a two-pathway analysis of meiotic crossing over and gene ... · and npds—allows a quantitative...

Copyright � 2010 by the Genetics Society of AmericaDOI: 10.1534/genetics.110.121194

A Two-Pathway Analysis of Meiotic Crossing Over and GeneConversion in Saccharomyces cerevisiae

Franklin W. Stahl1 and Henriette M. Foss

Institute of Molecular Biology, University of Oregon, Eugene, Oregon 97403-1229

Manuscript received February 17, 2010Accepted for publication July 31, 2010

ABSTRACT

Several apparently paradoxical observations regarding meiotic crossing over and gene conversion arereadily resolved in a framework that recognizes the existence of two recombination pathways that dif-fer in mismatch repair, structures of intermediates, crossover interference, and the generation of non-crossovers. One manifestation of these differences is that simultaneous gene conversion on both sides of arecombination-initiating DNA double-strand break (‘‘two-sidedness’’) characterizes only one of the twopathways and is promoted by mismatch repair. Data from previous work are analyzed quantitatively withinthis framework, and a molecular model for meiotic double-strand break repair based on the concept ofsliding D-loops is offered as an efficient scheme for visualizing the salient results from studies of crossingover and gene conversion, the molecular structures of recombination intermediates, and the biochemicalcompetencies of the proteins involved.

EUKARYOTES transit from the diplophase to thehaplophase via meiosis, which is associated with a

number of interrelated processes, including crossing overand gene conversion. These processes involve meiosis-specific, programmed DNA double-strand breaks (DSBs)and their repair (DSBr). DSBr, in turn, is associatedwith mismatched base pairs and their rectification, re-ferred to as ‘‘mismatch repair’’ or MMR (Bishop et al.1987). Current efforts to accommodate both the gene-tic and molecular phenomena associated with meio-tic DSBr in yeast (Saccharomyces cerevisiae) have beenthoroughly reviewed (e.g., Hollingsworth and Brill

2004; Hoffmann and Borts 2004; Surtees et al. 2004;Hunter 2007; Berchowitz and Copenhaver 2010),but none of the reviews commits to an overall picturewith quantitative predictions. This work aims to remedythat lack. Specifically, we have made use of salientpublished studies to develop, step-by-step, a compre-hensive model of meiotic DSBr and MMR. The mainfeatures of this model are summarized in Table 1.

RESULTS

For readers who are unfamiliar with yeast geneticsand/or the known details of MMR, we begin by review-ing (1) the basic principles and vocabulary of tetradanalysis in yeast, which expose the products of individ-

ual acts of meiosis, (2) the DSBr model of Szostak et al.(1983) as modified by Sun et al. (1991), which hasprovided a basic molecular interpretation of meioticrecombination, and (3) the known roles of mismatch-repair proteins such as Msh2 and Mlh1.

Relative frequencies of tetrad types provide meas-ures of linkage distance and crossover interference:Consider a population of diploid yeast cells heterozy-gous for two linked sites, A/a and D/d. When meiosisproceeds without a hitch, the resulting tetrads eachcontain four viable haploid spores. Because the geno-types of the spores are identifiable by the phenotypes ofthe colonies they give rise to, each spore in the tetradcan be characterized as a crossover or a noncrossoverwith respect to sites A/a and D/d. When the A/a andD/d sites are closely linked, the most frequent tetradscontain only the two genotypes that characterized theparents; i.e., they have two AD and two ad spores and aretherefore referred to as ‘‘parental ditype’’ tetrads (PD).Two other types of tetrads may be found in various fre-quencies: ‘‘tetratype’’ tetrads (T), i.e., those in which thespores are all different (AD, Ad, aD, ad), and ‘‘non-parental ditype’’ tetrads (NPD: Ad, Ad, aD, aD) represent-ing the two recombinant genotypes. This type of tetradanalysis—assessing the relative frequencies of PDs, T’s,and NPDs—allows a quantitative measure of crossingover (i.e., linkage distances and crossover interference).

Gene conversion as evidence of DSBr: The samediploid may be marked at one or two other sites, B/b(and/or C/c), closely bracketing a ‘‘DSB hotspot,’’ i.e., asite that receives a high frequency (e.g., 20%) of pro-grammed, meiosis-induced double-strand breaks. TheB/b (and C/c) sites serve to identify tetrads that have

This article is dedicated to the Institute of Molecular Biology,established January 1, 1959.

1Corresponding author: Institute of Molecular Biology, Onyx Room 287,1229 University of Oregon, Eugene, Oregon 97403.E-mail: [email protected]

Genetics 186: 515–536 (October 2010)

http://www.yeastgenome.org/cgi-bin/locus.fpl?dbid=S000005450


undergone a DSBr event at the hotspot (Gilbertson

and Stahl 1996). Such tetrads are recognized by theirfailure to exhibit Mendelian (i.e., 2:2) segregation ofthe markers among the spores. Instead, a ‘‘conversiontetrad’’ may contain three spores with a marker derivedfrom one parent, and one spore with the allele fromthe other parent (e.g., 3 B:1 b, or 3 b:1 B). This non-2:2distribution of genotypes is also termed ‘‘aberrant’’ or‘‘non-Mendelian.’’ Furthermore, because the chromo-some, a double-stranded DNA molecule, carries geneticinformation on each of its complementary strands, ahaploid spore may give rise to a ‘‘mixed colony,’’ consis-ting of both B and b (or C and c) cells. Tetrads contain-ing such a spore will be referred to as ‘‘half-conversions’’(HCs) or 5:3. They can be diagrammed as BB, BB, Bb,bb when B is in excess over b, or as bb, bb, bB, BBwhen b is in excess. In this article, we deal with the twomost common types of conversions: the HCs or 5:3’sas described above, and the ‘‘full conversions’’ (FCs) or3:1’s (aka 6:2’s), which may be diagrammed as BB, BB,BB, bb or bb, bb, bb, BB). In general, tetrads with an excessof B or of b are found at similar frequencies. A signif-icant deviation from this expectation is referred to as‘‘disparity.’’

Successful application of tetrad analysis requirescareful placement of the markers ABCD/abcd. Sites B/band C/c must be located within a few hundred basepairs from a hotspot to efficiently register DSBr events asgene conversions. In contrast, markers A/a and D/d,designed to monitor crossing over and crossover inter-ference, must be far enough from the hotspot to rarelysuffer gene conversion, but close enough to ensure thatmost crossovers between A/a and D/d are products ofthe DSBr events monitored by B/b and/or C/c.

Because of limitations on the availability of markers,only one of the two sites closely bracketing a hotspot hastypically been in a gene that determines a convenientlyscored phenotype. Screening for conversions at that sitehas been used to select for analysis those tetrads thathave undergone a DSBr event, involving nonsisterchromatids, at the marked hotspot. Within that pop-ulation, the markers at the second, less convenientlyscored site, have then been determined by DNA analysis.The use of conversion at one marked site, guaranteeingthat homologous DSBr has occurred at the hotspot,allows more meaningful scoring of the other site for 2:2segregation (as well as for FC or HC) of the marker. Bythis procedure, tetrads are identified as ‘‘two-sided’’(conversions for both B/b and C/c) and ‘‘one-sided’’(conversions for only the more conveniently scored site).

The Szostak/Sun model for meiotic DSBr: We canuse the Szostak/Sun DSBr model (Figure 1) to illustratehow DSBr could generate a variety of the observed tetrads.For example, Figure 1A illustrates how mismatched basepairs created by the loss of genetic information from thechromatid undergoing DSBr, and its replacement withinformation from the unbroken homolog, can create a

HC. Should a 39-end be degraded past the site of amarker near the DSB, the repair process is called ‘‘gaprepair’’ and results, invariably, in FC for the marker, asshown in Figure 1B. Such gap repair presumably occursindependently of MMR proteins. MMR, too, can gener-ate FCs, but it operates only in the presence of knownMMR proteins. MMR occurring at invasion or annealingwill be directed by the invading or annealing terminiand results only in FCs (Figure 1C). Should a mismatchescape MMR at invasion or annealing, it becomes sub-ject to MMR directed by the termini created by Hollidayjunction resolution. Because, in this model, both theWatson and the Crick chains are cut to effect resolution,MMR can, with presumed equal probability, result in anFC or in restoration to 2:2 segregation (Figure 1C and1D). Insofar as 2:2 segregation for a marker close to aDSB hotspot (in a tetrad with conversion for a closemarker on the other side of the DSB site) can be at-tributed to restoration, MMR directed by junction re-solution can be inferred. Note that Figure 1 does notshow all four chromatids, but illustrates the fate of onlythe two chromatids directly involved in the DSBr process.

Many basic features of the Szostak/Sun model havesurvived more than two decades’ worth of tests. Thesefeatures include steps leading up to the formation of thejoint-molecule, ligated DSBr intermediate (Figure 1A,step 4), and the existence of the intermediate is not indoubt (Schwacha and Kleckner 1995). The ligatedintermediate, however, is now understood to give rise(by an, as-yet, unknown mechanism) to crossovers only(Allers and Lichten 2001a; reviewed in Bishop andZickler 2004). In this work we present further depar-tures from the Szostak/Sun model inspired (1) by thedemonstration (Getz et al. 2008) that, in yeast, meioticDSBr occurs via either a ‘‘pairing pathway,’’ first pro-posed by Zalevsky et al. (1999), or a ‘‘disjunction path-way’’ (see Stahl et al. 2004), and (2) by the extensive dataof Hoffmann et al. (2005), which allow us to propose andquantify a set of DSBr-pathway-specific properties.

Since this analysis rests, to a large extent, on the knownfunctions of MMR proteins in meiosis, and since muchof our understanding of these proteins is based on studiesof the bacterial anti-mutation proteins MutS and MutL,we summarize here the current understanding of MutS,MutL and their eukaryotic homologs.

Conventional skinny on MMR in meiosis: The bac-terial MutS and MutL proteins have a demonstrated rolein correcting mismatches that arise during DNA repli-cation (Modrich 1991). Several MutS and MutL ho-mologs have been identified in S. cerevisiae and othereukaryotes (reviewed in Nakagawa et al. 1999; Culligan

et al. 2000; Argueso et al. 2002). In both bacterial andeukaryotic MMR, rectification of the mismatch is di-rected by a discontinuity, on one strand or the other, inthe DNA duplex. MMR sacrifices the mismatched markerthat is on the strand with the nearby end. The functionsof most eukaryotic homologs appear to be similar to

516 F. W. Stahl and H. M. Foss

those of their bacterial cousins. For example, MutShomologs recognize mismatches and attract MutL ho-mologs to the region, and MutL homologs attract theremaining components of the mismatch-repair machin-ery. The expected manifestations of such MMR in meio-sis are dependent on the DSBr structures in which it ispresumed to operate as well as on the intrinsic repair-ability of the particular mismatch.

