Previously published, and some unpublished, tetrad data from budding yeast (Saccharomyces cerevisiae) are analyzed for disparity in gene conversion, in which one allele is more often favored than the other (conversion disparity). One such disparity, characteristic of a bias in the frequencies of meiotic double-strand DNA breaks at the hotspot near the His4 locus, is found in diploids that undergo meiosis soon after their formation, but not in diploids that have been cloned and frozen. Altered meiotic DNA breakability associated with altered metabolism-related chromatin states has been previously reported. However, the above observations imply that such differing parental chromatin states can persist through at least one chromosome replication, and probably more, in a common environment. This conclusion may have implications for interpreting changes in allele frequencies in populations.
Gene conversion: Deviation from normal, 4:4 meiotic segregation, variable in position and involving only a small fraction of a chromosome in any given act. In budding yeast, conversion is characteristically seen either as a 6:2 or 2:6 segregation (full conversion, FC) or as a 5:3 or 3:5 segregation (half conversion, HC), with the number of copies of the dominant, usually wild-type, allele noted first.
Conversion disparity: A significant difference in the frequencies of 6:2 vs. 2:6 and/or in 5:3 vs. 3:5 tetrads.
Epigenetic: In this paper, epigenetic refers to a transmissible change in a phenotype of a gene whose nucleotide sequence remains unchanged.
THE primary metric of evolution is a change in the relative frequencies of a gene and its allele. The relative decline of an allele (see Vitalis et al. 2014, for example) is classically understood to indicate that this allele causes diminished reproductive success of the organism. As explained below, however, the same data could indicate that the allele is handicapped at being transmitted through meiosis.
Relevant Features of Meiotic Double-Strand-Break Repair
Meiosis in the yeast Saccharomyces cerevisiae, as in human males (Odenthal-Hesse et al. 2014), may be viewed in terms of the repair of programmed double-strand breaks (DSBs) occurring at DSB hotspots (Szostak et al. 1983). As shown in Figure 1, the repair process involves the loss of a stretch of nucleotides from the broken chromosome, often to be replaced with information from the intact homolog. If the lost nucleotide sequence includes a genetic marker, the repair product (tetrad of haploid cells) may occasionally fail to display normal segregation for the marker, with the allele contributed by the broken parent being underrepresented (gene conversion). If the two parental hotspots are equally subject to DSBs, as is typically true, such gene conversion per se will not cause an overall change in allele frequencies in the population; among half conversions (HCs: see Definitions), the frequency of 5:3 tetrads will statistically equal the 3:5 tetrad frequency and, among full conversions (FCs: see Definitions), the 6:2 and 2:6 tetrads will also be equal. If, however, one hotspot is consistently more subject to DSBs than is its allelic hotspot (DSB disparity), the 5:3 and 3:5 tetrad frequencies will be statistically unequal, as will the 6:2 and 2:6 tetrad frequencies. In the absence of any other source of conversion disparity, we expect these two inequalities to favor the same allele and to be of the same magnitude.
During an effort to reconcile a maze of contradictory conversion papers, we came to the conclusion that, depending on the protocol employed, DSB disparity can be manifested even when the two allelic hotspots at the His4 locus of yeast are presumed to be genetically identical. The protocols differed (1) in the number of generations through which the diplophase was propagated prior to sporulation and (2) in whether or not the diplophase was stored in the freezer prior to sporulation. Neither of these differences in protocol can be expected to have altered the nucleotide sequences at the hotspots. Thus, the discrepancy in hotspot properties is likely to reflect alterations in chromatin structure imposed by the differing conditions under which the two haploid parents were propagated prior to their union. To a degree, and depending on conditions, these differences in chromatin structure are retained, for at least one round, and probably more, of DNA duplication, after union of the mating cells. In Discussion, the possible significance of such epigenetic DSB disparity will be briefly indicated. Our primary task in this meta-analysis is to present the evidence for the existence of epigenetic changes that are expressed meiotically as disparity in gene conversion.
Materials and Methods
Some of the data discussed here are from the Ph.D. thesis (Rehan 2012) and notebooks of M.B.M.R. The strains and methods employed in that work are described here.
