Centromere Mapping Functions for Aneuploid Meiotic Products: Analysis of rec8, rec10 and rec11 Mutants of the Fission Yeast Schizosaccharomyces pombe

Corresponding author: Wayne P. Wahls, Department of Biochemistry, Vanderbilt University School of Medicine, 621 Light Hall, Nashville, TN 37232-0146., wahlswp{at}ctrvax.vanderbilt.edu (E-mail)

Communicating editor: M. LICHTEN

	ABSTRACT

TOP ABSTRACT MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

Recent evidence suggests that the position of reciprocal recombination events (crossovers) is important for the segregation of homologous chromosomes during meiosis I and sister chromatids during meiosis II. We developed genetic mapping functions that permit the simultaneous analysis of centromere-proximal crossover recombination and the type of segregation error leading to aneuploidy. The mapping functions were tested in a study of the rec8, rec10, and rec11 mutants of fission yeast. In each mutant we monitored each of the three chromosome pairs. Between 38 and 100% of the chromosome segregation errors in the rec8 mutants were due to meiosis I nondisjunction of homologous chromosomes. The remaining segregation errors were likely the result of precocious separation of sister chromatids, a previously described defect in the rec8 mutants. Between 47 and 100% of segregation errors in the rec10 and rec11 mutants were due to nondisjunction of sister chromatids during meiosis II. In addition, centromere-proximal recombination was reduced as much as 14-fold or more on chromosomes that had experienced nondisjunction. These results demonstrate the utility of the new mapping functions and support models in which sister chromatid cohesion and crossover position are important determinants for proper chromosome segregation in each meiotic division.

DURING meiosis each chromosome undergoes one round of DNA replication; homologous chromosomes then pair and undergo recombination. Subsequently, homologous chromosomes segregate from one another during meiosis I (MI) and then sister chromatids segregate from one another during meiosis II (MII). In most organisms, reciprocal recombination events (crossovers) help ensure proper MI segregation (ROEDER 1997 ).

Recent evidence suggests that the position of crossovers has an important role in chromosome segregation during both MI and MII. In several organisms, chromosomes that suffer spontaneous MI nondisjunction (MI NDJ) exhibit a preferential reduction of crossovers near the centromeres (GETHMANN 1984 ; RASOOLY et al. 1991 ; ROSS et al. 1992 ; MACDONALD et al. 1994 ; MOORE et al. 1994 ; SHERMAN et al. 1994 ; HASSOLD et al. 1995 ). In contrast, chromosomes that suffer spontaneous MII nondisjunction (MII NDJ) exhibit an elevated frequency of crossovers near their centromeres (MACDONALD et al. 1994 ; FISHER et al. 1995 ; KOEHLER et al. 1996A , KOEHLER et al. 1996B ; LAMB et al. 1996 ). Models invoking a synergistic interaction between crossover position and sister chromatid cohesion can best explain these observations (MOORE and ORR-WEAVER 1998 ; KRAWCHUK et al. 1999 ).

The rec8⁺, rec10⁺, and rec11⁺ genes of the fission yeast Schizosaccharomyces pombe were identified in a screen for mutations that decrease meiotic recombination (PONTICELLI and SMITH 1989 ; LIN et al. 1992 ; LIN and SMITH 1995 ; LI et al. 1997 ). In each mutant, crossover recombination is preferentially reduced toward the centers of each of the three chromosomes and, intriguingly, the mutations differentially affect chromosome segregation during MI and MII (MOLNAR et al. 1995 ; KRAWCHUK et al. 1999 ; PARISI et al. 1999 ). The rec8 mutants suffer aberrant segregation of homologous chromosomes during MI, at least part of which is attributable to the precocious separation of sister chromatids (PSS). The rec10 and rec11 mutants suffer aberrant segregation of sister chromatids during MII. The three genes are proposed to define a pathway of "meiotic chromatid cohesion" important for proper chromosome segregation in both meiotic divisions (KRAWCHUK et al. 1999 ). We therefore developed mapping functions to simultaneously measure centromere-proximal recombination and to determine the segregation patterns of each of the three S. pombe chromosomes in aneuploid meiotic products from each of the rec8, rec10, and rec11 mutants.