Among MutS homologs, the Msh4–Msh5 hetero-dimer (Burns et al. 1994; Hollingsworth et al. 1995;Pochart et al. 1997) stands out in several respects. First,the Msh4–Msh5 heterodimer alone is meiosis specific(Ross-MacDonald and Roeder 1994) and required forwild-type levels of crossing over and interference (Novak

et al. 2001) as well as for the formation of an intermedi-ate (Figure 1A, step 1) leading to (detectable) ligatedjoint-molecule DSBr intermediates (Figure 1A, step 4)(Borner et al. 2004). The meiosis specificity is consistentwith the failure of Msh4–Msh5 to affect the mitoticmutation rate. However, the absence of Msh4–Msh5 alsofails to manifest an increase in the frequency of HCs, the

expected consequence of defective meiotic MMR (Ross-MacDonald and Roeder 1994; Hollingsworth et al.1995; Wang et al. 1999). This, plus the observation thatMsh4–Msh5 protein has no identified mismatch recog-nition sequence like that of MutS and its yeast homologMsh2 (Culligan et al. 2000), has been taken as evidencethat Msh4–Msh5 lacks the ability to effect MMR. (Werevisit this view below.) The msh4–msh5-induced loss ofcrossing over, without a detected loss of either DSBr orMMR, suggests that the DSBs that were fated to have beeninterhomolog crossovers have, instead, been repairedusing the sister chromatid as jig and template. Armedwith this background, we first review the observationsthat force revision of the Szostak/Sun model of DSBrand, second, develop the alternative model (Table 1) forDSBr and MMR, along with arguments demonstratingthe adequacy and economy of the model.

Two pathways for meiotic DSBr: In an effort to revealthe relationship between DSBr and MMR, Getz et al.(2008) used tetrad analysis to monitor, at each of twohotspots, conversion of a palindrome marker (Nag et al.

Figure 1.—Classic DSBr. The model of Szostak et al. (1983) as modified by Sun et al. (1991) related double-strand break repair,crossing over, gene conversion, and mismatch repair in a well-defined series of steps with the following features: (A) A meiosis-specific double-strand break is followed by resection of the 59-ends created. (Step 1) With the aid of RecA-like proteins, one of thetwo resulting 39-ended single strands invades an intact homolog, displacing the complementary strand into a D-loop. (Step 2) Theinvading 39-end, acting as a primer, uses the homolog as a template to replace DNA lost by the resection. This synthesis furtherdisplaces the complementary strand, enlarging the D-loop, which then anneals with the other 39-ended single-stranded DNA.(Here, and in subsequent figures, the DSB site is indicated by a black vertical line; the invasion step is shown to the left ofthe line, while the annealing step is to the right.) (Step 3) Once annealed, this 39-end, too, primes DNA synthesis across the breaksite creating a joint molecule that contains two duplexes worth of DNA with the break site now bracketed by two regions of het-eroduplex DNA. (Step 4) Ligation completes the classic, double-Holliday-junction structure, which yields crossovers for markersbracketing the DSBr event when the two junctions are resolved in the opposite sense—the Crick strands being cut at one junctionand the Watson strands at the other. If the junctions are resolved in the same sense, noncrossovers result. In the absence of mis-match repair (MMR), any marked site between the two Holliday junctions will result in a half-conversion (HC) tetrad. (B) When a39-end is degraded past the site of a marker, strand extension following invasion or annealing (as shown here) generates a fullconversion (FC) tetrad by ‘‘gap repair.’’ (C) A FC tetrad can result from rectification of the mismatch by MMR during the invasionor, as shown here, the annealing step. (DNA removed and replaced by MMR is shown speckled.) (D) Mismatches that survive intothe completed double Holliday structure can be rectified by MMR that is directed by the nicks created by resolution of a Hollidayjunction. Depending on which strands are cut, a mismatch may yield a FC (shown here on the invasion side) or a restoration(shown here on the annealing side).

Crossing Over and Conversion 517




1989). DSBr-induced mismatches involving such palin-drome markers often fail to undergo MMR in the pre-sence of normal MMR proteins (Figure 1A). We refer tosuch mismatches as ‘‘poorly repairable mismatches’’ orPRMs. In addition, Getz et al. (2008) monitored cross-ing over between markers bracketing the palindromeand the DSB site. They conducted these crosses in thepresence or absence of Msh4, a protein required forwild-type levels of crossing over and interference asdescribed above. Their data show that the frequencies ofonly those crossover tetrads with FC or with nonconver-sion for the palindrome marker (in many of which aPRM had presumably undergone restorational repair)were dependent on the presence of Msh4 protein. Incontrast, the frequencies of both crossover and non-crossover tetrads with HC for the marker (i.e., those inwhich MMR of the PRM had failed) were, to a good ap-proximation, Msh4 independent. Similarly, in wild-typeyeast, the crossover tetrads with FC or nonconversion forthe palindrome marker showed positive interference,while the crossover tetrads with HC for the palindromelacked such interference.

Pathway-specific rules for MMR: The observations byGetz et al. (2008) provide good evidence that wild-typeyeast, unlike S. pombe (Cromie and Smith 2008), has twoDSBr pathways with different MMR properties, both ofwhich yield crossovers. Specifically, when DSBr creates aPRM via the Msh4-dependent, interference-generatingdisjunction pathway, the PRM undergoes efficient re-pair, yielding a crossover with either FC or nonconver-sion for the palindrome marker. In contrast, when thePRM is created by DSBr in the Msh4-independent, non-interference, ‘‘pairing pathway,’’ the PRM is refractoryto repair, yielding either a HC crossover or a HC non-crossover. (Note the implication that if any FCs for thepalindrome marker arise in the absence of Msh4, theymust have resulted from gap repair.)

Msh2 deletion and PRMs are equivalent ways ofeliminating Mmr from the pairing pathway: The resultsof Getz et al. (2008) provide an incentive to revisit, in theframework of two pathways for DSBr, the powerful study

by Hoffmann et al. (2005), which was also designed toexplore relationships between DSBr and MMR. Themethods used by Hoffmann et al. (2005) differ fromthose used by Getz et al. (2008). Specifically, Hoffmann

et al. (2005) monitored DSBr as conversion for markersthat make rather ‘‘well-repairable mismatches’’ (WRMs)in a wild-type background, and they created MMRdeficiencies by deletion of the MutS homolog Msh2 orthe MutL homolog Mlh1. Getz et al. (2008), instead,monitored DSBr events as conversions for a marker thatmakes PRMs near a DSB site. They noted that failed vs.successful MMR for the marker was associated withMsh4 independence or dependence, respectively, whichenabled them to assign DSBr events to one or the otherDSBr pathway. In particular, they noted that MMRwas effective only in the disjunction pathway (Getz

et al. 2008). Lest the reader protest that comparingHoffmann et al. (2005) with Getz et al. (2008) is com-paring apples and oranges, we argue, on the basis of thefollowing observations, that failure to undergo repair ofPRMs on the one hand and deletion of Msh2 on theother are equivalent manifestations of failed MMR inthe pairing pathway, and that pathway only.

Stone and Petes (2006) demonstrated that, fora WRM near a DSB site, deletion of MSH2 causes ashift from FCs to HCs independently of Msh4. Thisimplies that msh2-deletion mutants lack MMR in theMsh4-independent, pairing pathway, but have no con-spicuous MMR in the Msh4-dependent, disjunctionpathway. Getz et al. (2008) demonstrated that, in aMSH2 background, failure of the PRM to be repairedis also independent of Msh4. This implies that theobserved HCs for the PRM, too, represent failure ofMMR in the pairing pathway. Together, these obser-vations suggest that a PRM involving a palindrome ina MSH2 background may be defined as a mismatchthat is refractory to Msh2-dependent MMR. The workof Wang et al. (2003), showing that Msh2 interacts ab-errantly with a palindrome mismatch, further supportsour thesis that the methods of Hoffmann et al. (2005)and those of Getz et al. (2008) support each other.

TABLE 1

Proposed properties of two DSBr pathways

Features Pairing pathway Disjunction pathway

Products Crossovers and noncrossovers Crossovers onlyCrossover Interference No positive interference Positive interferenceMsh4–Msh5 dependence None TotalBimolecular intermediate Long with junctions not fully ligated Short with fully ligated Holliday

junctionsInvasion heteroduplex Partly ephemeral EphemeralMMR at invasion and annealing Dependent on Msh2 and Mlh1 NoneMMR near the DSB site Directed by 39 invading and annealing

endsMlh1 dependent; directed by junction

resolutionRole of Msh2 in MMR Recognizes mismatches and attracts Mlh1 NoneRole of Msh4–Msh5 in MMR None Attracts Mlh1






















Deletion of Mlh1 causes greater loss of MMR thandoes deletion of Msh2: In their exploration of DSBr andMMR, Hoffmann et al. (2005) had analyzed tetrads ofthe ABCD/abcd-type illustrated above, with markers his(which makes rather well repairable mismatches) andBIK (which makes WRMs) representing the generic B/band C/c sites bracketing the hotspot. Accordingly, theauthors registered DSBr events as conversions for his and/or BIK. Scoring, initially, conversion for his, they showedthat the elimination of either Mlh1 or Msh2 resulted ina shift from full- to half-conversion, as predicted by theSzostak/Sun model. However, the absence of Mlh1caused a greater MMR deficiency, i.e., a greater increasein HC/(FC1HC), than did the absence of Msh2 (Appen-dix A). In a one-pathway model for DSBr, this might implythat Mlh1 simply affects MMR more efficiently than doesMsh2. In a two-pathway context, on the other hand, thequantitative difference in phenotypes suggests a require-ment for Mlh1 to affect MMR not only in the pairingpathway in conjunction with Msh2, but also, withoutMsh2, in the disjunction pathway. Further analysis oftheir data supports the hypothesis of Mlh1-dependentMMR in the disjunction pathway, as described below.