Mating and sporulation
Haploid strains were mixed and allowed to mate on a solid YPD medium at 30° overnight prior to sporulation. Mated cells were then replicated to sporulation media, either complete potassium acetate (KAC) or minimal KAC. Plates were then incubated at 23° for 3–5 days until tetrads were formed.
To the extent they are available to the authors, reagents and strains will be made available.
The authors state that all data necessary for confirming the conclusions presented in the article are represented fully within the article.
Studies of conversion disparity due to DSB disparity can be complicated by a second type of conversion disparity, viz., the differential efficiencies of repair of the two kinds of mismatches [mismatch repair (MMR) disparity] that are formed during DSB repair. For historical reasons, the best available data sets for our studies manifest conversion disparities that are composed of these two disparities. In order to understand these complex data, we first look at data that demonstrate MMR disparity by itself. These data (Detloff et al. 1991) provide a statistically solid and historically logical foundation for our analysis.
MMR disparity only
The his4-ATC marker, located near the His4 DSB hotspot (Fan and Petes 1996), is the focus of our analysis. This base-pair transversion in the first codon of His4 is subject to MMR disparity because the two kinds of mismatches resulting from DSB repair (Figure 2) are differentially subject to MMR. When the his4-ATC parent is cut, the resulting mismatch, G/G, is well repairable. When the HIS4 parent is cut, however, the resulting mismatch is C/C, which is poorly repairable by the Msh2-dependent MMR diagrammed in Figure 2 (Stahl and Foss 2010). In budding yeast, Msh2-dependent repair of a mismatch near a DSB generates a 2:6 FC or a 6:2 FC tetrad, while failure to repair may lead to a 3:5 HC or a 5:3 HC tetrad. Since G/G mismatches are repaired, to FCs, more often than are C/C mismatches (Lichten et al. 1990; Detloff et al. 1991), the a priori expectation (Figure 2) is that 6:2 tetrads will be more frequent than 2:6, while 5:3 will be less frequent than 3:5. However, data of Detloff et al. (1991) (Table 1), collected from diploids formed between AS4 and AS13 strains (Stapleton and Petes 1991), fail to meet this expectation. Although FC tetrads in favor of HIS4 (6:2) outnumber those in favor of his4 (2:6), as expected, HC tetrads manifest no disparity at all. Judging from the statistical equality of the HC classes, we may presume that the two types of mismatches were formed in equal numbers by DSB repair. While many of the G/G mismatches were being repaired to give 6:2 FCs, the poorly repairable C/C mismatches were disappearing at the same rate, although most of those mismatches failed to become 2:6s. A proposal for the molecular basis of this striking feature of MMR at his4-ATC is in Discussion.
The his4-ATC marker is not unique in generating data in which the FCs differ while the HCs do not. Nag et al. (1989) collected conversion data for his4 palindromic insertions using the strain background and methods of Detloff et al. (1991), including storage of the diploids in the freezer. These data are telling in three respects: (1) For a given cross, the two FC classes (6:2 and 2:6) are significantly different from each other. (2) The two HC classes, though equally or more abundant than the FCs, are not significantly different from each other, and (3) the data are significantly different from the naïve expectation (Figure 2) that 5:3/3:5 = 2:6/6:2. These three conditions are met for the palindromic inserts his4-lop and his4-B2 (Table 2), in agreement with the his4-ATC data.
Before we examine the data indicative of environmentally imposed DSB conversion disparity at his4-ATC, we ask what the expectations are for such a combination of MMR and DSB disparities. Since DSBs are initiating events, any DSB disparity will affect the FCs and HCs equally. We take it as axiomatic that MMR disparity will be governed by disparity like that seen by Detloff et al. (1991) for G/G and C/C mismatches. This disparity leads to an excess of 6:2 tetrads over 2:6 tetrads and has no effect on the HCs. The combination of the two disparities will have different effects depending on which of the two DSB hot spots is the more active. If the hotspot cis to his4-ATC is cut more often than that of cis to HIS4, the 6:2/2:6 value will be increased beyond that due to the MMR disparity. On the other hand, if the HIS4 hotspot is the one that is cut more often, the MMR and DSB disparities will act on the FCs in opposite directions, tending to cancel each other. Regardless of which hotspot has the greater break frequency, the effect on the HCs will be to introduce conversion disparity where there was none, and to reveal, at a glance, the direction and magnitude of the DSB disparity.
