequence data are available from the National Centre for Biotechnology Information Sequence Read Archive: Accession number SRP082254. The raw recombination data files and the custom R scripts are available online at the Dryad data repository (http:// datadryad.org; http://dx.doi.org/10.5061/dryad.5vm4g).

RESULTS
Genome-wide recombination maps for mlh3D, pch2D, and mlh3D pch2D by whole genome sequencing mlh3D, pch2D, and mlh3D pch2D mutations were introduced in the S288c and YJM789 strains. Spore viability of mlh3D (85%) was similar to the wild-type S288c/YJM789 hybrid ( Figure S1 and Table 1). Spore viability of pch2D (75%), in the S288c/YJM789 hybrid, was reduced compared to wild-type hybrid (P = 0.0001, Fischer's exact test) (Figure S1 and Table 1). The mlh3D pch2D mutant also showed significantly less viability compared to wild type (59%, P = 7.9 · 10 221 , Fischer's exact test). We performed whole genome sequencing of spores from 54 four-viable spore tetrads of the S288c · YJM789 hybrid bearing mlh3D, pch2D, and mlh3D pch2D mutations (Table S2) (sequence data available from National Centre for Biotechnology Information Sequence Read Archive under accession number: SRP082254). Highresolution genome-wide recombination data were generated in mlh3D, pch2D, and mlh3D pch2D mutants by analyzing segregation of SNPs in the 54 tetrads (File S1). These include 19 tetrads in mlh3D, 15 tetrads in pch2D and 20 tetrads in mlh3D pch2D. Genome-wide recombination data for wild type were generated from 66 tetrads by combining previously published studies (Mancera et al. 2008;Krishnaprasad et al. 2015). Crossover and noncrossover counts for each of the 120 tetrads are shown in Table S3.

Crossover defects in mlh3D are distinct from msh4D
The mlh3D mutant showed a significant genome-wide reduction in crossovers compared to wild type (64 crossovers on average in mlh3D vs. 93 in wild type, P = 1.7 · 10 214 , t-test) ( Figure 1 and Table 1). These results are consistent with crossover data obtained from analysis of specific loci in mlh3D (Nishant et al. 2008;Sonntag Brown et al. 2013). Genome-wide crossover defects are therefore stronger in msh4D (average of 49 crossovers per meiosis) compared to mlh3D (P = 2.3 · 10 23 , t-test), although the Msh4-Msh5, Mlh1-Mlh3 proteins are thought to act in the same pathway for making crossovers (Chen et al. 2008;Krishnaprasad et al. 2015). Previous work by Sonntag Brown et al.
Since the crossover defects in mlh3D were not associated with a concomitant increase in noncrossovers, perhaps in the absence of the Mlh3 protein DSBs that were not repaired as crossovers may be repaired using the sister chromatid.
The effects of chromosome size on crossover distribution were analyzed using average crossover counts per chromosome ( Figure 2A and Table S4). The mlh3D mutant showed a significant decrease in crossovers on medium and large chromosomes ( Figure 2A and Figure  S2A). Crossovers on small chromosomes also showed a decrease in mlh3D, but these were not significant except for chromosome IX. Crossover defects in mlh3D are therefore different from msh4D and msh4-R676W, which had significant crossover reduction on all (small, medium, and large) chromosomes (Krishnaprasad et al. 2015). Noncrossover counts in mlh3D did not show significant differences on any of the chromosomes compared to wild type ( Figure  2B and Figure S2D). The noncrossover data in mlh3Δ are different from msh4D, where average noncrossover counts were increased on several chromosomes (Krishnaprasad et al. 2015). When the noncrossover counts are regressed against the crossover counts, we observed no correlation in wild type and mlh3D (wild type, r = 0.23, P = 0.06; mlh3D, r = 0.01, P = 0.95; Figure 2C).