Evidence for disjunction-pathway-specific, Mlh1-dependent MMR: Like msh4–msh5 mutants, but unlikemsh2 mutants, mlh1 mutants show reduced meioticcrossing over (Hunter and Borts 1997) and reducedinterference (Abdullah et al. 2004; Appendix B).Moreover, these mlh1 phenotypes are observed in aMSH4–MSH5 background only (Wang et al. 1999;Argueso et al. 2004). Thus, at least with respect to cross-ing over and interference, MLH1 functions in the dis-junction pathway. The data of Hoffmann et al. (2005)indicate that the observed mlh1-induced gain in HCsmentioned above represents twice the mlh1-induced lossin FCs (Appendix A). Data in the same article suggest(1) that the disjunction-pathway-specific, Mlh1-dependentFC tetrads were crossovers, while the mlh1-induced HCswere noncrossovers and (2) that these noncrossoversrepresented twice the number of Mlh1-dependent cross-overs (Appendix C). These observations imply that Mlh1does, indeed, play a role in MMR in the disjunction path-way and that �50% of the time, Mlh1-dependent MMRin the disjunction pathway restores Mendelian (2:2) se-gregation of the marker.

In the disjunction pathway, Mlh1-dependent MMRoccurs only in response to junction resolution: Theevidence that Mlh1-dependent, disjunction-pathway-specific MMR yields restoration and FC tetrads at equalfrequencies implies that such MMR was directed byresolution of the Holliday junctions of the ligated DSBrintermediate (which is the molecular hallmark of thedisjunction pathway) (Figure 1D). A corollary of thisview is that mismatches created at the invasion and/orannealing phases of disjunction-pathway DSBr fail toundergo MMR prior to being incorporated in theligated intermediate. Work by Allers and Lichten

(2001b) supports this interpretation. These authorsused gel electrophoresis of DNA from a MSH2 MLH1strain to characterize DSBr intermediates with respectto a palindrome marker that makes PRMs near a DSBsite. As expected, they found that the intermediatefrequently contained the marker in mismatched, het-eroduplex DNA, indicating a paucity of MMR prior toligation of the intermediate. Moreover, in none of theintermediates were all four of the marked DNA strandsderived from only one parent or the other, which wouldhave been an indication of MMR.

The results of Allers and Lichten (2001b) indicatethat PRMs in the disjunction pathway generally escapeMMR at the invasion and annealing phases of DSBr. Asdiscussed above, the data of Hoffmann et al. (2005),who used markers that make rather well-repairablemismatches, show that disjunction-pathway-specificMMR of WRMs, too, is directed by junction resolution.Thus, in wild-type yeast, the lack of MMR at the invasionand annealing phases appears to be a regular featureof disjunction-pathway DSBr. Yet, as demonstrated byGetz et al. (2008), mismatches induced by DSBr in thedisjunction pathway are invariably repaired. Thus, MMRin this pathway occurs always, and only, in response toHolliday junction resolution.

msh2-induced lack of Mmr reduces two sidedness: Asshown above, lack of MMR in the disjunction pathwayrevealed DSBr events that would not have been detectedin the presence of MMR. The data of Hoffmann et al.(2005) allow us to ask if the absence of Msh2-dependent(i.e., pairing-pathway specific) MMR would produce thesame result. These authors screened for tetrads withconversion at his. Within this his-conversion population,they compared conversion frequencies for their secondmarker, BIK, in msh2 vs. MSH2 strains. Their resultsshowed that deletion of Msh2 caused an increase in HCsamong conversion tetrads, as expected. At the sametime, however, two sidedness (the conversion frequencyof BIK among his conversions) was decreased, rather thanincreased in response to loss of Msh2. Getz et al. (2008)reported equivalent results from crosses in a MMR-proficient background. To select for DSBr events at thehotspot, they used a ‘‘B/b’’ site (close to a DSB hotspot)that made WRMs. The crosses contained a ‘‘C/c’’site (onthe other side of the DSB hotspot) to assess two sidedness.When the C/c site made WRMs, most of the C/c conver-sions tetrads were FCs, as expected. When they replacedthe WRM C/c site with a C/c site that made PRMs, most ofthe conversions at the C/c site were now HC, also as ex-pected, but two sidedness was significantly reduced.

Migrating D-loops and transient heteroduplex: Howcould loss of MMR cause these apparent reductions inconversion? One way is illustrated in Figure 2. Thefigure focuses on the heteroduplex created at the in-vasion stage of a DSBr event, and on the D-loop resultingfrom the invasion. While, in the Szostak/Sun model(Figure 1), extension of the 39-invading end simply en-



































larges the D-loop, in Figure 2 extension of the invadingend causes the lagging as well as the leading end of theD-loop to move toward the DSB site (Ferguson andHolloman 1996; Hoffmann and Borts 2005). As aresult, a mismatch formed at invasion is undone as theinvading strand is extruded to reunite with its originalpartner. If the mismatch undergoes MMR before it is‘‘undone’’ by the migrating D-loop, full conversion forthe marker will indicate that a mismatch had beencreated. If the mismatch fails to be repaired promptly,evidence that a mismatch had been created at invasionmay be erased by migration of the D-loop.

A role for Msh4–Msh5 in disjunction-pathway MMR:The concept of transient heteroduplex at invasion,together with ‘‘use-it-or-lose-it’’ conversion opportunities,satisfactorily accounts for MMR-dependent two sided-ness in the pairing pathway. [Unwinding of the in-vasion heteroduplex (SDSA, Paques and Haber 1999)could provide a second ‘‘use-it-or-lose-it’’ route to MMR-dependent two sidedness. As such, one sidedness due tolack of MMR would be enriched among noncrossoversrelative to crossovers (Merker et al. 2003; Getz et al.2008)]. A migrating D-loop, causing transient hetero-duplex, may well characterize disjunction pathway DSBralso. Indeed, data from Allers and Lichten (2001b) andSchwacha and Kleckner (1995) demonstrated that aconspicuous fraction of ligated (i.e., disjunction-pathway)DSBr intermediates had both Holliday junctions on thesame side of the DSB site. If the disjunction pathway does,in fact, have transient invasion heteroduplex, mismatchescreated at invasion will be lost without a trace, because thedisjunction pathway appears to routinely forego MMR atinvasion and annealing, even in wild-type crosses.

What could prevent MMR in wild-type strains fromacting at invasion and annealing in the disjunction

pathway? By way of answer, we suggest that the lack ofMMR prior to completion of the ligated intermediate inthis Msh4–Msh5-dependent pathway is due to the ab-sence of MutS function required for recognizing mis-matches in duplex DNA. Msh2 and Msh4–Msh5, theonly known candidates for this role, are both disquali-fied, although for different reasons—Msh2, which doesrecognize mismatches in duplex DNA, does not operatein the disjunction pathway (see Appendix A), whileMsh4–Msh5, which, by definition, does operate in thedisjunction pathway, fails to recognize mismatches induplex DNA. It remains to be considered how, in theabsence of mismatch recognition, PRMs, and WRMstoo, in the disjunction pathway are nevertheless invari-ably repaired to yield either FC or nonconversion tet-rads (Getz et al. 2008). Work by Snowden et al. (2004)suggests how the unique properties of Msh4–Msh5might allow the dimer to promote MMR in a joint-molecule double-Holliday-junction DSBr intermediate.

Snowden et al. (2004), working with human MutS andMutL homologs, concluded that the behavior of Msh4–Msh5 protein at a Holliday junction is like that of a MutSprotein at a mismatch in duplex DNA—Msh4–Msh5 bindsto a Holliday junction and then slides away (Acharya et al.2003). The high concentration of Msh4–Msh5 could thenattract the MutL homolog. In the case of the double-Holliday-junction intermediate, reiteration of such behav-ior, with sliding in either direction, could lead to a trafficjam of Msh4–Msh5 in the region between the junctions,attracting Mlh1 to the entire region. Now, when nicks areintroduced to resolve a junction, every mismatch betweenthe junctions is rectified. Whether the DNA removal andreplacement required for rectification is an inevitableconsequence of junction cutting or is dependent on themismatch is not answerable at this time.

The dog that didn’t bark: If, as we propose, there issuch a thing as Msh4–Msh5/Mlh1-dependent MMR inthe disjunction pathway, why then would msh4–msh5deletion mutants not have a MMR-deficiency pheno-type? This lack of msh4–msh5-induced increase in HCs iseconomically explained by the requirement of Msh4–Msh5 for the establishment of the disjunction pathway(Borner et al. 2004). Without the disjunction pathwayand its products to register the presence or absence ofMMR, there can be no msh4-induced increase in HCsto signal that MMR had failed. Hence, the apparentparadox—any MMR-deficiency phenotype of msh4–msh5mutants should be detectable only in the presence ofMsh4–Msh5 protein. Msh4–Msh5’s vital contribution tothe establishment of the disjunction pathway makes itimpossible to challenge directly the proposal that, withinthe disjunction pathway, MMR is Msh4–Msh5 dependent.A critical test of Msh4–Msh5’s involvement in MMRmay require an (as-yet hypothetical) msh4–msh5 mutantthat has retained the ability to form/stabilize the double-Holliday-junction DSBr intermediate, but has lost theability to recruit Mlh1. Perhaps such a separation-of-

Figure 2.—The traveling D-loop. (Step 1) A D-loop is cre-ated by invasion. (Step 2) The D-loop moves toward the DSBsite as the invading strand elongates (bricks of blue), reduc-ing the region of heteroduplex to the left of the DSB. (Steps 3and 39) Annealing brings migration of the junction to a haltearly (Step 3) or later (Step 39). See Figures 3 and 4 for thesteps specific to the proposed disjunction and pairing path-ways, respectively.




















function mutant will be found and will exhibit thetypical meiotic MMR-deficiency phenotype, viz., anincrease in HCs.

Where the rubber meets the road: The DSBr andMMR data from the extensive study by Hoffmann et al.(2005) were reported in terms of HCs and FCs for hisand BIK in wild-type, msh2 and mlh1 crosses. In addi-tion, as noted above, these authors screened tetrads fortwo sidedness. These data can be used to test whetherthe model is capable of generating those observedvalues. Such a test requires that we first identify andevaluate (see Appendix A) the probabilities for each ofthe steps that can lead to a specified outcome. They areof two kinds—those whose values are preset by themodel (nonadjustable parameters) and those that arespecific to the HIS4 DSB hotspot and the markers inHoffmann’s strains (adjustable parameters).

Our model implies the following values for the fournonadjustable parameters:

d The probability that his is on the annealing side ofany DSBr intermediate ¼ ½ (When his is not so sit-uated, BIK is)

d The probability that a mismatch on the annealing sideof the DSBr intermediate in the disjunction path-way is repaired ¼ 1

d The probability that repair in the disjunction pathwayleads to FC ¼ ½

d The probability that a mismatch on the invading sideof DSBr in the disjunction pathway remains withinthe migratory D-loop ¼ 0.

