Crossing-over during meiosis helps to establish physical connections (chiasmata) between homologs that promote accurate segregation at the first meiotic division (Page and Hawley, 2003). Chromosomes that fail to cross over also frequently fail to disjoin properly, yielding aneuploid gametes. Not surprisingly then, crossover formation is tightly controlled to prevent the occurrence of non-exchange chromosomes (Bishop and Zickler, 2004; Hillers, 2004; Kleckner et al., 2004).

Crossover control has several manifestations in most organisms. First, the distribution of crossovers among chromosomes is not random. Rather, the average number of crossovers per chromosome pair is extremely low (often as low as 1–2), yet non-exchange chromosomes are rare. The tendency toward guaranteed crossover formation is often referred to as the obligate crossover or chiasma (Jones, 1984). A second manifestation of crossover control is that crossovers are distributed nonrandomly along chromosomes when two or more occur on the same chromosome pair: a crossover in one region makes it less likely that another will be found nearby. This phenomenon, first described nearly a century ago (Muller, 1916; Sturtevant, 1915), is called crossover interference (reviewed in Hillers, 2004; Kleckner et al., 2004). The strength of interference diminishes as a function of distance along the chromosome, but the distances involved vary substantially from organism to organism, from tens of kb in S. cerevisiae (Malkova et al., 2004) to tens of Mb or greater in mammals (e.g., Broman and Weber, 2000).

The net result of crossover control is that each chromosome gets at least one crossover despite a low average number of crossovers per chromosome, and multiple crossovers on the same chromosome tend to be evenly and widely spaced. It is generally thought that these aspects of crossover control reflect a single underlying mechanism, although this remains to be formally proven (Hillers, 2004; Kleckner et al., 2004).

Crossovers are generated by homologous recombination initiated by DNA double-strand breaks (DSBs) formed by the topoisomerase-like Spo11 protein (Keeney, 2001). There are more DSBs than crossovers, in some cases substantially more (≥10-fold) (e.g., Moens et al., 2002). DSBs that do not become crossovers are repaired to give noncrossovers instead. DSBs interfere with formation of adjacent DSBs much less (if at all) than crossovers interfere with one another (e.g., Malkova et al., 2004). Thus, integral to crossover interference is a “decision” process by which a subset of randomly distributed recombination precursors (DSBs or later stage intermediates) enters a pathway that culminates in crossover formation, while all other precursors follow a pathway(s) that generates primarily noncrossover products (most likely with a few noninterfering crossovers) (Allers and Lichten, 2001; Borner et al., 2004; Copenhaver et al., 2002; Stahl et al., 2004). This decision occurs early, at or prior to the appearance of the first stable strand exchange intermediates (reviewed in Bishop and Zickler, 2004).

How one precursor over another is chosen for a crossover fate is not well understood. One possibility is that a subset of precursors is selected from the available pool and directed toward a crossover fate, with excess precursors—no matter how many or how few—resolved by a default, predominantly noncrossover pathway. This model would fit well with the obligate crossover as a programmed event that is mechanistically linked to interference. This scenario is also consistent with models in which crossover designation at a given site results in propagation of a physical signal that inhibits crossover formation nearby (see Discussion).

This model makes a clear prediction about what would happen if fewer DSBs were made, namely, that crossover numbers should tend to be maintained at the expense of noncrossovers. We tested this prediction in S. cerevisiae using a spo11 allelic series to vary Spo11 activity in vivo (Henderson and Keeney, 2004). We show here that crossovers indeed tend to be maintained at the expense of noncrossovers, such that the crossover/noncrossover ratio changes. These findings give insight into the fundamental logic of the interference decision and distinguish between existing mechanistic models of crossover control.

Figure 1 Reduction of DSBs does not decrease the number of crossovers in parallel.

Table 1 Reduced DSB formation in a series of spo11 hypomorphic mutants.