Other crosses using Detloff’s strains
The data of Detloff et al. (1991) look solid, but conversion data for his4-ATC collected subsequently differ from Detloff’s. Alani et al. (1994) examined conversion at his4-ATC using Detloff’s strains. However, instead of inducing meiosis in an established diploid culture recovered from the freezer, as Detloff et al. (1991) had done, these investigators induced meiosis in populations of diploid cells soon after their formation according to a then novel technique called “zero growth” (Reenan and Kolodner 1992), in which the diplophase may, in fact, involve a few generations of growth. The sparse data of Alani et al. (1994) (Table 3) differed from Detloff et al. (1991) by being in agreement with the a priori, naïve expectation of opposite disparities in the HCs and FCs.
Crosses in a different background (Y55)
Whereas the zero-growth wild-type (WT) data in Table 3 were only suggestive of HC disparity, abundant zero-growth data (Table 4), collected (but not previously published) by M.B.M.R. in the laboratory of R.H.B., clearly manifest HC disparity (5:3 < 3:5).
The excess of 3:5 over 5:3 tetrads in Table 4 (as in Table 3) identifies the hotspot cis to the HIS4 allele as the one that is receiving the greater share of DSBs. The disparity in the FCs in Table 4 is in the same direction, favoring the his4-ATC allele. The evident difference in the magnitudes of the two disparities is in accord with the expectation that, while the DSB disparity favors the his4-ATC allele (as shown by the HC disparity), the MMR disparity reduces that effect for the FCs by favoring the HIS4 allele, as in Table 1.
The conclusion that the observed HC disparity (Table 4) is the result of DSB disparity is confirmed by crosses in which known requirements for MMR were eliminated. In Detloff’s strain, induced to undergo meiosis with the zero-growth protocol, deletion of the MMR gene MSH2 resulted in 11 5:3s and 20 3:5s (Table 3) of 126 total tetrads (Alani et al. 1994). The direction and magnitude of the disparity in the HCs were both unchanged by this loss of MMR, as expected from the observation (Detloff et al. 1991) that MMR disparity does not cause disparity of HCs for the his4-ATC marker. (The combined wild-type and msh2 HC disparities reveal significant disparity in the HCs in Alani’s data (Table 3) (17 5:3 and 34 3:5; P = 0.025). Similarly, in the R.H.B. lab, Hoffmann et al. (2005) used the zero-growth protocol to collect conversion data for his4-ATC in two MMR-defective derivatives of the Y55 strains used in Table 4. In both mutants (msh2 and mlh1), the disparity in the HCs in favor of his4-ATC is significantly demonstrated (Table 5) and is essentially equal in extent in the two MMR-defective genotypes.
Insofar as MMR and DSB disparities are the only appreciable sources of conversion disparity, we may conclude that the disparity in the HCs seen in these MMR-deficient zero-growth crosses represents DSB disparity. By our hypothesis, the conversion disparity of the HCs at his4-ATC depends only on DSB disparity and, consequently, should be the same for the MMR proficient and deficient crosses. However, Hoffmann et al. (2005) ascribe significance to their failure to see, in the WT cross, the HC disparity that is evident in their MMR-defective crosses. This disagreement in interpretation requires that we quantitatively demonstrate the adequacy of our hypothesis for these data. We do so in Appendix, wherein we address the failure of Hoffmann et al. (2005) (Table 5), to see significant disparity in either the HCs or FCs in their MMR-proficient cross.
The HC data for the collection of zero-growth crosses (Table 6) are compatible with the null hypothesis that the disparities observed are independent of both the background of the strains involved and their MMR status.