Wild-type cells show variation in crossover density (centimorgan per kilobase) with chromosome size ( Figure 2D, and see Pan et al. 2011). Previous studies have shown that high crossover density on small chromosomes is mostly a consequence of higher DSB density on small chromosomes (Pan et al. 2011). We plotted crossover density vs. chromosome length for wild type, and observed a pattern similar to that observed for DSB density ( Figure S3, and see Pan et al. 2011). First, the crossover density decreases with chromosome size, indicating that larger chromosomes have fewer crossovers than expected for their physical length (assuming crossover density is equal on all chromosomes). Second, if we take into account this inverse relationship between chromosome length and crossover density, we observed that the smaller chromosomes deviate a lot from the regression line, indicating that they have a much higher crossover density than expected ( Figure  S3). mlh3D showed a significant negative correlation coefficient (r = 20.76, P = 6.3 · 10 24 ), implying an inverse relation between crossover density and chromosome size ( Figure 2D). The correlation coefficient for mlh3D was comparable to wild type (r = 20.84, P = 5.7 · 10 25 ). Crossover density was higher on smaller chromosomes in wild type and mlh3D, even when the analysis excluded the three smallest chromosomes (I, III, and VI), which have the highest DSB densities ( Figure S4A, and see Sun et al. 2015). Noncrossover density, as well as crossover plus noncrossover density, also showed a significant negative correlation with chromosome size in wild type and mlh3D ( Figure S4, B-D). The relationship between crossover or noncrossover density and chromosome size was therefore similar between wild type and mlh3D. These results suggest the regulation of DSB distribution based on chromosome size is intact in mlh3D like in wild type. Further, since most crossovers in wild type and mlh3D are Class I and Class II, respectively, these results suggest the chromosome size effect seen for crossover density variation is dependent on DSB density, and not on the recombination pathway as shown previously (Pan et al. 2011). It is important to note that using crossover and noncrossover density as a proxy for DSBs does not consider the effect of any changes in homolog bias in these mutants. Crossover and noncrossover distributions at centromere and telomere regions were comparable to wild type, but noncrossovers were elevated within 10 kb of centromere region in mlh3D (File S2). Chromosome-wide crossover distribution for mlh3D is shown in Figure S5.

Genome-wide increase in crossovers and noncrossovers in pch2D
Average crossovers in pch2D (137) were significantly more than wild type (P = 1.15 · 10 25 , t-test) (Figure 1). The increase in crossovers was statistically significant on all the medium and large chromosomes, n Table 1 Crossover (CO), noncrossover (NCO) counts and spore viability of mlh3D, pch2D, mlh3D pch2D mutants in the S288c/YJM789 hybrid Spore viability (S.V) data for wild type is from Krishnaprasad et al. (2015). N, number of tetrads analyzed for spore viability. a Merged data set from Krishnaprasad et al. (2015) and Mancera et al. (2008).
and on two of the smaller chromosomes (III and VI) (Figure 2A and Figure S2B). This result is consistent with increased crossovers observed at specific loci on medium and large chromosomes in SK1 background (Zanders and Alani 2009), but different from Joshi et al. (2009) who observed no increase in crossovers across nine intervals on three chromosomes. The increase in crossovers on chromosome III is different from the results observed by Zanders and Alani (2009) and San-Segundo and Roeder (1999). Such differences may be because of the limited number of chromosomal loci analyzed in the previous studies (San-Segundo and Roeder 1999;Joshi et al. 2009;Zanders and Alani 2009). Noncrossovers in pch2D (average of 86 per meiosis) were also significantly higher than wild type (46, P = 2.9 · 10 25 , t-test) ( Figure  1 and Table 1). Similar to the trend seen for crossovers, increased noncrossovers in pch2Δ were significant for all medium and large chromosomes ( Figure 2B and Figure S2E). These results suggest that specific regulation of DSB formation on medium and large chromosomes is affected in pch2Δ. Among the small chromosomes, Chromosome III was exceptional in showing an increase in both crossovers and noncrossovers. This might be due to an enhanced distribution of DSBs on chromosome III in pch2D mutants. An increase in DSB formation at the HIS4::LEU2 locus has been observed previously in pch2D (Farmer et al. 2012). Interestingly Borner et al. (2008) reported increased noncrossovers and decreased crossovers for the HIS4::LEU2 locus on chromosome III for pch2D. When the noncrossover counts are regressed against the crossover counts, we observed a well correlated linear relationship ( Figure 2C). pch2D cells with more crossovers also had more noncrossovers (r = 0.82, P = 1.9 · 10 24 ). Although pch2D showed a negative correlation coefficient (r = 20.30) between crossover density and chromosome size, it was not significant (P = 0.26), consistent with the enhanced crossovers on large and medium chromosomes ( Figure 2D). Unlike wild type, pch2D did not show a significant negative correlation between chromosome size and crossover density, noncrossover density, as well as crossover plus noncrossover density ( Figure S4). Crossover and noncrossover distributions within 10 kb of the centromere were comparable between wild type and pch2D (File S2). But crossover and noncrossover distributions in pch2D were suppressed for an extended distance from the telomere (up to 80 kb) compared to the wild type (File S2). These differences may reflect changes in DSB distribution near telomeres. Chromosome-wide analysis of crossover distribution showed distinct crossover peaks compared to wild type, including elevated crossovers around the rDNA locus ( Figure S6). This is consistent with the observation of increased DSBs and recombination at the outermost rDNA repeats in pch2D and the role of Pch2 in maintaining the integrity of the rDNA cluster (Vader et al. 2011).