Chromosome segregation defects were seen only in the more defective spo11 mutants, as revealed by spore viability patterns (Supplemental Table 3). Wild type yielded 95.2% viable spores, with 917 four-spore-viable tetrads out of 1049 dissected (87%). The spo11-HA strain yielded similar numbers (94.0% viable spores, 87% four-spore-viable tetrads), indicating that the ~20% reduction in DSBs in this strain had little or no effect on the efficiency of meiotic chromosome segregation. In contrast, spore viabilities were reduced in spo11yf-HA/spo11-HA (75.9% viable spores, 62% four-spore-viable tetrads) and spo11da-HA strains (69.7% viable spores, 56% four-spore-viable tetrads). Both strains had increased frequencies of two-spore-and zero-spore-viable tetrads, a hallmark of homolog nondisjunction at the first division (Supplemental Table 3). Thus, there appears to be a threshold between ~80% and ~30% of normal DSBs below which there is insufficient recombination to support the normal efficiency of chromosome segregation.

Our analysis reveals a nonlinear quantitative relationship between DSBs and crossovers (Figure 1D), from which we infer that crossover numbers tend to be maintained despite reduction in the number of initiation events. We refer to this phenomenon as crossover homeostasis. Importantly, this relationship was observed even in the spo11-HA strain, which had normal spore viability. Thus, quantitative differences between crossovers and DSBs cannot be ascribed solely to selection bias imposed by analysis of four-spore-viable tetrads (see Discussion).

Figure 2 Crossover homeostasis occurs at the expense of noncrossovers.

The effects of the spo11 mutations on conversion frequencies at ARG4 were first determined. As expected, the spo11 mutants yielded fewer Arg+ recombinants than wild type (Table 1). The results were similar to the effect of these mutations elsewhere in the genome, except for spo11da-HA, which had a more severe effect on frequencies of conversions and DSBs at ARG4 than at most other genomic regions (Table 1 and data not shown).

To measure what fraction of Arg+ recombinants had exchanged the flanking markers, random spores were plated on medium lacking arginine, then Arg+ spore clones were scored for the configuration of flanking markers by replica-plating on medium lacking uracil or threonine (Figure 2C). In the SPO11+ strain, 54.8% of Arg+ recombinants had a nonparental configuration of the flanking markers, and this fraction increased progressively in the three spo11 mutants (Table 2). This was the expected pattern for crossover homeostasis: if a greater fraction of recombination events are crossover-associated in the spo11 mutants, then a greater fraction of Arg+ recombinants should have nonparental flanking markers. However, when the flanking markers have been exchanged, the exchange could have arisen from the same recombination event that gave the Arg+ conversion, or could have arisen from an independent event elsewhere in the interval. The latter is referred to as an incidental exchange, and could complicate interpretation of the results if it occurred frequently. We therefore analyzed the configuration of the NdeI restriction site polymorphisms closely flanking ARG4 (Figure 2B). A crossover associated with the Arg+ conversion would exchange the NdeI polymorphisms along with the more distant markers, whereas incidental exchange outside the region between the NdeI sites would leave a parental NdeI configuration (see Supplemental Figure 1 for more detail).

Table 2 Random spore analysis of recombination at the ARG4 locus.

For the SPO11+ strain, 77 clones of the majority nonparental class (Ura− Thr+) were scored. Of these, 70 (91%) also had a nonparental NdeI configuration, consistent with a single crossover associated with conversion at ARG4 (Supplemental Table 5). In the spo11yfHA/spo11-HA mutant, 86 of 89 Ura− Thr+ clones analyzed (97%) also had a nonparental configuration of NdeI sites, not significantly different from wild type (p>0.15) (Supplemental Table 5). Of the remaining Ura− Thr+ clones from both strains, nearly all had a marker configuration consistent with a noncrossover conversion of arg4-Nsp plus a single incidental exchange (Supplemental Table 5 and Supplemental Figure 1). Incidental exchanges played a more significant role in generating the minority (Ura+ Thr−) class of nonparental Arg+ recombinants, because only ~70% had the expected pattern for a single exchange associated with the Arg+ conversion for both SPO11 (6 of 9 clones analyzed) and spo11yf-HA/spo11-HA (5 of 7 clones) (Supplemental Table 5 and Supplemental Figure 1). These findings indicate that incidental exchanges accounted for only ~12% of nonparental Arg+ clones. More importantly, this fraction varied little with SPO11 genotype, ruling out the possibility that the differences we observed in the spo11 mutants were caused by changes in the contribution of incidental exchanges.