Unwinding and MMR
The lack of disparity between the two classes of HCs in the data of Detloff et al. (1991) (Table 1) provides evidence that the G/G and C/C mismatches were created equally. How is it that they remain equal when they are differentially subject to MMR? In other words, how is it that the relatively unrepairable C/C mismatches seem to “disappear” as often as the G/G mismatches are repaired to give 6:2 tetrads? Following Detloff et al. (1991), we propose that the way to get rid of a C/C mismatch without repairing it is to unwind it, with the likely result that it gives rise to a 4:4 tetrad (e.g., as in Figure 1E, on the left side of the DSB site).
To account for the unwinding of the C/C mismatches occurring pari-passu with the MMR of G/G, we suggest that Msh2p, after binding equally well to C/C or G/G, activates both a helicase and an endonuclease. When the mismatch is G/G, the endonuclease often makes a nick in the invading strand on the side of the mismatch opposite the invading terminus, while for a C/C mismatch, it does so less often (Wang et al. 2003; Qiu et al. 2012). The observed equality of the two HC classes is then accounted for by assuming that helicase unwinding, which begins at the invading 3′ end, stops at the MMR-dependent nick. Polymerase then copies the intact strand, completing the MMR. In the absence of a nick to stop it, the helicase unwinds the entire heteroduplex (heteroduplex rejection).
Why was Detloff et al. (1991) ignored?
Detloff’s observed FC disparity appears not to have been taken seriously by Hoffmann et al. (2005), who did not reference the work, perhaps because of undefined concerns regarding cryptic mismatches in Detloff’s strains (P. Detloff, personal communication).
We have explained the appearance of disparity in the HCs of most of the crosses done subsequently to Detloff et al. (1991) as being due to DSB disparity arising from the use of the zero-growth protocol. However, data presented pre-Detloff by Lichten et al. (1990) are not so easily explained. Lichten et al. (1990) offered a set of numbers compatible with the naïvely expected conversion disparity of HCs (Table 7). They arrived at these numbers by summing two sets of data on conversion at a G-to-C transversion (arg4-nsp) close to the Arg4 DSB site. However, only one of the two data sets in the sum manifests the expected FC disparity, while only the other set significantly manifests the naïvely expected HC disparity (Table 7).
Thus, while the conversion disparities in the summed numbers reported by Lichten et al. (1990) conform to the naïve expectation for disparate MMR, they cannot be taken seriously. On the other hand, the differences between the MGD409 and the ORD002 data sets have an obvious explanation within the framework of the thesis developed here. For both the FCs and the HCs, the ORD002 data conform with the Detloff data for his4-ATC, while the MGD409 data conform with the zero-growth data for his4-ATC (i.e., less disparity in the FCs than in the HCs; e.g., Table 4). However, the zero-growth protocol was not introduced until 1992. Consequently, we were tempted to conclude that the MGD409 data look like zero-growth data because this diploid, like the diploids of a zero-growth cross, was not frozen before it was sporulated. Instead, a diploid colony was isolated and then maintained as a patch on a nutrient agar Petri plate. This custom, common now as it was then, allows an estimated minimum of 30–35 generations of diploid growth. Our surmise that MGD409 was maintained on a plate, rather than being frozen, has been confirmed by the recollection of the responsible author (N. Schultes, personal communication). Our appeal to all the authors of Lichten et al. (1990) for information regarding ORD002 has so far failed.
Interpretation and significance of the protocol-dependent DSB differences
Abdullah and Borts (2001) demonstrated that a change in the metabolic state of a diploid cell can influence the frequency of gene conversion. Presumably it does so by introducing a change in chromatin structure and, hence, in susceptibility of the hotspot to meiotic DSBs (e.g., Merker et al. 2008). The meta-analysis of His4 data conducted herein provides evidence that epigenetic differences between allelic DSB hotspots, imposed during growth of the parental haploid cultures, can be retained in zygotes resulting from union of those haploids. The Arg4 data argue that (1) the epigenetic distinction between the homologs that determines their relative DSB rates is maintained for many generations and that (2) some aspect of freezing (or thawing) the diploid removes that distinction.
Of course, the conclusions and surmises of this paper are testable by the execution of properly controlled crosses, studies that we are unable to undertake ourselves. Such studies are needed to clear up the published discrepancies exposed here as well as to prevent the occurrence of further confusions in the yeast meiosis literature. It might also stimulate analyses of the possible importance of epigenetic DSB disparity in genomic studies such as those of allele frequencies in populations (Lamb 1998) or of the fate of newly introduced alleles in finite populations (Nagylaki 1983).