Genome-wide recombination analysis showed a correlated increase in both crossovers and noncrossovers in pch2D (Figure 1 and Figure  2C). The simplest explanation is that pch2D makes more DSBs. Rad51 focus analysis can provide information on whether pch2D mutants show increased DSBs. We measured Rad51 focus counts in wild type and pch2D mutants in three independent meiotic time courses to determine changes in cellular DSB frequency. pch2D mutants showed a 2 hr delay in meiotic divisions, as observed previously (Wu and Burgess 2006;Zanders and Alani 2009) (Figure 3A). We analyzed Rad51 foci in 1 hr increments from 2 to 7 hr time points in wild type, and from 2 to 8 hr time points in pch2D. For wild type and pch2D, maximum Rad51 foci were detected at 3 hr, and representative images are shown in Figure 3B. The maximum (average) Rad51 focus counts for pch2D (37) were reduced compared to wild type (49). However, unlike wild type, where the Rad51 foci peaked at 3 hr and could not be detected after 7 hr, pch2D showed a gradual decline of Rad51 foci over an extended time from 3 hr until 8 hr ( Figure 3C). In wild type, the percentage of cells that show Rad51 foci was negligible (3.7%) at 7 hr, while, in pch2D, almost 50% of the cells showed Rad51 foci ( Figure 3D). The persistent presence of DSBs may be due to ongoing formation and repair of new DSBs (turnover), which may explain the increased crossovers and noncrossovers observed in pch2D. In addition, such a pattern may be caused by delayed repair of DSBs, which may cause more DSBs, and, in turn, result in more crossovers and noncrossovers (Hochwagen et al. 2005;Borner et al. 2008). The cytological observations are consistent with a prophase delay in pch2D for a variable amount of time, during which additional DSBs are made asynchronously, so that there is a much greater range in the total number of crossover and noncrossover events (Figure 1, Figure 2C, and Table 1). Persistent DSBs in the pch2Δ mutant have been observed previously at the HIS4::LEU2 locus by Southern blot analysis, and also from analysis of Rad51 foci in pch2D ndt80D mutants (Hochwagen et al. 2005;Subramanian et al. 2016).
The mlh3D pch2D mutant has wild-type crossover frequency and uniform crossover density on all chromosomes Since pch2D shows increased crossovers in wild-type background as well as in crossover mutants like msh5D and mms4D (Zanders and Figure 1 Crossover, noncrossover and total events per meiosis for wild type, mlh3D, pch2D, and mlh3D pch2D. The box plots show minimum, first quantile, median, third quantile, and maximum count. Alani 2009), we were curious to see if a pch2D mutation in the mlh3D background would restore crossovers to wild-type frequencies. mlh3D pch2D made, on average, 100 crossovers per meiosis, comparable to the wild-type S288c · YJM789 hybrid ( Figure 1 and Table 1) (P = 0.22, t-test). None of the chromosomes (except chromosomes I and XV) in mlh3D pch2D showed significant differences in crossovers compared to wild type (Figure 2A and Figure S2C). Noncrossovers in mlh3D pch2D (average of 94 per meiosis) were significantly more than wild type (P = 1.84 · 10 27 , t-test) and comparable to pch2D (P = 0.40, t-test). These results suggest most of the increase in noncrossovers in pch2D mutants comes from the activity of the structure-specific endonucleases, which are less biased toward resolution of the dHJs into crossovers. The increase in noncrossovers was observed across small (VI, III, and IX), and all medium and large chromosomes (except V) ( Figure 2B and Figure S2F). Similar to the pattern observed in pch2D, crossover, and noncrossover counts in mlh3D pch2D were positively correlated (r = 0.83, P = 5 · 10 26 ) ( Figure 2C).
The crossover density in mlh3D pch2D was uniform across all chromosome sizes and the correlation coefficient (r = 0.04, P = 0.88) was close to zero ( Figure 2D). A similar lack of correlation was seen for crossover, noncrossover, and crossover plus noncrossover density with chromosome size (including/excluding the smallest chromosomes I, III, and VI) ( Figure S4). Like pch2D, crossover and noncrossover distributions were suppressed for an extended distance from the telomere (up to 80 kb) in mlh3D pch2D (File S2). Chromosome-wide distribution showed distinct crossover peaks in mlh3D pch2D compared to wild type, especially around the rDNA locus ( Figure S7).