	MATERIALS AND METHODS

TOP ABSTRACT MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

S. pombe strains and culture media:
The S. pombe strains used for this study are listed in Table 1. Rich medium was yeast extract agar (YEA) or liquid (YEL); sporulation media was synthetic sporulation agar (SPA); minimal media was nitrogen base agar (NBA) or liquid (NBL). All media formulations and culture techniques were as described (GUTZ et al. 1974 ). YEA-B was YEA containing 2.5 µg/ml of Phloxin-B (Sigma, St. Louis) and 100 µg/ml of adenine. SPA, NBA, and NBL were supplemented with required amino acids, adenine, and uracil at 100 µg/ml. The growth factor requirement of pro2 mutants is partially satisfied by arginine. Therefore, citrulline (50 µg/ml), which does not satisfy the growth factor requirement of the pro2 mutants, was used to satisfy the growth factor requirement of the arg3 mutants.

Mating and meiosis:
Strains to be crossed were grown at 32° in 5 ml of YEL to a density of 1 x 10⁷ cells/ml. The cultures were combined, the cells were harvested by centrifugation, washed with water, resuspended in 100 µl of water, and spotted on SPA. The mating mixtures were incubated at room temperature for 3–5 days. Asci and vegetative cells were harvested into 0.5 ml of 0.5% glusulase and incubated at room temperature for 8 hr to liberate spores and kill vegetative cells. The suspensions were then treated with an equal volume of 60% ethanol for 30 min to kill any remaining vegetative cells. Spore suspensions were washed once with water, diluted, and plated on the appropriate media.

Diploid spore isolation and haploidization analysis:
Spores were plated on YEA-B and incubated for 3 days at 32° to distinguish the diploid spore colonies from the haploid spore colonies. On Phloxin-B-containing plates, haploid cells produce light pink colonies whereas diploid cells produce dark pink colonies (GUTZ et al. 1974 ). The ploidy was confirmed by microscopic examination of the cells. Diploid cells are both longer and wider than haploid cells and can be readily distinguished under the microscope.

The parental haploid strains that were crossed had different alleles at several loci on all three chromosomes. The genotypes of the resulting diploid spore colonies were determined by analysis of haploidized colonies on diagnostic plates. Diploid spore colonies were haploidized with m-fluorophenylalanine (m-FPA; KOHLI et al. 1977 ). After 2 days incubation at 32° in supplemented NBL containing 0.4–0.8% m-FPA, the liquid cultures were diluted and plated on YEA-B to determine haploidization efficiency, which ranged from 40 to 95%. Fifty haploidized colonies derived from each individual diploid spore colony were patched onto YEA to score for the two different ade6 alleles. On media with limiting amounts of adenine, such as YEA, S. pombe strains carrying the ade6-M26 allele form dark red colonies while strains carrying the ade6-52 allele form pink colonies (GUTZ 1971 ; GUTZ et al. 1974 ). After genotyping the ade6 locus, the patches were replica plated to various differentially supplemented minimal media to genotype the pro2 and arg3 loci. The mating-type locus on chromosome II was scored for allele type by analysis of the diploid spore colonies. Diploid spore colonies were patched onto SPA and incubated at room temperature for 2–3 days. Iodine vapor staining was used to distinguish the heterozygous diploids (h⁺/h^-, sporulate and stain with iodine) from the homozygous diploids (h⁺/h⁺ or h^-/h^-, do not sporulate and stain with iodine; GUTZ 1971 ; GUTZ et al. 1974 ).

Development of mapping functions:
In a meiosis that generates four haploid products the centromeres undergo first division segregation (FDS). Loci unlinked to the centromere undergo second division segregation (SDS) 67% of the time. This is due to the statistical probability of the various patterns by which the unlinked alleles can enter the ascus. By extension, disomics or diploids arising from MI NDJ will be 100% heterozygous for the centromere and 67% heterozygous for unlinked loci. Likewise, disomics or diploids arising from MII NDJ will be 0% heterozygous for the centromere and 67% heterozygous for unlinked loci. The HALDANE 1919 mapping function describes the relationship between the frequency of recombinants and genetic distance in haploid meiotic products,

(1)

where M is the genetic distance in Morgans (1M = 1 exchange) between two markers and RF is the fraction of recombinants. In the Haldane mapping function the RF reaches a theoretical maximum of ¹/₂ because of multiple recombination events: the second exchange event in a genetic interval restores the parental linkage of markers. As the genetic distance becomes large the probability of even numbers of crossovers (that remove recombinants) equals the probability of odd numbers of crossovers (that create recombinants). Hence, for two unlinked markers and a sufficiently large sample size the intermarker RF will reach a plateau of (¹/₂), which is the limiting multiplier in the Haldane equation.