The adjustable parameters are:

d g, the probability, specific for each marker, that a mis-match in the pairing pathway becomes FC by gap

TABLE 2

Summary of Sudoku

Parameter Valuea

A. Values for adjustable parameters at hisD, disjunction pathway events per 1000 tetrads 154P, pairing pathway events per 1000 tetrads 171E, fraction of P retaining heteroduplex on invasion side 0.3R, probability that heteroduplex rejection does not occur 0.643ghis, probability of gap repair at his 0.127gBIK, probability of gap repair at BIK 0.04mhis, probability of mismatch rectification to FC at his in pairing pathway 0.726mBIK, probability of mismatch rectification to FC at BIK in pairing pathway 0.96

Class Obs.b Calc.c

B. Conversion at hismlh1 HC 171 174mlh1 FC 21 21.8msh2 HC 97 97msh2 FC 61 60.3WT HC 17 17.1WT FC 120 122

Cross Obs.d Calc.e

C. Fraction of two-sided his conversionsmlh1 0.26–0.47 0.31msh2 0.22–0.46 0.39WT 0.58–0.77 0.71

Cross Obs.f Calc.e

D. FC/(FC1HC) for BIK among his conversionsmlh1 4/41 0.10msh2 3/51 0.10WT 89/92 0.97

a From Tables A2, A3, and A4.b From Table A1.c From Tables A2 and A3.d 95% confidence interval on data from Table 5 of Hoffmann et al. (2005, Table 5).e From Table A4.f From Hoffmann et al. (2005, Table 5).





repair (Szostak et al. 1983) or FC-biased ‘‘short-patch repair’’ (Coıc et al. 2000)

d R, the probability that heteroduplex rejection in thepairing pathway (Chambers et al. 1996; Goldfarb

and Alani 2005) does not occur (see Appendix A)d m, the probability, specific for each marker, that

mismatches in the pairing pathway are repaired(always to FC rather than 2:2)

d E, the probability that, on the invasion side of a pair-ing pathway DSBr event, the mismatch remainscovered by the traveling D-loop so that it appears asan HC in MMR-deficient crosses

d P, the probability (expressed as number of DSBs perthousand tetrads) that a DSB is repaired by way ofthe pairing pathway

d D, the probability (expressed as number of DSBs perthousand tetrads) that a DSB is repaired by way ofthe disjunction pathway.

This list of parameters intentionally excludes thepossibility of restoration of 2:2 segregation by MMRacting on a mismatch that is close to an initiating DSB.In so doing we minimize the number of parameters.

Sudoku: To estimate values for the adjustable param-eters, we adopted the conventional strategy of startingwith the parts of the puzzle that look easiest. Forexample, to obtain a value for D, we made use of themodel’s feature that DSBr products contributed by thepairing pathway should be strictly the same for mlh1 asfor msh2 crosses. Hence, any differences between thosetwo crosses should lead directly to estimates of D, theonly adjustable parameter in the disjunction pathway.To determine the values of ghis, P, and E, we first esti-mated E on the basis of the frequency of tetrads, in theMMR mutants, that were simultaneously conversions forBIK and his (two-sided tetrads). We assume a single valuefor E, rather than assuming his- and BIK-specific values,on the grounds tha, if we can fit the data with a singlevalue, we could surely fit them with separate values. Theremaining two parameters were then chosen to givesatisfactory fits to the FC and HC data for the MMRmutants (Appendix A).

To obtain a his-specific value for m and a value of R , weturned to the HC and FC frequencies in the wild-typecross. We held D, ghis, E, and P at the values deducedfrom the MMR-mutant crosses, and, for simplicity, as-sumed m to apply equally to mismatches created at in-vasion or annealing (Appendix A). The strategy forobtaining values for the only remaining parameters, mbik

and gbik, is described in Appendix A.With a value for each of the parameters, it was then

possible to compare the expected values for FC, HC,and two sidedness with the observed values. Thesummary (Table 2) demonstrates that a single set ofplausible parameter values satisfies both the HC and FCdata, as well as the two sidedness, for each of the threegenotypes, msh2, mlh1, and WT. It is gratifying that, with

eight adjustable parameters, the model can account for12 observations.

DISCUSSION

The data of Hoffmann et al. (2005) and Getz et al.(2008) call for an updated view of DSBr and MMR. Ourinterpretation of these data, above, has allowed us to

Figure 3.—Proposed features of the disjunction pathway ofDSBr in MLH1 meiosis. (Step 1) The 39-strand invades the ho-molog (blue) creating a D-loop (Hunter and Kleckner

2004). (Steps 2 and 3) Strand extension, shown as bricks ofblue, often moves the trailing edge of the D-loop across theDSB site, undoing any mismatch that might have been createdby invasion. D-loop migration is then blocked by annealing.The absence of MMR at invasion and annealing is character-istic of wild-type DSBr in the disjunction pathway. (Steps 4 and5) Formation of the right-hand junction, promoted by Msh4–Msh5 binding, limits the length of the four-stranded struc-ture, often to a region shorter than the resection. (Steps 6and 69) Junction resolution by cutting gives crossover prod-ucts that are 4:4 on the invasion side and either FC or 4:4on the annealing side, with the stretch of DNA that has lostinformation by MMR shown speckled. The arrows identifythe junctions that are cut ‘‘vertically’’ and ‘‘horizontally.’’‘‘Vert. first’’ and ‘‘Hori. first’’ indicate whether the verticalor the horizontal cut was made first, respectively. When reso-lution is by 69, the DNA synthesis is on different product du-plexes, as reported by Terasawa et al. (2007). (In an mlh1mutant, the resulting products would be noncrossovers thatare 4:4 on the invasion side and HC on the annealing side.)






assign specific attributes to each of two pathways forDSBr in wild-type yeast (Table 1), leading to a molecularmodel that illustrates how repair of the programmed,meiotic double-strand breaks might occur in each of thetwo pathways (Figures 3 and 4).

The model invites us to revisit several meiotic phe-nomena previously published and interpreted. Theseinclude the wide variation in the estimated lengths ofregions of heteroduplex resulting from DSBr, MMR-dependent two sidedness, the apparent mutual exclu-

sivity of interference and gene conversion in Sordariafimicola, and an unexpected DSBr intermediate. Below,we review these phenomena and offer interpretationswithin the framework of our two-pathway model withtraveling D-loops.

Heteroduplex lengths: Several studies of DSBr inyeast have yielded data that create impressions of thelength of the regions of heteroduplex created at theinvasion and/or the annealing stages of DSBr. Someestimates were based on physical analyses (e.g., micros-

Figure 4.—Proposed features of the pairing pathway of DSBr in msh2 and mlh1 meioses. (A) Noncrossovers: (Step 1) A D-loop isinitiated by strand invasion on one side of the DSB. (Steps 2, 3, 39) Under the impetus of strand extension, the D-loop migrates,causing the region of heteroduplex arising from invasion to be reduced in extent (Step 3) or even eliminated (Step 39) beforeannealing brings the D-loop migration to a stop. (Step 4) DNA synthesis proceeds leftward as far as the junction. (Steps 49, 5)Withdrawal and reannealing (SDSA of Paques and Haber 1999) reconstitute the duplexes. (Steps 5, 59) In the absence of gaprepair, the tetrads are HC on both sides or 4:4 on the invasion side and HC on the annealing side. In the event of gap repair (or ofMMR in wild-type cells), the invading side and/or the annealing side would be FC. (B) Crossovers: Through steps 3 and 39, eventsare as for noncrossovers. (Steps 4 and 49) Strand extension continues on the annealing side, which expands the D-loop. (Steps 5and 59) Strand extension is followed by trimming as necessary. (Steps 6, 69; 7, 79) Following a proposal by Cromie and Smith

(2008), the intermediates are drawn without a pair of Holliday junctions and are presumed to be resolved by Mus81–Mms4 aspictured in of Hollingsworth and Brill (2004, Figure 3, A and B). (Steps 7 and 79) In the absence of gapping, the resultingcrossovers, like the noncrossovers, are HC on both sides or 4:4 on the invasion side and HC on the annealing side of the DSB. Inthe event of gap repair (or of MMr in wild-type cells), the invading side and/or the annealing side would be FC. The role ofextended synthesis in the production of crossovers derives from Maloisel et al. (2004), who proposed ‘‘ . . .a model in whichDNA synthesis determines the length of strand exchange intermediates and influences their resolution toward crossing over.’’Unbridled creation and extension of structures 4 and 49, accompanied by branch migration that creates invasive 39-ends couldlead to the accumulation of multimolecular structures in meioses lacking the endonuclease Mus81–Mms4 and the helicase Sgs1(Oh et al. 2008; Jessop and Lichten 2008).


copy or gel electrophoresis), others on genetic analyses.The problem is that the impressions appear to contradicteach other. For example, genetic analyses suggest thatconversion tracts (which depend on regions of hetero-duplex) may often be ‘‘long’’ (Detloff et al. 1992; Foss

et al. 1999). Microscopy by Bell and Byers (1983), on theother hand, indicates that double-Holliday-junction in-termediates tend to be ‘‘short.’’ This estimate by micros-copy is consistent with gel electrophoresis data reportedby Schwacha and Kleckner (1995), which imply thatthe region of DNA between two Holliday junctions inobserved intermediates is usually short. Our modelsuggests that these apparent discrepancies reflect thedifferences between the pairing and disjunction path-ways. Both the gel electrophoresis and the microscopyfocus on double-Holliday-junction intermediates, i.e.on disjunction-pathway intermediates, which, in ourmodel, are short (Figure 3, and see below). In contrast,the genetic studies indicating long regions of hetero-duplex (Figure 4; Detloff et al. 1992; Foss et al. 1999;Hillers and Stahl 1999) were based on HC tetrads,which are manifestly products of the pairing pathway(Getz et al. 2008; and see above). This interpretation isalso consistent with the msh4-induced increase in theaverage length of conversion tracts, as deduced fromgenetic data of Mancera et al. (2008)—according toour model, the absence of Msh4 would eliminate thedisjunction pathway with its short conversion tracts,thereby increasing the average conversion tract length.

It should be noted that electrophoresis studies haveyielded little evidence on the structure of pairing-pathway intermediates. While this could reflect anephemeral nature, we suggest that it reflects (insteador also) the variable and ‘‘unfinished’’ nature of theseintermediates (Figure 4) and/or a length that frequentlyexceeds the distance between the restriction sites usedby the investigator to liberate the intermediates fromthe chromosome. Furthermore, frequent erosion of the39-single-strand ends at the DSB in the pairing pathway(g . 0) could confound the detection of DSBs specificto that pathway.