Enhanced gene conversion frequencies and long gene conversion tracts in pch2D mutants
Most markers (.97.5%) showed 2:2 segregation in wild type and mlh3D mutant (Table S5). pch2D mutants showed higher gene conversion frequencies than wild type or mlh3D mutant. The percentage of SNP markers segregating 2:2 was 94.7% in pch2Δ, compared to .97.5% in wild type and mlh3D. Like the pch2D single mutant, the mlh3D pch2D mutant also showed higher gene conversion frequencies than wild type (94% of markers segregating 2:2). Increases in gene conversion frequencies in pch2D at specific loci have been previously observed by Zanders and Alani (2009) and Joshi et al. (2009). The median gene conversion tract lengths associated with crossovers (2.4, 2.7, and 3.9 kb) were significantly longer than the noncrossover gene conversion tract lengths (1.7, 1.8, and 2.2 kb) for the mlh3D, pch2D, and mlh3D pch2D mutants ( Figure S8, A-C and Table S5). These results are similar to observations in wild type and other crossover mutants (Terasawa et al. 2007;Chen et al. 2008;Mancera et al. 2008;Oke et al. 2014;Krishnaprasad et al. 2015). Both crossover-and noncrossoverassociated gene conversion tract lengths were significantly longer in mlh3D, pch2D, and mlh3D pch2D compared to wild type ( Figure S8, A-C and Table S5). In addition, long gene conversion tracts associated Figure 2 Crossover and noncrossover distribution on chromosomes for wild type, mlh3D, pch2D, and mlh3D pch2D. (A, B) Bar plot showing average crossover and noncrossover counts per chromosome for wild type, mlh3D, pch2D, and mlh3D pch2D. The asterisk symbol ( Ã ) shows chromosomes with significant difference (P , 0.05, t-test) in crossover or noncrossover counts compared to wild type. Chromosomes are arranged according to size from left to right. Error bars are "mean 6 SE." (C) Crossover vs. noncrossover scatter plot with correlation coefficient (r) and P values for wild type, mlh3D, pch2D, and mlh3D pch2D. (D) Crossover density (centimorgans per kilobase) plotted as a function of chromosome length (megabase) for wild type, mlh3D, pch2D, and mlh3D pch2D along with the correlation coefficient (r) and P values.
with crossovers (.4 kb) and noncrossovers (.2 kb) were overrepresented in pch2D and mlh3D pch2D compared to wild type and mlh3D ( Figure S8, B and C, see Discussion).
Most crossovers in mlh3D pch2D are made by the Mus81-Mms4 pathway Although mlh3D has $30% reduction in crossovers, mlh3D pch2D has wild-type crossover frequency. In S. cerevisiae, the major pathway for resolving joint molecules into crossovers involves Mlh1-Mlh3/Exo1 proteins (De Muyt et al. 2012;Zakharyevich et al. 2012). Joint molecules are also resolved into crossovers by minor pathways involving the structure selective nucleases Mus81-Mms4, Yen1, and Slx1-Slx4 (De Muyt et al. 2012;Zakharyevich et al. 2012). Yen1 is thought to process joint molecules that escape Mus81-Mms4 (Matos et al. 2011). We were curious to know how wild-type frequency of crossovers is possible in mlh3D pch2D in the absence of the major resolvase (Mlh3). We tested the role of the two joint molecule resolvases, Mus81-Mms4 and Slx1-Slx4, in making crossovers in the mlh3D pch2D background. For testing the role of Mus81-Mms4, a meiotic depleted allele of MMS4 (mms4-md) was used (De Muyt et al. 2012). Spore viability and genetic map distances of mlh3D pch2D mms4-md, and mlh3D pch2D slx4D, were compared with mlh3D pch2D in the EAY1108/EAY1112 background (Argueso et al. 2004). mlh3D pch2D has 71% spore viability in the EAY1108/EAY1112 background and has a spore viability pattern (4, 2, and 0 viable spore tetrad class .3 and 1 viable spore tetrad class) suggesting Meiosis I nondisjunction (Figure 4). Introduction of mms4-md and slx4D mutations reduced the spore viability to 34% and 41%, respectively (Figure 4). Genetic map distances in four intervals in mlh3D pch2D (113.6 cM), based on four-viable spore tetrads was similar to wild type (105.4 cM), in agreement with the whole genome sequencing data from the S288c/YJM789 hybrid (Figure 1 and Figure 5A). However, map distances when all viable spores were considered showed a reduction in mlh3D pch2D (79.9 cM) relative to wild type (96.6 cM) ( Figure 5B). These results suggest restoration of crossovers in mlh3D pch2D to wild-type frequency occurs through an increase in both single crossovers measured as tetratypes (TT), as well as double crossovers measured as nonparental ditypes (NPDs). The increase in double crossovers (NPDs) contributes to map distances from tetrad data but not from spore data (Table S6 and Table S7). More NPD tetrads are also observed in pch2D mutants relative to wild type (Joshi et al. 2009;Zanders and Alani 2009). mlh3D pch2D slx4D (91.2 cM) showed reduced genetic map distances compared to mlh3D pch2D (113.6 cM) in measures based on complete tetrads, but the genetic map distances from spore data were similar: 77.8 cM in mlh3D pch2D slx4D compared to 79.9 cM in mlh3D pch2D ( Figure 5, A and B and