The fraction of Arg+ conversions that are crossover-associated can be estimated by correcting for the observed frequency of incidental exchanges (i.e., scoring 10% of the Ura− Thr+ clones and 30% of Ura+ Thr− clones as noncrossover even though they had an exchange). (Incidental exchanges could also “erase” crossovers that were associated with Arg+ conversion, but such events are very infrequent because they require ≥2 crossovers in the small interval between CEN8::URA3 and THR1.) From this estimate, 47.8% (1539/3220) of Arg+ conversions were crossover-associated in wild type, and this fraction increased to 52.1% (1715/3293) in spo11-HA/spo11-HA, to 58.8% (2112/3656) in spo11yf-HA/spo11-HA, and to 60.4% (1429/2366) in spo11da-HA/spo11da/HA. These increases were statistically significant (p≤0.0004, Fisher's exact test mid-p). Thus, decreased DSB frequencies cause an increase in the ratio of crossovers to noncrossovers (Figure 2D), confirming that crossover numbers tend to be maintained at the expense of noncrossovers.

Interestingly, these results also reveal that crossover homeostasis does not provide an absolute guarantee that a DSB will give rise to a crossover. If crossover homeostasis were completely efficient, the crossover-noncrossover ratio should increase rapidly with decreasing DSB frequency, reaching a situation in which every recombination event yields a crossover. The observed crossover-noncrossover ratios diverge substantially from this expectation for the more severely DSB-defective strains (Figure 2D). Possible reasons for this behavior are addressed in the Discussion.

Figure 3 Crossover interference is maintained when Spo11 activity is reduced. Interference was assessed by comparing the genetic distance in an interval with vs. without a crossover in the adjacent interval (see text for details). Solid black arcs connect adjacent (more ...)

In wild type, interference was observed between several adjacent intervals (interference ratios of 0.3–0.5): between his4-leu2 and leu2-CEN3 on chromosome III, between lys5-met13 and met13-cyh2 on chromosome VII, and between CEN8-thr1 and thr1-cup1 on chromosome VIII (Figure 3 and Supplemental Table 6). The patterns on chromosome VII were comparable to those from an earlier study (Malkova et al., 2004). No interference was detected between CEN3-MAT on the right arm of chromosome III and either of the intervals on the left arm. It is possible that the physical distances are simply too large to detect interference (CEN3-MAT is ~90 kb).

Importantly, in nearly all cases where interference was seen in the wild type strain, it was also observed at comparable levels in each of the spo11 mutants (Figure 3 and Supplemental Table 6). The apparent exception was for comparisons involving the cyh2-trp5 interval on chromosome VII, where there was evidence for weak interference in wild type but not in the mutants (Figure 3). This interval is very large (>130 kb, ≥35 cM; Figure 1B, C), so the size may make it difficult to detect interference with adjacent intervals. (This interpretation is consistent with a study with more closely spaced markers in this region (Malkova et al., 2004)). Indeed, additional analysis (see below) reveals evidence for interference within this interval in wild type and the spo11 mutants.

Interference was not stronger in the spo11 mutants than in wild type as judged by the interference ratio; if anything, there may have been slight weakening in some cases (Figure 3). Also, intervals that showed no evidence for interference in wild type did not begin to show interference in the mutants (Figure 3 and Supplemental Table 6), indicating that interference does not extend over greater distances in the spo11 mutants.

Interference was also assessed within each interval by comparing the number of observed nonparental ditypes (double crossovers involving all four chromatids) to the number expected if there were no interference (Papazian, 1952). Nearly all of the intervals showed significant evidence for interference in wild type and the spo11 mutants (Supplemental Table 7). The exceptions, leu2-CEN3 and met13-cyh2, were too small for this analysis. Importantly, there was strong evidence for interference within the cyh2-trp5 interval and, consistent with results for other intervals, the strength of interference (judged from the magnitude of the nonparental ditype ratios) was similar in wild type and spo11 mutants (Supplemental Table 7).