MMR-dependent two sidedness: Hoffmann et al.(2005) explained the phenomenon of MMR-dependenttwo sidedness with the suggestion ‘‘... that in wild-typecells the initial DSB repair event is two sided. Theabsence of MMR, by either mutation or use of poorlyrepaired palindromes, allows a second, unbiased mis-pair removal pathway to restore a proportion of hetero-duplexes, leading to apparent one-sided events.’’ Thisproposal suffers from several problems, one of which isthat the short-patch system hypothesized by Hoffmann

et al. (2005) to be responsible for this unbiased MMR isclaimed by its discoverers in yeast (Coıc et al. 2000) to bebiased against the marker on the invading strand, thusfavoring FCs over restorations (and see Appendix A,Disparity between the two classes of HCs). Our modelsuggests, instead, that a traveling D-loop in the pairing

pathway allows a mismatch created at invasion only atransient opportunity to enjoy MMR (Figure 4). Thus,the one sidedness (fraction of conversions for one of thebracketing markers that are 2:2 for the other) reflects thefailure of MMR to turn such a mismatch into an FC beforethe heteroduplex containing the mismatch is undone.

Gene conversion in Sordaria: Our model for DSBrobliges us to revisit the observation by Kitani (1978)that, unlike yeast crossovers, Sordaria crossovers thatexhibit gene conversion have no crossover interference,and vice versa. Stahl and Foss (2008) had suggestedthat, in both organisms, MMR in the disjunctionpathway is directed by junction resolution. In yeast suchMMR would result in interfering crossovers with FC or2:2 segregation for the marker with equal probabilitywhile, in Sordaria, junction-directed MMR would yieldinterfering crossovers with only 2:2 segregation. Thisproposal rested on the assumption that the disjunction

Figure 5.—The JM2 DSBr intermediate of Allers andLichten (2001a,b). Steps 1 and 2 are as in Figure 3. (Steps3 and 4) If the traveling D-loop overshoots the marker to theright of the DSB site before being halted by annealing, themarker is in heteroduplex composed of an old red strandand a new blue strand. (Steps 5 and 6) Prior to the comple-tion of the Holliday junction on the right, the unligated junc-tion, posing as a nicked junction, directs Mlh1-dependentMMR of the mismatch, restoring the parental state (speckled)of this disjunction pathway intermediate. Schwacha andKleckner (1995) reported a high frequency of JM2s (theirtype IIA). Prediction: double-Holliday-junction intermediatesisolated from a strain lacking Mlh1 would lack JM2s.




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pathways for the two organisms differ from each otherin the same manner as do the pairing pathways; viz. yeasthas predominantly asymmetric heteroduplexes, revealedby 5:3 segregation, while Sordaria has a high frequencyof symmetric heteroduplex, revealed as aberrant 4:4segregation (Kitani and Olive 1967; Stahl and Hillers

2000; Stahl and Foss 2008). We now suggest a secondpossibility as to why interference and conversion appearmutually exclusive in Sordaria. This possibility is basedon our understanding that Kitani’s monitored markerswere not selected for proximity to a DSB hotspot. If, as foryeast, Sordaria’s regions of heteroduplex in disjunction-pathway intermediates are relatively short, Kitani’smarkers might only rarely generate disjunction-pathwaymismatches, in which case the interfering crossoverswould usually lack conversion regardless of whether theintermediate had symmetric or asymmetric heterodu-plex. In contrast, crossovers in the pairing pathway, withits longer conversion tracts, would be relatively morelikely to involve a marker far from the DSB site inheteroduplex.

This explanation (for the frequent lack of detectableDSBr participation in the disjunction pathway formarked sites relatively remote from the DSB site)may apply also to the apparent lack of BIK’s participa-tion in disjunction pathway DSBr (Appendix A, The BIKdata).

An unexpected DSBr intermediate: Allers andLichten (2001b) reported a DSBr intermediate that theylabeled JM2. JM2 had two Holliday junctions, identifyingit as a disjunction-pathway intermediate. The junctions,however, were on the same side of the DSB site, beyond apalindrome marker located near the DSB site (on theright in Figure 5). Moreover, the palindrome marker wasin parental configuration, which the authors had somedifficulty explaining. Within the framework of our modelfeaturing a traveling D-loop and junction-directed repairin the disjunction pathway, we offer the scheme illustratedin Figure 5. A most attractive feature of the scheme is that,in harmony with the observations of Allers and Lichten

(2001a), it yields restoration intermediates but never FCones. We note that if JM2s had been frequent in the dataof Hoffmann et al. (2005), our model would demand thatthe excess of HCs seen in the mlh1 cross would be morethan twice the excess of FCs seen in the MLH1 msh2 cross.The data do not lean that way.

Predictions: Our view of the roles of the variousMut homologs in meiotic MMR makes a number ofpredictions:

1. Crosses carried out with a poorly repairable mis-match close to a DSB site in a MSH2 backgroundshould have the same HC/(FC 1 HC) ratios as docrosses in a msh2 background with a marker, at thesame site, that makes well-repairable mismatches.

2. The proposal that deletion of MSH4 in yeast elimi-nates a crossover pathway that yields only noncon-

versions and one-sided FCs implies that msh4 mutantsshould show a modest increase not only in the HC/(FC 1 HC) ratio for a palindrome marker at HIS4 (bydecreasing FC crossovers as shown by Getz et al.2008), but also in the fraction of DSBr events that aretwo sided (by decreasing the one-sided tetrads).

3. Getz et al. (2008) noted that, in msh4 mutants, theloss of conversion crossovers appeared to resultconspicuously in a gain in nonconversion noncross-overs (presumably by sister repair). The studies ofHoffmann et al. (2005) suggest that, in contrast,deletion of MLH1 appears to turn FC interferingcrossovers into HC noncrossovers. The possibilitythat these HC noncrossovers would interfere witheach other is a heady one, but difficult to test.

4. Another test of the model concerns the effect of Msh4on HC/(FC 1 HC) ratios in msh2 and mlh1 mutants.Although these two single mutants differ appreciablywith respect to HC/(FC 1 HC) ratios at his, when thedisjunction pathway is removed by deletion of MSH4the msh2 msh4 and mlh1 msh4 double mutants shouldbe seen to have identical values for that ratio.

5. According to our model, only the pairing pathwayproduces two-sided tetrads, implying that two-sidedcrossovers should not manifest positive interference.Expected and observed phenotypes for a variety ofrelevant genotypes are summarized in Table 3.

A prudent investigator aiming to challenge thesepredictions would probably choose to work at HIS4and with the strains of Hoffmann et al. (2005).

We thank Eva Hoffmann, John Fowler, Rhona Borts, NancyHollingsworth, Elizabeth Housworth, Michael Lichten and anony-mous reviewers for helpful comments. Jette Foss provided invaluableeditorial assistance on Appendix A. Unless otherwise specified, statis-tical calculations were conducted with the aid of VassarStats (http://faculty.vassar.edu/lowry/VassarStats.html).

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Communicating editor: M. Johnston

APPENDIX A: ASSIGNING PARAMETER VALUES (F.W.S.)

Hoffmann et al. (2005) reported the values for therelative frequencies of two- vs. one-sidedness as well asthose of HCs and FCs for his and BIK in wild-type, msh2,and mlh1 crosses. To test whether the DSBr modelproposed above (Table 1 and Figures 3 and 4) canaccommodate these values it was necessary to evaluatethe parameters that were identified as defining themodel (Table 2). This appendix describes how suchevaluation was achieved.

Parameter values were assigned on the basis of data inHoffmann et al. (2005, Table 5). The key observation isthat the fraction of FCs among conversions in the mlh1mutant strain (12/112) is significantly less than that inthe msh2 strain (33/86; P , 0.0001). These data providethe statistical support for the view that, whereas Mlh1 isrequired for MMR in both the pairing and disjunctionpathways, Msh2 has no role in the disjunction pathway.

To allow comparison between the observed andexpected his conversion frequencies (Table 2) in msh2,mlh1, and wild-type strains, we expressed the entries inHoffmann et al. (2005 Table 5) as events per 1000tetrads, rounding to whole numbers (Table A1; aconvenience that exaggerates the significance of themsh2 and mlh1 data, while reducing that of the wild-type data). In addition, we combined the four conver-sion classes (6:2, 2:6, 5:3, 3:5) of Hoffmann et al.(2005) into two classes, FC and HC, ignoring for nowthe implications of some conversion disparities (Ap-pendix D). Finally, we assumed that the BIK and his ends

of the broken chromosome are equally likely to initiateinvasion.

We now have the tools to evaluate the adjustableparameter D. Following the model, which assumes thatmsh2 and mlh1 have identical phenotypes in the pairingpathway, the excess of HCs in the mlh1 strain over HCsin the MLH1 msh2 strain (171 � 97 ¼ 74: Table A1)corresponds to D/2, the number of tetrads in which his isinvolved on the annealing side of a disjunction-pathwayevent. Also by the model, the excess of FCs in MLH1 msh2over FCs in mlh1 should be D/4. That excess is 61� 21¼40 (Table A1). We arrive at a value for D by comparing thetwo mutants with respect to HCs (D/2¼ 74; D¼ 148) and,independently, by comparing them with respect to FCs(D/4 ¼ 40; D ¼ 160). We average these values to get aworking estimate of D ¼ 154 (Table A2).