Table S6, and Table S7). These results suggest Slx1-Slx4 does not significantly contribute to increased crossovers in mlh3D pch2D except for contributing to the NPD class. This is consistent with the meiotic role of the Slx1-Slx4 complex in the non-ZMM pathway characterized by multi-chromatid joint molecules (Zakharyevich et al. 2012;Kaur et al. 2015). mlh3D pch2D mms4-md mutants showed strong reduction in genetic map distances (23.7 cM) compared to mlh3D pch2D (79.9 cM) ( Figure 5B and Table S7). Map distances from tetrad data could not be accurately estimated in mlh3D pch2D mms4-md due to the low frequency of four-spore viable tetrads and the strong reduction in the map distances. These results suggest that the majority of the crossovers in mlh3D pch2D are made through the Mus81-Mms4 pathway. Genetic interference is reduced across a range of crossover frequencies in the mlh3D, pch2D, and mlh3D pch2D mutants Interference limits crossover number and ensures that multiple crossovers along the chromosome are widely spaced (Muller 1916;Hillers 2004;Kleckner et al. 2004;Stahl et al. 2004). Intercrossover distances modeled using a gamma distribution can be used to determine the strength of genetic interference: g = 1 corresponds to no interference, while g . 1 indicates positive interference (Anderson et al. 2011). Intercrossover distances in physical units were converted into genetic distances (centimorgans) in wild type, pch2D, mlh3D, mlh3D pch2D, to account for differences in crossover frequencies (Materials and Methods) ( Figure 6A). To account for differences in the number of tetrads analyzed, we also converted the counts for intercrossover distances as a fraction of the total for wild type and each mutant ( Figure 6B). For the wild-type strain, the g value was 1.83. Interference was reduced in pch2D (g = 1.33), mlh3D (g = 1.29) and mlh3D pch2D (g = 1.13) compared to wild type. Interference analysis using the two pathway model that incorporates contribution from both interfering and noninterfering pathways also showed reduced interference in mlh3D, pch2D, and mlh3D pch2D (File S3, and see Copenhaver et al. 2002;Housworth and Stahl 2003). We also analyzed interference from the genome wide crossover data using the CoC method (Materials and Methods, and see Anderson et al. 2015). Statistical significance of the difference between observed and expected frequency of double crossovers was estimated using the chi-square test. Interference (1 -CoC) was significantly reduced in mlh3D (P = 0.00033), pch2D (P = 4.36 · 10 26 ), and mlh3D pch2D (P = 1.85 · 10 29 ) relative to the wild type ( Figure 6C).
The reduced interference in mlh3D is consistent with the two pathway model for crossover formation (Copenhaver et al. 2002;Stahl et al. 2004;Getz et al. 2008). pch2D has been shown previously to lack genetic interference (Joshi et al. 2009;Zanders and Alani 2009). However, analysis of Zip3 foci that mark DSB sites that will be repaired as crossovers, suggests that interference is observed in pch2D at the crossover designation stage (Zhang et al. 2014). The loss of genetic interference in pch2D was thought to be due to the misregulation of the crossover/ noncrossover decision step, and not because of the excess crossovers (Zanders and Alani 2009). We observe an increase in both crossovers and noncrossovers in pch2D mutants and Zip3 localization is known to be maintained in pch2D (Table 1, Zhang et al. 2014). Therefore, the reduced interference in pch2D is most likely due to the excess crossovers made by the MutLg-dependent interfering, and the Mus81-Mms4dependent noninterfering crossover pathways.
Since mlh3D pch2D also makes more noncrossovers, it is unlikely that the loss of interference is due to impairment of the crossover/ noncrossover decision. The loss of interference is most likely because nearly all crossovers in mlh3D pch2D are made through the Mus81-Mms4 pathway ( Figure 5B). Loss of interference in the mlh3D pch2D mutant is also supported from the uniform crossover density observed across all chromosome sizes ( Figure 2D). The loss of genetic interference in mlh3D pch2D is particularly interesting as it makes as many crossovers on average as wild type. In summary, genetic Figure 4 Spore viability analysis of wild type, mlh3D pch2D, mlh3D pch2D slx4D, and mlh3D pch2D mms4-md in the EAY1108/EAY1112 genetic background. The viable spores per tetrad (x axis) and the percentage of each tetrad class (y axis) are shown. N, number of tetrads dissected; S.V, percentage spore viability.
interference is reduced across all three categories of crossover frequencies (reduced, equivalent, and greater than wild-type crossovers for mlh3D, mlh3D pch2D, and pch2D, respectively). No chromatid interference was observed among wild type, mlh3D, and pch2D mutants (P . 0.05, chi-square test), but negative chromatid interference characterized by a slight excess of two strand crossovers may be present in mlh3D pch2D mutants (0.01 , P , 0.05, chi-square test) (Table S8).