We conclude that reducing Spo11 activity within the range examined here has little or no effect on either the strength of crossover interference or the distance over which interference can be detected. Thus, interference within a chromosomal region appears to be largely independent of the number of DSBs in that region. These findings help discriminate between existing models for crossover interference (see Discussion).

Figure 4 Little or no crossover homeostasis at the HIS4LEU2 DSB hotspot

Two HIS4LEU2 alleles differ by a single base change in the DSB site such that one allele (“Mom”) contains a BamHI site and the other (“Dad”) contains an NgoMIV site. Because of the central placement of the restriction sites, essentially every DSB at this locus results in incorporation of the mismatch into heteroduplex DNA, and thus this marker undergoes gene conversion very frequently. Flanking XhoI restriction polymorphisms allow crossover products to be resolved from parental-length fragments by one-dimensional gel electrophoresis of XhoI-digested genomic DNA, detected by Southern blotting and indirect end-labeling (Figure 4A) (Hunter and Kleckner, 2001). To detect noncrossover products, XhoI-digested DNA was separated in the first dimension, then DNA was digested with BamHI in the gel slice prior to electrophoresis in the second dimension (Figure 4B). On Mom, conversion from BamHI to NgoMIV without crossing over yields a spot that migrates as parental length in the first dimension but is resistant to cleavage with BamHI. On Dad, conversions without crossing are also parental length in the first dimension but are cut by BamHI (Figure 4B).

We determined the effect of spo11 mutations on DSB formation at this locus in strains that differed only in their SPO11 genotype and that carried the rad50S mutation, which causes DSBs to accumulate (Figure 4C). In SPO11+, 20.9 ± 2.4% of the DNA had a DSB (mean ± s.d. for 3 cultures, t=6 hr). DSBs were reduced in the spo11 mutants: 10.4 ± 2.5% in spo11-HA (50% of wild type) and 0.9 ± 0.4% in the spo11da-HA homozygote (4.3% of wild type). Similar to ARG4, the reduction in spo11da-HA was ~five-fold greater for HIS4LEU2 than for most other regions assayed (compare with Table 1). Because the defect was so severe, recombinant products were not detected over background (data not shown), and the heterozygote spo11-daHA/spo11-HA was used instead (DSB frequency of 4.2 ± 2.5%; 20% of wild type).

We applied the two-dimensional gel assay to RAD50+ strains carrying the SPO11 allelic series (Figure 4D). In SPO11+, 22.0 ± 4.7% of the DNA had a crossover configuration and 8.3 ± 1.5% had undergone a noncrossover gene conversion (mean ± s.d. for 4 cultures), for a crossover/noncrossover ratio of 1.3 ± 0.2. (This ratio is obtained by dividing one-half the crossover frequency by the noncrossover frequency, which corrects for the fact that each crossover event yields two recombinant DNA molecules while each noncrossover event yields just one.) Surprisingly, as Spo11 activity was reduced, both crossovers and noncrossovers dropped in parallel (Figure 4D). The crossover/noncrossover ratios were 1.6 ± 0.4 (spo11-HA/spo11-HA, n=5 cultures) and 1.1 ± 0.3 (spo11da-HA/spo11-HA, n=4). The differences between the ratios are not statistically significant (p≥0.1, two-tailed t-test). These results suggest that the HIS4LEU2 hotspot shows little or no crossover homeostasis.

The physical recombination assay provides several internal consistency checks. For example, amounts of Mom and Dad parental length species should equal one another, amounts of the two reciprocal crossover products should equal one another, and 50% of the DNA should be BamHI-sensitive. These criteria were routinely met (data not shown). More importantly, frequencies of recombinant products agreed well with DSB frequencies, indicating that essentially every DSB results in a detectable recombination event. Correcting for the two-fold overrepresentation of crossover molecules, recombinants were 19.3 ± 3.5%, 11.9 ± 4.4%, and 5.3 ± 1.2% of total DNA for the three SPO11 genotypes, indistinguishable from the rad50S DSB frequencies (see above and Figure 4C; p>0.45, two-tailed t-test). Thus, the lack of crossover homeostasis at HIS4LEU2 is not an artificial consequence of a substantial number of ‘invisible’ recombination events whose frequency varies with SPO11 genotype.