We are indebted to Elizabeth Housworth for help on a statistical matter, to Gerald Smith for useful comments, to Charles Laird for advice and encouragement, to Michael Lichten and Eric Foss for information on yeast laboratory practices, and to anonymous referees for helpful criticism. The work was supported in part by a Wolfson-Royal Society Research Merit Award to R.H.B.
Analysis of Conversion at his4-ATC in Zero-Growth Crosses
Franklin W. Stahl
In contrast to the data in Table 4, the MMR-proficient cross of Hoffmann et al. (2005), using strains of the same background (Y55) and employing the same, zero-growth protocol, failed to demonstrate disparity in either the HCs or the FCs. Our analysis will show that this failure is statistically insignificant and that all features of those data of Hoffmann et al. (2005) are compatible with the following concepts (Stahl and Foss 2010): (1) DSB repair in yeast proceeds by two pathways (Figure 1); (2) these pathways differ with respect to MMR; (3) MMR in the meiotic pathway (Kohl and Sekelsky 2013, referred to as the disjunction pathway in Stahl and Foss 2010) is dependent on Mlh1, but not Msh2, and always occurs in the MMR-proficient cross, leading half the time to FC and half the time to 4:4 (restoration); (4) MMR in the mitotic pathway (Kohl and Sekelsky 2013, referred to as the pairing pathway in Stahl and Foss 2010) depends on both Mlh1 and Msh2 and sometimes fails in the MMR-proficient cross.
As elaborated below, the test will consist of calculating a value for the number of tetrads expected in each of the 12 possible conversion categories of Table 5, followed by testing the calculated values for compatibility with observed values. The calculated values will reflect the concepts of Stahl and Foss (2010), reviewed above. These concepts allow us to identify and evaluate, for each pathway, a minimal set of parameters that determine conversion at his4-ATC. Whether a DSB repair event will, in fact, result in an FC, an HC, or in 4:4 segregation of the his4 marker depends on the probabilities that the event suffers a double-strand gap (resulting in an FC) or forms a heteroduplex that either does or does not undergo MMR or simply unwinds (Figure 1E). The parameters for these contingencies are defined in Table A1.
The parameters listed in Table A1 are those whose values dictate the frequencies of each of the four classes of tetrads in the three crosses of Hoffmann et al. (2005). A test of the adequacy of our hypothesis requires estimation of those parameters within the framework of the DSB-repair model of Stahl and Foss (2010). That model asserts that MMR in the meiotic pathway occurs only at resolution of the double-Holliday structure by junction cutting and that, in this pathway, all mismatches in the MLH1 crosses enjoy MMR on that occasion. In MLH1 crosses, meiotic pathway mismatches are equally likely to be repaired to FC as to 4:4 (Figure 1, L and M), depending on the disposition of the cuts that resolve the double Holliday structure (Stahl and Foss 2010). In the mlh1 cross, all mismatches are recovered as HCs. Thus, since events in the meiotic pathway are immune to MMR disparity, as in human males (Odenthal-Hesse et al. 2014), the only adjustable parameters relevant to the frequencies of tetrad types deriving from that pathway are D, B, and g.
Estimating B, the breakage index:
Since neither MMR-deficient cross is subject to MMR disparity, B can be estimated directly from the raw data of each cross (Table 5) as B = (6:2 + 5:3)/(FC + HC). The estimates for msh2 and mlh1 are 0.372 ± 0.10 and 0.357 ± 0.09, respectively, with an average value of 0.365, which we use for our calculations.
If conversion disparity in the MMR-deficient crosses is, in fact, due only to DSB disparity, then the same value for B, 0.365, should be applicable to both the fractions of 6:2 and 2:6 tetrads within the FC tetrads and the fractions of 5:3 and 3:5 tetrads within the HC tetrads. The statistical tests in Table A2 give large P-values, indicating compatibility with that expectation.