Noninterfering crossovers are less efficient in promoting crossover assurance We tested the effect of a wide range of crossover frequencies on obligate crossovers using data from genome-wide analysis of meiotic recombination in the mlh3D, pch2D, and mlh3D pch2D mutants. We determined the frequency of meiosis with nonexchange events in mlh3D, pch2D, and mlh3D pch2D mutants. The percentage of meiosis with 1 or .1 nonexchange chromosome was 3% for wild type, 7% for pch2D, 47% for mlh3D, and 20% for mlh3D pch2D (Table S3). mlh3D, which showed a decrease in both genetic interference and crossover frequencies, had the highest number of meioses with nonexchange events. In 5% of the meioses, the mlh3D mutant also had .1 nonexchange chromosome. However, mlh3D had an overall lower amount of nonexchange events among four-spore viable tetrads (47%) compared to msh4D (72%) but similar to msh4-R676W (42%, Krishnaprasad et al. 2015). These results suggest that, even though mlh3D makes 64 crossovers, the obligate crossover is not maintained. These findings reinforce our earlier observations that simultaneous reductions in crossover frequencies and genetic interference compromise the obligate crossover (Krishnaprasad et al. 2015). In pch2D, the number of meioses with nonexchange events (7%) was comparable to wild type (3%) (P = 0.37, Binomial test). This is likely due to the excess crossovers made in pch2D that compensate for the loss of genetic interference. Previously, we had estimated that, if the crossovers are distributed randomly, a wild-type yeast cell would require up to $200 crossovers to ensure (with probability .0.98) the absence of nonexchange chromosomes (Krishnaprasad et al. 2015). The observations with the pch2D mutant support the theoretical predictions that genetic interference reduces the number of crossovers required for crossover assurance. The results also suggest that pch2D does not significantly increase nonexchange chromosome frequency through other mechanisms. The mlh3D pch2D mutant was most interesting, since, although it made as many crossovers as wild type, the percentage of meiosis with nonexchange events (20%) was significantly more than wild type (3%) (P = 2.7 · 10 23 , Binomial test). These data experimentally demonstrate that if the wild-type frequency of crossovers were randomly distributed in S. cerevisiae, there would be more nonexchange chromosomes.
To further test how crossover frequency affects obligate crossovers, we estimated the percentage of meiosis with no nonexchange chromosomes expected for mlh3D, pch2D, and mlh3D pch2D by modeling the crossovers as a Poisson distribution (the Poisson distribution assumes Figure 5 Crossovers in mlh3D pch2D are made predominantly by the Mus81-Mms4 pathway. Genetic map distances for complete tetrads (A) and total spores (B) are shown for a set of four intervals on chromosome XV in the EAY1108/EAY1112 genetic background. Raw data are shown in Table S6 and Table S7 for complete tetrads and total spores, respectively. the crossover events are independent) (Figure 7). The expected percentage of meiosis with no nonexchange chromosomes, 46% (mlh3D), 80% (mlh3D pch2D), 93% (pch2D) matched well with the experimental observations: 53% (mlh3D), 80% (mlh3D pch2D) and 93% (pch2D). Crossover distributions in mlh3D, pch2D, and mlh3D pch2D, therefore, approximate a Poisson process. For wild type, the percentage of meiosis with nonexchange chromosomes (3%) is significantly lower than expected (24%) due to the presence of interference. These observations are consistent with the requirement for higher crossover frequencies in the absence of genetic interference to ensure obligate crossovers (Krishnaprasad et al. 2015;Berchowitz and Copenhaver 2010;Kaback et al. 1999).
In mutants with reduced genetic interference, adjacent crossovers may be closely spaced. As a result, they could be annotated as double noncrossovers inflating the number of nonexchange chromosomes. We inspected each nonexchange chromosome in the wild type, mlh3D, pch2D, and mlh3D pch2D mutants for ambiguity in the annotation for double crossovers and double noncrossovers, and did not find any significant difference in the estimate of nonexchange chromosomes (Table S9). All nonexchange chromosomes, except one, had gene conversion events (Table S9). This observation suggests that lack of an obligate crossover was not a consequence of the absence of recombination interactions between the homologs, but rather a failure to convert even one of them into a crossover.
Small chromosomes are most sensitive to loss of the obligate crossover We analyzed the influence of chromosome size on the occurrence of nonexchange chromosomes in the wild type, mlh3D, pch2D, and mlh3D pch2D mutants (Figure 8). For mlh3D, nonexchange chromosomes included small (I, VI, and IX), medium (XI), and large chromosomes (XVI). This observation is similar to the distribution of nonexchange chromosomes in msh4D observed previously, except that the number of nonexchange chromosomes is much less in mlh3D (Krishnaprasad et al. 2015). For pch2D, the only nonexchange chromosome was a small chromosome (IX). For mlh3D pch2D, only small chromosomes (I and VI) were nonexchange. These observations suggest that small chromosomes are particularly susceptible to the loss of the obligate crossover when there are crossover and/or interference defects. A stronger reduction in crossover frequencies, as observed in mlh3D mutants, is required for the loss of obligate crossovers on medium and large chromosomes. These observations further consolidate our previous results showing that small chromosomes are particularly sensitive to variations in crossover frequency (Krishnaprasad et al. 2015). A high frequency of nonexchange has been observed for smaller chromosomes in other crossover defective mutants, and also in human meiosis (Chen et al. 2008;Fledel-Alon et al. 2009). Among the small chromosomes, we observed a lack of E0s for the chromosome III. A similar phenomenon was seen in Krishnaprasad et al. (2015), where chromosome III had the fewest E0s among the small chromosomes. Analysis of copy number variation using read depth information did not detect aneuploidy in any of the mlh3D, pch2D, and mlh3D pch2D sequenced tetrads ( Figure S9).