To rule out the possibility that the lack of crossover homeostasis was due to differences in strains relative to the experiments described above, recombination was also assessed using markers flanking the hotspot and an adjacent interval (Figure 4A). Tetrads were dissected from the same strains used for physical analysis as well as the spo11da-HA homozygote, and genetic distances were measured (Figure 4E). In the interval adjacent to the hotspot (his4–MAT), genetic distances were not significantly affected by the spo11 mutations (p≥0.18, G test). Thus, these strains are competent for crossover homeostasis. In the same tetrads, genetic distances in the interval encompassing the hotspot (URA3–his4) were decreased in spo11-HA/spo11-HA and spo11da-HA/spo11-HA to ~75% of wild type, but these decreases were not statistically significant (p≥0.1, G test). In contrast, crossing over in the spo11da-HA homozygote was significantly reduced (32% of wild type; p<<0.001, G test) (Figure 4E). The differences between the two intervals support the conclusion that HIS4LEU2 is less capable than other regions of displaying crossover homeostasis. However, the spo11 mutants had less effect on crossing over between URA3 and his4 than on crossovers localized specifically at the strong DSB site. Thus, the data also reveal that the larger region encompassing the hotspot can compensate for reduced DSBs to some degree, even if the DSB hotspot itself does not. The genetically assayed interval is larger than the region assayed physically and includes additional DSB sites. The compensation detected genetically is likely due in part to crossover homeostasis at these other DSB sites. We conclude that there is little or no crossover homeostasis at the strong DSB site in the HIS4LEU2 hotspot. Possible reasons for the unusual behavior of this locus are discussed below.

Reducing the number of DSBs, and thus total recombination events, does not cause a parallel reduction in the number of crossovers. Instead, there is a tendency for crossovers to be maintained at the expense of noncrossovers. This buffering mechanism, crossover homeostasis, is a new manifestation of crossover control and was, to our knowledge, not previously anticipated. The findings suggest that the decision at the heart of crossover control involves crossover-designation of an appropriate number and distribution of recombination precursors from a larger pool, accompanied by repair of all other precursors through a largely noncrossover pathway(s).

Our findings cannot be explained solely as an artifact of selection bias caused by a requirement for viable progeny. First, crossover homeostasis was seen with a spo11-HA mutation, which does not affect viability. Second, analysis at ARG4 is less sensitive to this concern because four-spore-viable tetrads are not required. Third, this idea can not explain the pattern near HIS4LEU2, where the same tetrads revealed strong homeostasis in one interval but not in another. Fourth, our findings agree with a prior study showing that numbers of Zip3 complexes did not decline in parallel with decreased Spo11 activity (Henderson and Keeney, 2004). Zip3 complexes mark crossover-designated sites (Fung et al., 2004), and cytological analysis of their formation is viability-independent.

If crossover homeostasis were completely efficient, then a single DSB would be enough to assure a crossover. This appears not to be the case in yeast, at least not at ARG4, where there was an apparent maximum chance for a DSB to give a crossover of ~60%. There are several possible reasons why crossover homeostasis did not drive to 100% crossover designation. For example, the system may be inherently limited in its ability to form a crossover. This could be because the molecular mechanism of the crossover-noncrossover decision is itself limited in enforcing crossover formation, or because there is more than one type of DSB, such that some DSBs are formed on a pairing-only pathway and are incapable of giving rise to crossovers. Alternatively, indirect effects of reduced DSBs might antagonize the normal functioning of crossover control. For example, low DSB levels are accompanied by defects in synaptonemal complex (SC) formation, perhaps because of homologous pairing defects (Henderson and Keeney, 2004). SC components are required for crossover maturation (Borner et al., 2004), so SC defects might lead indirectly to defects in generating products from crossover-designated intermediates.

Crossover homeostasis may also contribute to the observation that bisected (i.e., shortened) chromosomes in budding yeast have increased crossover densities (Kaback et al., 1992; but see also Turney et al., 2004). This interpretation predicts that the crossover/noncrossover ratio increases on bisected chromosomes instead of, or in addition to, an increase in DSB frequency. By the same reasoning, crossover homeostasis may explain cases where a crossover always forms within a region that represents only a tiny fraction of the genome, such as on micro-chromosomes in birds (Rahn and Solari, 1986), or in the pseudoautosomal region of the XY pair in mammals (Burgoyne, 1982). Finally, we note that crossover homeostasis is not expected to occur in organisms that do not show interference, such as S. pombe (Munz, 1994).