In a similar fashion, the following equation relates diploid heterozygosity to genetic distance in those diploids arising from MII NDJ:

(2)

In this case, the RF_heterozygous is the fraction of diploids that are heterozygous for the locus being studied and m is the genetic distance between the marker being studied and the centromere. (We apply a lowercase m for the genetic distance between a marker and the centromere to distinguish from the uppercase M used for the genetic distance between two markers.) Because of the way that alleles assort into the diploids, the heterozygosity resulting from MII NDJ can range from 0 to 67%, so the Haldane multiplier of ¹/₂ becomes ²/₃, but the remainder of the equation is unchanged. By solving for m we can determine the genetic map distance of the locus from the centromere as a function of the frequency of heterozygosity in the MII NDJ diploids:

(3)

A similar equation describes the relationship between frequency of heterozygosity and genetic distance in those diploids arising from MI NDJ:

(4)

In this case, 1 - RF_heterozygous is the fraction of diploids that are homozygous for the locus being studied. Because of the way that alleles assort into the diploids, the homozygosity values for MI NDJ diploids can range from 0% for the centromere to 33% for an unlinked marker. Thus, the Haldane multiplier of ¹/₂ becomes ¹/₃. Solving for m gives the MI NDJ diploid mapping function

(5)

For PSS during MI, followed by random assortment of all the chromatids in both meiotic divisions, 67% of the diploid meiotic products are expected to be heterozygous for the centromere. This is because the centromeres become essentially nonfunctional for segregation and thus partition into the diploids with the same statistical probability as the various patterns by which the unlinked alleles can enter the ascus. Therefore, no diploid mapping function can be derived for PSS events, because markers linked to the centromere and markers unlinked to the centromere will each yield the same fraction (67%) of heterozygous diploids.

	RESULTS AND DISCUSSION

TOP ABSTRACT MATERIALS AND METHODS RESULTS AND DISCUSSION LITERATURE CITED

Centromere mapping functions for aberrantly segregated chromosomes:
In a normal (wild-type) meiosis, two rounds of chromosome segregation produce haploid meiotic products (Figure 1A). MI NDJ (Figure 1B), MII NDJ (Figure 1C), and PSS (Figure 1D) can be inferred from the segregation patterns of centromere-linked genetic markers. In S. pombe, most disomic aneuploids are unstable and cannot be readily studied (Figure 1E; NIWA and YANAGIDA 1985 ). However, because fission yeast contains only three pairs of chromosomes, aberrant chromosome segregation leads to a relatively high frequency of stable diploid meiotic products, thus permitting segregation analyses of all three pairs of chromosomes within individual meioses (KRAWCHUK et al. 1999 ).

View larger version (37K): In this window In a new window Download PPT slide   Figure 1. Types of chromosome segregation in meiosis based upon inheritance of centromere-linked markers. Only a single homologous chromosome pair is shown for the sake of clarity. The lines represent individual chromatids within homologous chromosomes. (A) Normal meiosis results in four haploid products. (B) Meiosis I nondisjunction: homologous chromosomes fail to segregate during the reductional division, resulting in meiotic products that contain two heterozygous chromosomes. (C) Meiosis II nondisjunction: sister chromatids fail to segregate during the equational division, resulting in meiotic products that contain two homozygous chromosomes. (D) Precocious separation of sister chromatids: if both sets of sister chromatids separate precociously, and individual chromatids distribute at random during both MI and MII, 67% of disomic or diploid spores will be heterozygous (MATERIALS AND METHODS). (E) Fates of meiotic products.

The principle of centromere mapping (Figure 2, A and B), coupled with the genetic mapping function of HALDANE 1919 , allowed us to develop mathematical functions that describe the relationship between the type of meiotic segregation error, the frequency of heterozygosity of any given locus in the meiotic diploids (or disomics), and the genetic distance of that locus from the centromere (Figure 2C). For alleles of loci unlinked to the centromere, 67% of the diploids will be heterozygous regardless of the type of missegregation that occurs. PSS will also produce 67% heterozygous diploids regardless of whether or not the marker is linked to the centromere. In contrast, any significant departure from 67% heterozygosity demonstrates that the locus in question is genetically linked to its centromere. Furthermore, heterozygosity values of >67% reveal MI NDJ events, while heterozygosity values of <67% reveal MII NDJ events (Figure 2C).