DISCUSSION
We previously analyzed genome-wide crossovers in a msh4 hypomorph to demonstrate that a random distribution of reduced number of crossover events can increase nonexchange chromosome frequencies (Krishnaprasad et al. 2015). Our current work generalizes this observation to a larger context by analyzing nonexchange events when there is a random distribution of reduced, wild-type, and greater than wild-type frequency of crossovers using the mlh3D, pch2D, and mlh3D pch2D mutants.
Obligate crossover is sensitive to crossover frequencies and genetic interference Genetic interference is affected in mlh3D, pch2D, and mlh3D pch2D due to increased contributions from the noninterfering pathway. Interference is also compromised in mlh3D and mlh3D pch2D because of defects in converting crossover designated sites into actual crossovers. The pch2D results suggest that mutants with reduced genetic interference can maintain an obligate crossover if crossover frequencies are significantly higher than in wild type (Figure 7). If the crossover frequency is reduced compared to wild type, there is a loss of the obligate crossover, as in the case of mlh3D. In mlh3D pch2D, we observed crossover frequencies equivalent to wild type (100 crossovers per meiosis), but an increased proportion of nonexchange chromosomes. Three lines of evidence support enhanced nonexchange chromosome frequency in mlh3D pch2D. First, we observe nonexchange chromosomes in 20% of meiosis in mlh3D pch2D in the S288c/YJM789 hybrid ( Figure 8 and Table S3). Second, theoretical predictions by modeling the mlh3D pch2D crossover distribution as a Poisson process also support higher nonexchange chromosome frequencies consistent with the experimental results (Figure 7). Third, mlh3D pch2D showed spore viability pattern typical of Meiosis I nondisjunction in the SK1 EAY1108/1112 background (Figure 4). Since most crossovers in mlh3D pch2D are made by the Mus81-Mms4 pathway ( Figure 5B), these observations are consistent with noninterfering crossovers being less efficient in supporting an obligate crossover. The higher E0 frequency in mlh3Δ pch2Δ also supports the prediction that S. cerevisiae will require up to 200 crossovers in the absence of genetic interference to Figure 7 Probability of observing no E0 (chromosomes with zero crossovers per meiosis) for wild type, mlh3D, pch2D, and mlh3D pch2D. The probability of observing no E0 events is plotted against the crossover frequency modeled as a Poisson distribution. The dotted lines indicate the probabilities for finding no E0s in the absence of genetic interference for the experimentally observed average crossover counts per cell (mlh3D: 64; wild type: 93; mlh3D pch2D: 100; pch2D: 137).
Triple mutant analysis with another resolvase (Slx4) showed that genetic map distances measured from spore data were not significantly different between mlh3D pch2D (79.9 cM) and mlh3D pch2D slx4D (77.8 cM). However, map distances from tetrad data showed significant differences between mlh3D pch2D (113.6 cM) and mlh3D pch2D slx4D (91.2 cM). These results suggest Slx4 only makes a minor contribution to crossovers in the mlh3D pch2D mutant. Slx4 may be involved in resolving a fraction of closely spaced double crossovers that contribute to the NPD class of tetrads.