HIS4LEU2 provides a dramatic case of regional variability, with little or no crossover homeostasis at the strong DSB site despite clear evidence of crossover homeostasis in surrounding areas. Why is HIS4LEU2 unique? It is possible that this locus does not respond to normal controls, but another possibility is that this site is particularly likely to be crossover-designated such that it influences recombination nearby rather than being influenced itself. This interpretation is supported by the observation that the crossover fraction at this locus in SPO11+ was comparable to the maximum attained at ARG4 when DSBs were greatly reduced.

Kleckner and colleagues have proposed a model for crossover interference in which mechanical stress is generated by expansion of chromatin against constraining elements (Borner et al., 2004; Kleckner et al., 2004). Stress promotes structural and enzymatic processes that are necessary for crossover formation, and these processes are accompanied by a local relief of stress. Since stress is needed for crossover designation, propagation of stress relief along the chromosome inhibits crossover formation nearby. One reason this model is attractive is that it provides a single mechanism that integrates crossover interference with a tendency toward an obligate crossover. Interference is enforced by the inhibitory “signal” of stress relief; formation of at least one crossover is ensured by sufficient stress or by sufficient sensitivity to stress (i.e., ability of the recombination machinery to respond appropriately) (see Borner et al., 2004; Kleckner et al., 2004 for more detailed discussion). Importantly, the model also predicts the phenomenon of crossover homeostasis. Our findings are thus consistent with this mechanism for crossover control.

In contrast, our findings offer strong evidence against a “counting” model (Copenhaver et al., 2002; Foss et al., 1993; Stahl et al., 2004), which provides a mechanistic interpretation consistent with an example of a chi-square mathematical model for crossover interference (e.g., McPeek and Speed, 1995). The counting model posits that adjacent crossovers are separated by a fixed number of noncrossovers (with or without an additional small number of non-interfering crossovers). We show here that the crossover/noncrossover ratio varies as Spo11 activity varies. Thus, a “counting number” (i.e., the number of noncrossovers between adjacent crossovers) cannot be a genetically fixed parameter. Moreover, the counting model predicts that interference should extend further as DSBs decrease, because longer physical distances would be needed to satisfy the counting number. We found no evidence for such an increase.

It has also been proposed that one group of DSBs always gives rise to randomly distributed events (noncrossovers plus a few non-interfering crossovers) while a second (perhaps later) round of nonrandomly distributed DSBs gives rise only to interfering crossovers (Stahl et al., 2004). Although we can not exclude this hypothesis, it would require that our spo11 mutations affect only the non-interfering class of DSBs, not the later interfering ones. This possibility seems unlikely because the mutants have biochemically distinct defects: the epitope tag is speculated to interfere with protein-protein interactions; heterozygosity for the DSB-null spo11yf-HA mutation yields a mixed population of active and inactive Spo11 dimers; and homozygosity for spo11da-HA yields a uniform population of catalytically crippled proteins (Diaz et al., 2002).

An important challenge is now to define the genetic underpinnings of crossover homeostasis, especially its suggested relationship to crossover interference. Notably, the crossover homeostasis assay at ARG4 is easier than classical interference measurements by tetrad dissection, which should facilitate further analysis.

We extend special thanks to Stéphane Marcand for support to E.M. that made completion of this work possible. We are grateful to Gareth Jones, Nancy Kleckner, Frank Stahl, Anne Villeneuve, and members of the Keeney lab for stimulating discussions. We thank A. Jambhekar, C. Townsend, and C. Arora for help with strain construction and tetrad dissection. S.K. extends thanks to Frank Graves for support and encouragement. This work was supported by NIH grant R01 GM58673 (to S.K.). N.H. is supported in part by R01 GM74223. E.M. is supported in part by an “aide au retour” fellowship from the Fondation pour la Recherche Médicale, France. S.K. is a Leukemia and Lymphoma Society Scholar.