View larger version (37K): In this window In a new window Download PPT slide   Figure 2. Centromere mapping principles and practice. Loci can be mapped relative to the centromere based upon the frequencies of first division segregation (FDS; markers segregate during MI) and second division segregation (SDS; markers segregate during MII). (A) The centromere exhibits 100% FDS. (B) Recombination between the centromere and an unlinked locus generates 33% FDS and 67% SDS of alleles at that locus. Any deviation from 67% SDS of alleles indicates that the locus is linked to the centromere and the genetic distance can be calculated with a mathematical equation derived from the mapping function of HALDANE 1919 . This principle can be applied to the meiotic diploid (or disomic) spores to reveal both the segregational and recombinational history of loci relative to the centromere. (C) Mapping functions showing the relationship between the frequency of heterozygous diploids, the type of chromosome segregation error, and genetic distance. By definition, MI NDJ generates diploids that are all heterozygous at the centromere, while MII NDJ generates diploids that are all homozygous at the centromere. Departures from these diploid heterozygosity values are due to the genetic distance of the locus from the centromere (i.e., recombination, thick lines), or NDJ events of the opposite type (e.g., dashed line), or the presence of PSS, or some combination of the three. The diploid heterozygosity mapping function thus sets the upper limit for genetic distance and the lower limit for the type of NDJ. Diploid heterozygosity values from Table 2 are superimposed upon the mapping functions (thin lines)—these are further described in the text.

The assay system:
As a test of our mathematical functions, we examined chromosome segregation patterns in diploid meiotic products from one mutant (rec8) with a known defect in MI segregation and two mutants (rec10 and rec11) with known defects in MII segregation (MOLNAR et al. 1995 ; KRAWCHUK et al. 1999 ). We used strains that allowed us to monitor simultaneously the segregation of markers on all three chromosomes. As an internal control we used alleles of the ade6 locus, which is linked (12 cM) to the centromere of chromosome III. For chromosome II, we selected the mat1 locus, which maps ~100 cM from centromere II in wild-type cells. We also monitored the segregation of alleles of the pro2 and arg3 genes, which map close together ~300 cM from the centromere of chromosome I. If centromere-proximal recombination on chromosomes I and II were normal in the rec8, rec10, and rec11 mutants, we would expect the chromosome I and II marker alleles to assort independently of their centromeres. In other words, the markers on chromosomes I and II would be heterozygous in ~67% of the diploid meiotic products. Conversely, if centromere-proximal recombination were sufficiently reduced in the rec mutants, the markers would become linked to their respective centromeres and would therefore exhibit missegregation patterns characteristic of centromere-linked markers (MOLNAR et al. 1995 ; KRAWCHUK et al. 1999 ).

MI NDJ in rec8 mutants:
In the rec8 mutants, the ade6 alleles on chromosome III were heterozygous in 85% of the meiotic diploids (Table 2). This value falls on the MI NDJ curve (Figure 2C) and is significantly higher than the frequency (67%) of heterozygosity expected as a result of PSS. Thus, the chromosome III segregation defect is unlikely the result of PSS alone, and some MI NDJ must have occurred. But how much? It is not possible to determine the precise value, but the mapping functions allow us to set the absolute limits. Three possible models are considered.

Model 1, elevated recombination and 100% MI NDJ: Exclusively MI NDJ accompanied by some level of recombination might account for the data. Examination of the mapping functions (Figure 2C) or Equation 5 (MATERIALS AND METHODS) reveals that a genetic distance of 30 cM would produce the 85% heterozygosity that was observed (Table 2). In other words, a 2.5-fold increase in recombination relative to wild-type cells (Table 3) and 100% MI NDJ can explain the data. Recombination cannot have been increased by >2.5-fold, because this would further reduce the genetic linkage between centromere III and ade6, thereby producing a frequency of heterozygosity <85% (Figure 2C). However, 30 cM only defines the upper limit to the amount of recombination because some fraction of the homozygous diploids could have been generated by PSS and/or MII NDJ (Figure 1).