Since the population sizes of the three crosses of Hoffmann et al. (2005) differ, calculations that draw upon data from different crosses require that the observed numbers be normalized to the same population size (Table A3).
Estimating additional parameters from MMR-deficient crosses (Table A4):
Estimating remaining parameters from MMR-proficient cross (Table A5):
The D and g values from Table A4 permit calculation of the number of FC tetrads from the meiotic pathway, which is not subject to MMR disparity.
Next, we subtract these estimated numbers of 6:2 and 2:6 meiotic pathway FCs from the observed numbers of 6:2 and 2:6 tetrads, revealing the number of FCs from the WT mitotic pathway. Whereas the total FCs favored 2:6s, the calculated mitotic pathway FCs favor 6:2s, indicative of MMR disparity (39.6 to 36.7) (Table A5). When the FCs due to gapping are removed from the mitotic pathway FCs, the MMR-disparity value of m/n = 2.2 (Table A5) provides a fit of calculated-to-observed values for the FCs (Table A6). (Unless m/n is strain specific, this ratio is probably an underestimate, judging from the FC disparity in Table 1, where the 6:2-to-2:6 ratio is ∼3 and is itself an underestimate of m/n depending on the fraction of events in the meiotic pathway. However, since this fraction is apt to be small in the crosses of Table 1, as argued in Strain-specific differences, below, the two estimates of m/n are in reasonable agreement.)
Since the fit to the HCs is statistically satisfactory, the entire WT data set of Hoffmann et al. (2005) is consistent with the two-pathway rules of Stahl and Foss (2010) as further specified by the demonstration (Detloff et al. 1991) that MMR disparity imposes no conversion disparity on HCs at his4-ATC. The analysis results in estimates of B < 0.5 and m > n, supporting the view (Stahl and Foss 2010) that the failure of Hoffmann et al. (2005) (Table 5) to find conversion disparity in their WT cross is a result of opposing MMR and DSB disparities in the FCs combined with a shortage of data for the HCs.
Calculations of the standard errors of the parameter values is unnecessary, as well as difficult (but they are certainly large). Our calculation serves as a demonstration that a complex case of conversion disparity can be successfully modeled within the conventional framework for meiotic DSB repair in budding yeast (Stahl and Foss 2010), and obviates the need to invoke, as did Hoffmann et al. (2005), an unknown short-patch mismatch-repair activity functioning only in the absence of Msh2 or Mlh1.
Without further assumption, the nature of the relationship of MMR to unwinding is not revealed by these data. The interesting possibility would be that the unwinding that is responsible for the failure of MMR disparity to be manifested as disparity in HCs is a unique class, executed by the MMR system itself. The excess in the estimated value of u (0.915) over that of v (0.51) (Tables A5 and A6) permits such a test, yielding maximal values of m = 1.1 (essentially equal to the theoretical maximum for a probability) and n = 0.5. A value of unity for m is the one expected for the simple proposal that the unwinding responsible for the failure of MMR disparity to induce conversion disparity in HCs (Detloff et al. 1991) is, in fact, unwinding that occurs only as an action of the MMR system itself (Table A5), as proposed in Discussion. To make this attractive possibility more than a suggestion would require larger data sets.
The two AS4 × AS13 data sets differ from the two Y55 sets in two respects. The HC/(HC + FC) ratios in the AS4 × AS13 crosses of Table 1 (156/366 = 0.43) and Table 3 (20/35 = 0.57) are greater than those in the Y55 crosses of Table 4 (62/1069 = 0 .06) and Table 5 (29/236 = 0.12), indicating a higher fraction of mitotic pathway events in the former crosses and suggesting that the high conversion frequencies characteristic of AS4 × AS13 crosses are due to a high rate of predominantly mitotic pathway events. This difference may be intrinsic to the strains or dependent on the differing conditions (e.g., temperature) under which the sporulations are conducted.
Communicating editor: J. A. Nickoloff
Supplemental material is available online at www.genetics.org/lookup/suppl/doi:10.1534/genetics.116.191635/-/DC1.
- Received May 14, 2016.
- Accepted June 23, 2016.
- Copyright © 2016 by the Genetics Society of America
Available freely online through the author-supported open access option.