To obtain values for P and ghis for each of the mutantstrains, msh2 and mlh1, we write expressions for thenumber of tetrads demanded by the model to result inFC or HC for his:

For MLH 1 msh2: FC ¼ P g his 1 D=4;

HC ¼ ðP=2ÞðE 1 1Þð1� g hisÞ:

For mlh1: FC ¼ P g his;

HC ¼ ðP=2ÞðE 1 1Þð1� g hisÞ 1 D=2

Based on the approximately 30% of two sidedness(measured as the fraction of his conversion tetrads that






















are also conversions for BIK) and the rarity of BIK FCsamong these two-sided events (Hoffmann et al. 2005,Table 5; Table A4A), we set E, the fraction of pairingpathway events in which the sliding D-loop comes to restover the BIK marker on the invasion side of the DSB atE ¼ 0.3. Absent an estimate of E for his, we assume thesame 0.3 value. With D ¼ 154 and E ¼ 0.3, values forP can be extracted from the equations. Solving the FCand HC equations for msh2, we get P¼ 172, while solvingthe equations for mlh1 gives P ¼ 166. We can then getvalues for ghis from both the msh2 and the mlh1 data.These are 0.131 and 0.127, respectively. The P and ghis

values for the two strains are, as expected, similar, andwe settled on P ¼ 171 and ghis ¼ 0.127 for personal

reasons. (Recall that our modest goal is to determinewhether there is a set of parameters that allows the modelto fit the data, rather than to determine best estimates ofthose parameters.) Calculating the values for the FCs andHCs in the wild-type crosses (Table A3) required theevaluation of two additional parameters—one for theprobability (mhis) that Msh2–Mlh1-dependent MMRleads to full conversion in the pairing pathway and onefor the probability (R) that heteroduplex rejection doesnot occur. The need for R in the wild-type cross issignaled by the otherwise puzzling observation (TableA1) that total conversions at his are lower in wild typethan in the MMR mutants despite the greater twosidedness in wild type. In limiting the model to eight

TABLE A1

Conversions at his

Conversion type per thousand tetradsa

6:2 2:6 FCb 5:3 3:5 HCc Tetrads (FC 1 HC)% HC/(FC 1 HC)%

Wild type 56 64 120 8 9 17 1731 13.7 12.4msh2 28 33 61 31 66 97 545 15.8 61.4mlh1 9 12 21 60 111 171 585 19.2 89.1

Conversions of the marker his4–ATC (his), close to the DSB site. Adapted from Hoffmann et al. (2005, Table 5).a Ignores a few rare tetrad classes. Conversion types are rounded to the nearer whole number.b 6:2 1 2:6.c 5:3 1 3:5.

TABLE A2

Worksheet for confirming parameter values for his in MMR mutants

Pairing pathway: P ¼ 171a Disjunction pathway: D ¼ 154b

Invasion: 1/2 Annealing: 1/2 Invasion: 1/2 Annealing:1/2

FC HC FC HC FC HC FC HC

msh2 g0.127

E(1 � g)0.262

g0.127

1 � g0.873

0 0 1/2 0

N 10.9 22.4 10.9 74.6 0 0 38.5 0

Summed conversions: Calculated: Observed:

FC 10.9 1 10.9 1 38.5 ¼ 60.3 61HC 22.4 1 74.6 ¼ 97 97

mlh1 g0.127

E(1 � g)0.262

g0.127

1 � g0.873

0 0 0 1

N 10.9 22.4 10.9 74.6 0 0 0 77


FC 10.9 1 10.9 ¼ 21.8 21HC 22.4 1 74.6 1 77 ¼ 174 171

a Estimated number of tetrads per thousand that enjoyed a DSB at HIS4 and were repaired on a homolog via the pairing path-way.

b Estimated number of tetrads per thousand that enjoyed a DSB at HIS4 and were repaired on a homolog via the disjunctionpathway. g¼ 0.127 is the probability of gap repair (or short-patch repair to FC in the pairing pathway). E¼ 0.3 (see Table A4) is theprobability that the marker (BIK or his) on the invasion side of the DSB remains within the heteroduplex. N is the number, perthousand tetrads, expected by the model evaluated with these parameter values. The observed numbers are from Table A1. As-signing the same probability, ½, to the invasion and annealing sides of the DSB implies an assumed lack of left vs. right sequencepreference in the invasion events.






adjustable parameters, we ignore a variety of possibleadditional factors with the hope that in so doing we arebetter exposing the skeletal features of the model. Forinstance, we are assuming that, for our markers, MMR inthe pairing pathway is directed by the invading andannealing ends created by the DSB, with the result thatall MMR in that pathway results in FC. Justification forthis simplification is found in the adequacy of oursimple model (Table 2).

We next address the features of the model that linktwo sidedness directly to MMR (Table A4). Since BIKand his are simultaneously present in all the crosses,their conversions must depend on common values of P,D, and R . Because we have assumed that E, also, is thesame for his and BIK, we need pick only m and g valuesfor BIK. If there were a large body of BIK data analogousto the his data, we might have estimated mBIK and gBIK

as we did mhis and ghis. However, the best data come fromthe BIK conversions among tetrads selected for beinghis conversions, forcing a change in strategy. Thus, forboth the MLH1 msh2 and mlh1 crosses, we sought andfound a gBIK value (0.04, by trial and error) that gavesatisfactory fits to these two-sidedness data as well as tothe FC/(FC 1 HC) value for BIK among his conversionsin the two MMR-defective strains (Table A4A). For thewild-type cross, the only remaining parameter to beestimated is mBIK, which we chose to fit the two-sidednessdata exactly (Table A4B). This mBIK value proved to givea good fit to the wild-type HC/(FC 1 HC) ratio for BIKamong his conversions, supporting the view that the Mlh1-and Msh2-dependent two sidedness is a reflection ofMMR per se.

Disparity between the two classes of HCs: Data ofHoffmann et al. (2005) showed disparities in the rates ofconversion to his and HIS. In our Sudoku, we ignoredthe disparity, raising the possibility that in doing so wehave concealed important information. The defaulthypothesis for disparity is differential rates of DSBson the two homologs, and disparity so caused wouldbe without consequence for our analysis. However,

Hoffmann et al. (2005), noting that the disparity wasstatistically significant only for the HCs, attributed it todifferent rates of restoration, by short-patch repair(Coıc et al. 2000), for the two different mismatches.This interpretation appeared to strengthen the authors’proposal that short-patch repair, operating primarily inthe absence of Msh2 and Mlh1, was responsible for theone sidedness seen in the msh2 and mlh1 crosses.Shortcomings of this proposal, along with support forthe differential DSB hypothesis, are detailed in Appen-dix D. The significance of a well-supported proposal fordifferential DSBs is that it undermines restoration byshort-patch repair as an explanation for the one sidedness.

The BIK data: Hoffmann et al. (2005) noted thatthe rate of conversion at BIK, especially in the MMRmutants, is less than that at his. Other aspects of the BIKdata combine with this observation to suggest that ourSudoku is not quite finished. Most of the BIK data, inHoffmann et al. (2005, Table 5), were collected fromtetrads that were preselected as his conversions. As such,they were two sided and, according to our model, mustbe from the pairing pathway. Consequently, those BIKdata were expected to be the same for the mlh1 and themsh2 crosses, which they seem to be (mlh1—3 FC, 48HC; msh2—4 FC, 37 HC; P ¼ 0.7). That’s cool, but BIK,in unselected tetrads, fails to show the HC and FCdifferences that characterize the his data; i.e., for BIK,there is no evidence of mlh1-specific HCs or of MLH1msh2-specfic FCs. (mlh1—1 FC, 10 HC; msh2—0 FC, 9HC). The numbers are small and could be ignored forthat reason. However, the 0:9 ratio for BIK in the msh2cross is significantly different (P ¼ 0.02) from thecorresponding ratio, 33:53, for his. An economicalinterpretation for both the relatively low conversionrate of BIK (Hoffmann et al. 2005) and its failure toshow properties characteristic of his in the disjunctionpathway is that the disjunction pathway conversiontracts usually fail to include BIK. This may be simplybecause conversion tracts in the disjunction pathway areshort and BIK is farther (maximum �600 bp) from the

TABLE A3

Worksheet for confirming parameter values for his in wild type

Pairing Pathway: RP ¼ 0.643 3 171 Disjunction Pathway: D ¼ 154

Invasion: 1/2 Annealing: 1/2 Invasion: 1/2 Annealing: 1/2

FC HC FC HC FC HC FC HC

g 1 m(1�g)0.760

E(1�g)(1�m)0.0718

g 1 m(1�g)0.760

(1�g)(1�m)0.239

0 0 1/2 0

N 41.8 3.9 41.8 13.2 0 0 38.5 0


FC 41.8 1 41.8 1 38.5 ¼ 122 120HC 3.9 1 13.2 ¼ 17.1 17

P, D, g and E values are as in Table A2. R¼ 0.643 and m¼ 0.726 were determined by fitting the model to the observed HC and FCnumbers (per thousand tetrads, Table A1) for this wild-type cross.





















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38.5

)¼

0.97

(9/

101)

/(9

6/54

5)¼

0.51

60.

33b

mlh

1g

BIK

:0.

04(3

.4)

his:

0.12

7(1

0.9)

E(1�

g)B

IK:

0.28

8(2

4.6)

his:

0.26

2(2

2.4)

gB

IK:

0.04

(3.4

)hi

s:0.

127

(10.

9)

1�

gB

IK:

0.96

(82.

1)hi

s:0.

873

(74.

6)

00

01

BIK

:0.

5(7

7)hi

s:0.

5(7

7)F

C1

HC

BIK

:0.

328

(28.

0)hi

s:0.

389

(33.

3)

FC

1H

CB

IK:

1(8

5.5)

his:

1(8

5.5)

FC

1H

CB

IK:

0hi

s:0

FC

1H

CB

IK:

0.5

(77)

his:

0.5

(77)

Pro

per

ties

of

BIK

con

vers

ion

sC

alcu

late

dO

bse

rved

Fre

q.

two

-sid

edte

trad

sam

on

ghi

sco

nve

rsio

ns

(28.

01

33.3

)/(3

3.3

185

.51

77)¼

0.31

29/

81¼

0.26�

0.47

a

FC

/(F

C1

HC

) BIK

amo

ng

his

con

vers

ion

sA

sin

msh

2¼

0.10

3/51

b

FC

/(F

C1

HC

} BIK

inu

nse

lect

edte

trad

s(6

.8)/

(113

.51

77)¼

0.04

1/11

b

(FC

1H

C) B

IK/(

FC

1H

C) h

is(1

13.5

177

)/(1

18.8

177

)¼

0.97

(14/

106)

/(11

6/58

5)¼

0.67

60.

34b

B.

WT

Pai

rin

gp

ath

way

:R

P¼

0.64

33

171

Dis

jun

ctio

np

ath

way

:D¼

154

Inva

sio

n:

1/2

An

nea

lin

g:1/

2In

vasi

on

:1/

2A

nn

eali

ng:

1/2

FC

HC

FC

HC

FC

HC

FC

HC

g1

m(1�

g)B

IK:

0.96

2(5

2.9)

his:

0.76

1(4

1.8)

E(1�

g)(1�

m)

BIK

:0.

0115

(0.6

)hi

s:0.

0718

(3.9

)

g1

m(1�

g)B

IK:

0.96

2(5

2.9)

his:

0.76

1(4

1.8)

(1�

g)(1�

m)

BIK

:0.

0384

(2.1

)hi

s:0.

239

(13.

2)

00

1/2

BIK

:0.

5(3

8.5)

his:

0.5

(38.

5)

0

FC

+H

CB

IK:

0.97

3(5

3.5)

his:

0.83

3(4

5.8)

FC

+H

CB

IK:

1.0

(55.