Segregation of nonexchange chromosomes in mlh3D
Since mlh3D and wild type have identical spore viability in the S288c/ YJM789 hybrid and similar proportion of the four-viable spore tetrad class, we tested the association of spore viability with the nonexchange chromosome frequency. Mlh3 acts downstream of Msh4/5 at the final steps of Holliday Junction resolution (Baker et al. 1996;Lipkin et al. 2002;Snowden et al. 2004;Kolas et al. 2005). mlh3D mutants, therefore, provide an advantage in relating variations in crossover frequency with the loss of obligate crossovers without the confounding effects that may arise in other mutants that have an early role in the crossover/ noncrossover decision step or that affect DSB formation. It is also important to recognize that the data for the nonexchange chromosome frequency comes from the analysis of the four viable spore tetrads only. mlh3D has high spore viability (85%), strong crossover defects (64 crossovers per meiosis), and abundant single nonexchange chromosomes ( Figure 8 and Table 1). These data are similar to the pattern seen with msh4-R676W earlier (Krishnaprasad et al. 2015). The mlh3D mutant reinforces the idea that a reduction in crossover frequency results in loss of the obligate crossover, even though the average crossover number is still four times the number of homologs. The high spore viability of mlh3D, suggests these single nonexchange chromosomes are efficiently segregated as observed with msh4-R676W (Krishnaprasad et al. 2015), supporting the hypothesis that crossovers facilitate but are not essential for chromosome segregation. Other mechanisms, such as distributive segregation, spindle checkpoint, and centromere pairing may also contribute to the segregation of achiasmate chromosomes in S. cerevisiae (Guacci and Kaback 1991;Shonn et al. 2000;Kemp et al. 2004). These observations also suggest spore viability is a poor measure of the status of obligate crossovers. The mlh3D mutant showed 64 crossovers genome-wide compared to 49 reported in msh4D (Krishnaprasad et al. 2015). These results provide support to previous observation on Msh4/5 dependent but Mlh1/3 independent crossover pathways (Argueso et al. 2004). It is also expected if, in mlh3D, some of the crossover precursor joint molecules are resolved by structure selective nucleases as both crossovers and noncrossovers.

Recombination maps in pch2D capture DSB variation
We observed a simultaneous increase in crossovers and noncrossovers in pch2D, which suggested that DSBs are increased in pch2D. Previous studies have shown a complex role for Pch2 in DSB formation, with increased DSB formation at certain loci, such as the rDNA locus (Vader et al. 2011), and a general reduction in DSBs at other loci (Farmer et al. 2012). Pch2 also has a role in the processing of early DSBs (Joshi et al. 2015). These studies suggest overall DSB levels may remain constant in pch2D, and the effects need to be examined on a per locus/chromosome basis (Farmer et al. 2012). High-resolution crossover and noncrossover data in pch2D provide an indirect readout of variation in DSB formation. For example, pch2D mutants do not show negative correlation of chromosome size with crossover plus noncrossover density. We observe more crossovers around the rDNA locus in pch2D mutants. pch2D, as well as mlh3D pch2D, also show suppression of both crossovers and noncrossovers near telomeres, which may suggest an altered Figure 8 The percentage of meiosis that are nonexchange for each chromosome for wild type, mlh3D, pch2D, and mlh3D pch2D. Chromosomes are shown in increasing order of size.
DSB distribution near telomeric regions. Also, we observed increased crossovers as well as noncrossovers on Chr III, consistent with increased DSB formation on chr III (Farmer et al. 2012). Such differences in DSB distribution, possibly by regulating Hop1 function (Borner et al. 2008;Wojtasz et al. 2009), and the use of the Mus81-Mms4 pathway, may be responsible for the differences in crossover and noncrossover patterns in pch2D and mlh3D pch2D compared to wild type ( Figure S4, Figure S6, and Figure S7).
Although Rad51 foci analyses do not give information on regional DSB variation, it can provide information on total cellular DSB levels and its turnover. We did not observe peak Rad51 focus counts in pch2D to be greater than wild type. This is consistent with the physical analysis of DSBs, which suggests that, at least at specific loci, there is no increase in DSB formation in pch2D mutants (Zanders et al. 2011;Farmer et al. 2012;Joshi et al. 2015). Instead, pch2D showed the persistence of peak DSB foci over an extended period of the meiotic time course from 3 to 8 hr. It is possible there is DSB turnover in pch2D, so that DSBs are made and repaired and the process is repeated, leading to an overall increase in crossover and noncrossovers. Such a possibility is supported by previous observations of the accumulation of Rad51 foci in pch2D mutants (Subramanian et al. 2016). The only other alternative is that there is more repair of DSBs by the interhomolog pathway in pch2D mutants, which may account for increased crossovers and noncrossovers. But all available evidence suggests that in pch2D there is more intersister recombination than in wild type (Zanders et al. 2011;Joshi et al. 2015). Defects in DSB processing (e.g., longer resection) may also result in longer ssDNA filaments stabilized by Rad51 that may account for the long gene conversion tracts observed in pch2D mutants ( Figure  S8, B and C). The role of Pch2 in DSB regulation requires further investigation.
In conclusion, the mlh3D pch2D data provides experimental support from genome-wide analysis that wild-type crossover frequencies distributed randomly cannot maintain an obligate crossover on all homolog pairs (Kaback et al. 1999;Berchowitz and Copenhaver 2010;Krishnaprasad et al. 2015). The distribution of crossovers and noncrossovers suggest that chromosome-size dependent DSB formation is affected in pch2Δ. pch2D mutants also show that obligate crossovers can be ensured through a random distribution of excess crossovers. These results are consistent with MutL gamma dependent interfering crossovers being more efficient in promoting homolog disjunction compared to the Mus81-Mms4 dependent noninterfering crossovers.