0)hi

s:1.

0(5

5.0)

FC

+H

CB

IK:

0.5

(38.

5)hi

s:0.

5(3

8.5)

(con

tin

ued

)


HIS4 hotspot than is his (maximum �266 bp) (E. R.Hoffmann, personal communication). This possibility,which is of no consequence for our basic Sudoku,predicts that most or all BIK conversion crossoverscome from the pairing pathway and, consequently,will have weaker interference than do his conversioncrossovers.

Multiple events? In all studies of conversion at re-combination hotspots in yeast there are tetrads that wouldbe interpreted on the basis of any model as due to multipleDSBr events, and these tetrads are usually exemptedfrom interpretation. However, as pointed out by Merker

et al. (2003), the identification of the less obvious mul-tiple events is unavoidably model dependent. Further-more, the estimation of expected frequencies of multipleevents is confounded by the possibility of negative in-terference between DSBs at the same level (Lamb andWickramaratne 1973). Among other candidates for com-plex events we note two-sided HCs that are crossoverswith heteroduplex on the same chromatid in the transconfiguration (Hoffmann and Borts 2005). Such tetrads

TA

BL

EA

4

(Co

nti

nu

ed)

Pro

per

ties

of

BIK

con

vers

ion

sC

alcu

late

dO

bse

rved

Fre

q.

two

-sid

edte

trad

sam

on

ghi

sco

nve

rsio

ns

(53.

51

45.7

)/(4

5.7

155

.01

38.5

)¼

0.71

61/

90¼

0.57�

0.77

a

FC

/(F

C1

HC

) BIK

amo

ng

his

con

vers

ion

s1�

(0.6

/53

.5)(

1/1.

831)�

(2.1

/55

.0)(

0.83

1/1.

831)¼

0.97

89/

92¼

0.97

b

HC

/(F

C1

HC

} BIK

inu

nse

lect

edte

trad

s(2

.7)/

(108

.51

38.5

)¼

0.02

0/9b

(FC

1H

C) B

IK/(

FC

1H

C) h

is(1

08.5

138

.5)/

(100

.71

38.5

)¼

1.06

(10/

107)

/(24

3/17

31)¼

0.67

60.

40b

Val

ues

for

P,D

,R,

and

E,

asw

ell

asfo

rm

his

and

g his,a

reas

inT

able

sA

2an

dA

3.E¼

0.3

and

g BIK¼

0.04

wer

ep

icke

dto

fit

the

(FC

1H

C)

and

the

FC

/(F

C1

HC

)d

ata

for

BIK

amo

ng

his

con

vers

ion

s.m

BIK¼

0.96

was

then

sele

cted

tofi

tth

eW

Tsi

ded

nes

sd

ata.

Exp

ecte

dn

um

ber

s(N

)ar

ein

par

enth

eses

afte

rea

chex

pec

ted

con

vers

ion

freq

uen

cy.

aH

OF

FM

AN

Net

al.

(200

5,T

able

6).

bH

OF

FM

AN

Net

al.

(200

5,T

able

5).

Figure A1.—Crossovers that are trans-HC on the samechromatid. Steps 1–4 are as steps 1–4 in Figure 4. Steps 4and 5: An intermediate in the pairing pathway has enjoyedD-loop expansion but unwinds and reanneals. Step 6: The39-whisker arising by branch migration on the resulting non-crossover product may promote crossing over with the bluechromatid or a third chromatid.



might result from a pairing-pathway noncrossover beingaccompanied by a not-so-incidental exchange (Ray et al.1989) provoked by the 39-end of a protruding SS-DNAwhisker (Hotchkiss 1971) (Figure A1).

APPENDIX B: CROSSOVER INTERFERENCEIN mlh1 CROSSES (F.W.S.)

Deletions of Mlh1 cause a reduction in crossing over,generally to a lesser degree than do deletions of Msh4 orMsh5 (Wang et al. 1999; Abdullah et al. 2004; Argueso

et al. 2004). Deletions of Mlh1 are hypostatic to deletionsof Msh4 (Wang et al. 1999; Argueso et al. 2004), clearlyindicating that Mlh1 promotes crossing over in thedisjunction pathway. Consequently, it is a strong expec-tation of our simple two-pathway model that mlh1D

mutants should have reduced interference, commensu-rate with the degree to which they have reducedcrossing over. Confirmation of this expectation is

befogged by claims in the literature regarding the effect,if any, of Mlh1 on crossover interference.

Abdullah et al. (2004) wrote, ‘‘ . . . as might be predictedfor genes of the MSH4 pathway, interference was abolishedby deletion of MLH1 and MLH3.’’ In the same year,Argueso et al. (2004) wrote, ‘‘In wild type, interference wassignificant at all intervals analyzed in chromosome XV. . ./These values did not significantly change in mlh1 . . .strains, which were shown previously to maintain interfer-ence.’’ These two authors have reached extreme, oppositeconclusions, neither of which is in concordance with thetwo-pathway model (Getz et al. 2008).

Shortcomings in the analyses by Abdullah et al.(2004): Abdullah et al. (2004) presented a three-factortest for interference on chromosome III. The datarevealed interference in wild type and fit well with thenull hypothesis of no interference in the mlh1 deletionmutant. The conclusion that mlh1D lacked interferencewas embraced by the authors as being expected.

TABLE B1

Map distances and interference

Chromosome XVa ADE–HIS URA–LYS LYS–HIS URA–LEU

wt mlh1 msh5 wt mlh1 msh5 wt mlh1 msh5 wt mlh1 msh5

PD: 343 400 496 264 351 513 278 344 465 607 486 643T: 709 211 215 759 261 300 744 261 242 456 128 76NPD: 16 5 9 45 4 7 48 11 13 5 2 1cM: 37.7 19.6 18.7 48.2 23.1 16.8 47.8 26.5 22.2 22.8 11.4 5.7m: 4.5 0.8 0.0 3.1 1.9 0.9 2.7 0.7 0.0 2.1 0.5 0.0P: ,0.0001 0.06 0.73 ,0.0001 0.0006 0.01 ,0.0001 0.06 0.91 ,0.0001 0.35 0.94

Chromosome IIIb LEU–MAT HIS–LEU

wt mlh1 msh4 msh5 wt mlh1 msh4 msh5

PD: 595 570 213 153 744 583 193 121T: 722 370 62 46 496 191 39 16NPD: 51 14 3 1 20 5 1 1cM: 37.6 22.0 14.4 13.0 24.4 14.2 9.7 8.0m: 0.6 0.6 ,0 0.3 0.6 0.2 0.0 ,0P: 0.0044 0.042 0.55 0.66 0.025 0.46 0.94 0.19

Chromosome VIIb TRP–CYH CYH–MET

wt mlh1 msh4 msh5 wt mlh1 msh4 msh5

PD: 316 487 413 141 1039 781 514 190T: 1023 451 128 61 395 140 25 9NPD: 113 25 4 2 6 2 1 0cM: 58.6 31.2 13.9 17.9 15.0 8.2 2.9 2.3m: 2.0 0.6 0 0.3 0.9 0.1 ,0 —P: ,0.0001 0.028 0.82 0.62 0.011 0.59 0.042 0.82

Map lengths (cM) for the intervals are calculated on the assumption that the number of exchanges per bivalent in any interval isnot more than two (Perkins 1949). m is an index of the strength of interference (Stahl and Lande 1995; Stahl and Housworth

2009); m ¼ 0 implies no interference. P is the probability that such an observed deviation of the data from the hypothesis of nointerference would occur by chance alone, calculated according to Stahl (2008). The map for chromosome XV is URA–LEU–LYS–ADE–HIS. The intervals on chromosomes III and VII are all nonoverlapping.

a Argueso et al. (2004).b Abdullah et al. (2004).

















However, the authors appear to have similar data forchromosome VII, but they present no analysis of thosedata for interference. The authors make no tests of theirtwo-factor data for either chromosome.

Shortcomings in the analysis by Argueso et al.(2004): Argueso et al. (2004) conducted both three-factor and two-factor tests for interference and reportedsignificant levels of interference in mlh1D crosses,leading them to conclude that deletion of MLH1 iswithout effect on interference. However, their analyses,too, have several problems:

1. The authors represent their tests as supporting theconclusion that ‘‘[interference] did not significantlychange in mlh1 . . . strains. . . .’’ However such a con-clusion requires statistical tests of mlh1 vs. wild-typedata, while the only tests presented are of mlh1 andwild type vs. the null hypothesis of no interference.

2. To test their two-factor data for interference, theauthors used an inefficient method (Papazian 1952)for calculating the expected frequency of NPDs. In2004, shortcomings of statistical tests based on thatexpectation were not generally appreciated. Morerecently (Stahl 2008) such tests were shown to givefalse positives—i.e., to give chi-square P-values thatare too small. Two of Argueso’s conclusions ofsignificance at the 5% level seem to have fallen victimto that shortcoming of the test (LYS–HIS and ADE–HIS, Table B1). Further undermining the usefulness ofthese data for concluding that interference did notsignificantly change in mlh1 strains is that the ADE–HISinterval comprises a major fraction of the LYS–HISinterval, so those two observations are not independent.

3. As a test for interference revealed by three-factorcrosses, Argueso et al. (2004) calculated coefficientsof coincidence). These ‘‘COC tests’’ look convincingfor the presence of interference in the mlh1 strain(Shinohara et al. 2003, Table 4) for the URA–LEU–LYS intervals, but not for the LEU–LYS–ADE intervals,where the tetrad data do not indicate interference atthe 5% level of significance. Their ‘‘Spore’’ data forthe LEU–LYS–ADE intervals, on the other hand, arereported as manifesting interference significant at

the 5% level. However, the description provided byArgueso et al. (2004) of their COC test for ‘‘Spore’’data suggests that it has incorrectly indicated signif-icance. Since these data are simply their disaggre-gated tetrad data, supplemented by spore data fromtetrads with fewer than four viable spores, theconclusion of significance is justified only if theanalysis recognizes that many of the recombinantsin the data set arose in pairs. Since the ‘‘RANA’’software employed assumes that all spores arise fromindependent events (S. E. Zanders and E. Alani,personal communication), P-values based on thosedata are underestimated. Furthermore, as a test foran mlh1-induced change in interference, COCs sufferfrom being a function both of the map distancesinvolved and the distribution of crossovers with re-spect to each other (Stahl and Housworth 2009).

Reanalyzing the data: We test our view that deletionof MLH1 reduces, but does not eliminate, interferenceusing the two-factor data of Abdullah et al. (2004) andArgueso et al. (2004). For a set of tetrads that containsat least one NPD, we assess the magnitude of thedeviation of the data set from the hypothesis of nointerference by determining the counting number (m;Foss et al. 1993; Stahl and Lande 1995). Although thecounting model was written for integer values of m,the calculator at Stahl Lab Online Tools (http://www.molbio.uoregon.edu/~fstahl/tetrad.html) allowsestimates of noninteger values of m by visual interpola-tion. If we do this for the wild-type, mlh1, and msh4/5data of Abdullah and of Argueso, we expect to see that mgoes down as crossing over goes down, reaching zero formsh4/5. This analysis is tabulated in Table B1 along withP-values for the null hypothesis of no interference.

The m values for mlh1 are between the wild-type andmsh4 values everywhere but once (Table B1), whereinterference was very low in the wild type. We concludethat mlh1 has interference that is intermediate betweenthat of wild type and msh4, as expected for a strain that ismissing a fraction of its disjunction pathway crossovers(and for which the linkage-map distances between the

TABLE B2

Map distances and interference: Chromosome III (WANG et al. 1999)

URA–HISLEU HISLEU–MAT URA–MAT

wt mlh1 msh3 wt mlh1 msh3 wt mlh1 msh3

PD: 483 564 697 506 603 689 258 391 450T: 483 345 370 451 301 388 646 502 585NPD: 7 8 6 24 12 17 72 37 47cM: 27.0 21.4 18.9 30.3 20.4 21.9 55.2 38.9 40.1m: 2.7 0.9 1.0 0.6 0.3 0.3 1.1 0.6 0.5P: ,0.0001 0.004 0.0015 0.027 0.34 0.24 0.0004 0.016 0.027

See Table B1 for explanations.


















remaining disjunction pathway exchanges may havebecome more variable). Data by Wang et al. (1999) arefully compatible with this conclusion (Table B2). For twointervals and the inclusive interval, the m-values for bothmlh1 and mlh3 deletion strains are less then those for wildtype, indicating reduced interference. The three P-valuesfor wild type are all less than 0.05, while the mlh1 and mlh3P-values for one interval (in which wild-type interferenceis weak) are greater than 0.05, while for the other intervaland the inclusive interval they both are less than 0.05.Thus, interference, although weakened, is abolished inneither the mlh1 nor mlh3 mutants.

This analysis implicates Mlh3 as the partner to Mlh1in promoting crossing over in the disjunction pathwayand raises the question of which MutL homologcooperates with Mlh1 in disjunction-pathway MMR.Mlh3 would surely be the prime suspect were it not fordata that failed to demonstrate an MMR phenotype formlh3 mutants (Wang et al. 1999). However, for a testmarker to manifest an Mlh1-dependent MMR pheno-type, the marker must participate in conversion in thedisjunction pathway. As pointed out in Appendix A, BIKappears to be a marker that, while participating inconversion in the pairing pathway, fails to do so inthe disjunction pathway, perhaps because it is rarelyincluded in the short intermediate. Reported failures(e.g., Wang et al. 1999) to see a meiotic MMR pheno-type for mlh3 may simply mean that the few markersmonitored for meiotic MMR in those crosses happenedto be of that sort.

APPENDIX C: DELETION OF mlh1 CHANGESSOME ONE-SIDED CROSSOVERS INTOONE-SIDED NONCROSSOVERS (F.W.S.)

Hoffmann et al. (2005) scored tetrads from wild-type,msh2, and mlh1 crosses for one vs. two sidedness forconversion at sites B/b and C/c and for being crossedover (or not) with respect to linked sites A/a and D/d(Hoffmann et al. 2005, Table 7). They then compared

each of the mutants to wild type and to each other withrespect to the distribution of events among the fourclasses scored. They wrote, ‘‘Both MMR mutant strainsshowed a difference in the distribution of events intothose four classes compared to the wild-type strain (P ,

0.05; G-test of homogeneity), reflecting that the mlh1D

and msh2D strains contain more one-sided events. Whenwe compared the distribution of mlh1D to that of themsh2D strain, we did not observe a significant differ-ence’’ (p. 1299).

Had Hoffmann et al. (2005) thought to compare themutants with respect to crossover vs. noncrossoverfrequencies for the one-sided tetrads only, they wouldhave found a significant difference in crossover/non-crossover ratios between the mlh1 and the MLH1 msh2strains (Table C1). Among the one-sided tetrads, theloss of Mlh1 resulted in an mlh1-specific loss of one-sidedcrossovers accompanied by a gain of twice as manynoncrossovers. Since the loss of Mlh1 results in a majorfailure of MMR, these data imply that, among disjunction-pathway one-sided tetrads, the mlh1-induced increasein HCs represents twice the number of FCs lost. Thelarger data set in Appendix A supports this sugges-tion. We propose that the twofold mutation-inducedexcess of HCs gained over FCs lost reflects the existenceof disjunction-pathway-DSBr intermediates whose mis-matches, in the presence of Mlh1, would have beenrectified equally to either 2:2 (restoration) or FC ofthe his marker. Furthermore, MMR resulting in resto-ration must have been directed by the junctionbecause, as posited in Appendix A, the invasion andannealing opportunities for MMR would have yieldedonly FCs for a marker so close to the DSB. The furtherimplication of this interpretation, that disjunction-pathway mismatches usually persist throughout theformation of the ligated double Holliday junctionintermediate, is supported by the observations ofAllers and Lichten (2001a,b) and is consistent withour hypothesis that disjunction-pathway mismatchesare repaired only and inevitably via Mlh1-dependent,

TABLE C1

mlh1 phenotype in two- and one-sided tetrads

Two-sided tetrads One-sided tetrads

CO NCO pa CO NCO pa pb Total tetrads

Wild type 35 19 1 9 8 0.067 0.39 1731mlh1 15 9 10 29 0.007 585MLH1 msh2 9 6 0.86 17 15 0.027 0.76 545

Among one-sided tetrads, the mlh1 mutation causes the mlh1-specific loss of approximately 17 � 10 ¼ 7 crossovers (COs) cou-pled with the appearance of 29 � 15¼ 14 noncrossovers (NCOs). The similarity in total population size of the mlh1 and msh2 datasets justifies this direct comparison of observed numbers. Data from Table 7 of Hoffmann et al. (2005).

a Probability by two-tailed Fisher exact probability test that these data and those for mlh1 could have been drawn randomly fromthe same universe.

b Probability by two-tailed Fisher exact probability test that the one-sided and two-sided data could have been drawn randomlyfrom the same universe.































resolution-directed MMr (and see Getz et al. 2008; Stahl

and Foss 2008).

APPENDIX D: DISPARITY AND ONE SIDEDNESS (F.W.S.)

In the total data of Hoffmann et al. (2005) thereare 182 conversions to HIS and 252 to his, a clear indi-cation of disparity (P ¼ 0.0009). In the MMR-defectivecrosses, 3:5 (HIS/his) tetrads were about twice asfrequent as 5:3 (HIS/his) tetrads, while the 2:6 and6:2 tetrads (at HIS) showed a statistically insignificantdisparity in the same direction (Table D1). Hoffmann

et al. (2005) reported that the wild-type cross showedno significant disparity among HCs, FCs, or total con-versions. To account for their observations, Hoffmann

et al. (2005) proposed that the G:G HIS/his mismatchesthat would give 5:3 segregation in the absence of Msh2or Mlh1 be subject to unbiased short-patch repairrather than terminus-directed MMR (Radford et al.2007; but see Coıc et al. 2000, who reported that short-patch repair in yeast favored FCs). We note, however,that the wild-type HC data of Hoffmann et al. (2005)are not significantly different from either of the twomutant data sets or from the sum of those two sets.Similarly, for none of the crosses are the HC datasignificantly more disparate than the FC data. Moretroubling for the unbiased short-patch-repair explana-tion for the disparity is the observation that the biasthat is shown by the FCs, albeit insignificant, is in thedirection opposite to that predicted. In their model,selective removals of 5:3 HIS/his mismatches, whilegenerating disparity in the HCs, would result in adisparity in the FCs which was half as great, but in the

opposite direction, i.e., favoring 6:2 HIS/his. Since thedisparities in the FCs and HCs are in the same di-rection, a differential frequency of DSBs on the twohomologs has to be the favored explanation.

The simple explanation of differential DSBs is furthersupported by the disparity observed at BIK. If the disparityin HCs at his were due to mismatch-specific restoration ofincipient 5:3 tetrads, there would be no expectation thatunselected BIK conversions would show a related dispar-ity. However, the unselected ‘‘subset’’ BIK conversions domanifest disparity [20 (2:6 1 3:5) and 9 (6:2 1 5:3)],which is significant (P ¼ 0.03) and in the directionexpected if the disparities at the two loci both resultedfrom the homologs being unequally subject to DSBs.

What might account for a differential frequency of DSBson the two homologs? Since sporulations were conductedwith little or no growth following mating, it is plausible thatthe HIS4 hotspots on the two chromosomes were in dif-ferent states with respect to Spo11 sensitivity (Abdullah

and Borts 2001; Cotton et al. 2009). Hoffmann et al.(2005) physically measured DSBs at HIS4 and found nodifferences between the homologs. However, the physicalstudies were conducted on an established HIS/his diploidculture in which the homologs could not be expected tomanifest a physiology-dependent difference.

We conclude that the work of Hoffmann et al. (2005)provides no support for their thesis that one sidednessreflects restoration by short-patch repair in MMR-defective crosses. At the same time, their work contra-dicts a proposal by Getz et al. (2008) that one sidednessis caused by resolution-directed MMR in the disjunctionpathway, affected by an unidentified MMR enzyme (asimagined in Figure 1D).

TABLE D1

Disparity at his

FC HC

6:2 2:6 5:3 3:5 P a P b

Wild type 96 111 14 15 1.0 –mlh1 5 7 35 65 0.75 0.28msh2 15 18 17 36 0.31 0.23mlh11msh2 20 25 52 101 0.27 0.21S three crosses 116 136 66 116 0.053 –P c 0.23 0.0003

Data from Hoffman et al. (2005, Table 5).a Chi-square probability that a difference in disparity between FCs and HCs that is this great or greater could

arise by chance alone.b Chi-square probability that a difference in disparity between the mutant strain and WT that is this great or

greater could arise by chance alone.c Chi-square probability for the data summed over the three crosses that an observed disparity this great or

greater could arise by chance alone.







a two-pathway analysis of meiotic crossing over and gene ... · and npds—allows a quantitative...

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