Model 2, normal recombination and 70–90% MI NDJ: In wild-type cells, ade6 is 12 cM from centromere III. Examination of the mapping functions (Figure 2C) or Equation 2 and Equation 4 (MATERIALS AND METHODS) can convert this into the frequency of heterozygosity at ade6 expected for each type of segregation error. Exclusively MI NDJ would produce 93% heterozygosity, exclusively MII NDJ would produce 14% heterozygosity, and exclusively PSS would produce 67% heterozygosity. One can determine algebraically what proportions of each would generate the observed 85% heterozygosity. Segregation errors of 70% MI NDJ and 30% PSS, or of 90% MI NDJ and 10% MII NDJ, would fit the data if recombination in the rec8 mutants occurred at wild-type levels. If both PSS and MII NDJ contribute to the segregation errors, then, depending upon their relative contributions, the frequency of MI NDJ would be somewhere between 70 and 90%.

Model 3, reduced recombination and 55–85% MI NDJ: In the absence of recombination, ade6 would be genetically inseparable from centromere III. Exclusively MI NDJ would produce 100% heterozygosity, exclusively MII NDJ would produce 0% heterozygosity, and exclusively PSS would produce 67% heterozygosity. Thus, segregation errors of 55% MI NDJ and 45% PSS, or of 85% MI NDJ and 15% MII NDJ, would fit the data if centromere III-proximal recombination were absent in the rec8 mutants.

In summary, the mapping functions demonstrate that between 55 and 100% of the rec8 mutant meioses suffered MI NDJ of chromosome III. While the mapping functions cannot provide the precise frequency, we favor a combination composed predominantly of MI NDJ and PSS. Centromere-proximal recombination is reduced in the rec8 mutant meioses (KRAWCHUK et al. 1999 ; PARISI et al. 1999 ), and 4.4% (genetic assay)–20% (cytological assay) of rec8 mutant meioses exhibit unambiguous PSS (MOLNAR et al. 1995 ), thus supporting model 3.

Similar results were obtained for the markers on chromosome II. In the rec8 mutants, the mat1 locus was heterozygous in 79% of the meiotic diploids (Table 2). This value falls on the MI NDJ curve (Figure 2C) and is significantly higher than the frequency (67%) of heterozygosity expected as a result of PSS. Exclusively MI NDJ accompanied by wild-type levels of recombination could account for the data (just on the edge of the 95% confidence interval). However, the mapping functions (Figure 2C) indicate that recombination is reduced two-fold or more between centromere II and mat1 (Table 3). Thus, the rec8 mutants suffer missegregation of chromosome II as a result of MI NDJ events accompanied by some level of PSS, MII NDJ, recombination, or some combination of the three. By the same rationale and types of calculations applied to the chromosome I data, the frequency of MI NDJ for chromosome II in the rec8 mutants must fall between 38 and 100%.

The chromosome I marker loci were heterozygous in 63% of the rec8 meiotic diploids (Table 2). The 95% confidence interval of the data encompasses an uninformative area at which the MI NDJ, PSS, and MII NDJ mapping functions converge. Exclusively MI NDJ accompanied by recombination, PSS, and exclusively MII NDJ accompanied by recombination would each produce ~67% heterozygosity (Figure 2C).

MII NDJ in rec10 mutants:
In the rec10 mutants the ade6 markers were heterozygous in 12% of the meiotic diploids (Table 2). This value falls on the MII NDJ curve (Figure 2C) and is significantly lower than the frequency (67%) of heterozygosity expected as a result of PSS. Thus, the rec10 mutants suffer some level of MII NDJ of centromere III. Exclusively MII NDJ accompanied by normal levels of recombination would produce 14% heterozygosity at ade6 (Figure 2C; MATERIALS AND METHODS, Equation 2), close to the observed value. The mapping functions also revealed an upper limit to the crossover frequency near that of wild-type meioses (Table 3), consistent with such a model. However, centromere-proximal recombination might be reduced much further, perhaps even eliminated, in the rec10 mutants. In that case, the observed 12% heterozygosity would be due to a low level of MI NDJ and/or PSS. Segregation errors of 82% MII NDJ and 18% PSS, or of 88% MII NDJ and 12% MI NDJ, would fit the data if centromere III-proximal recombination were absent. Therefore, the mapping functions demonstrate that between 82 and 100% of the rec10 mutant meioses suffer MII NDJ of chromosome III, and the precise value is dependent upon the relative additional contributions from recombination, MI NDJ, and PSS.

Nine percent of the rec10 mutant meiotic diploids were heterozygous for the mat1 locus on chromosome II (Table 2). Thus, the rec10 mutants suffer predominantly MII NDJ of chromosome II (Figure 2C). Interestingly, the maximum possible genetic distance in those meioses leading to aberrant segregation was 7.3 cM, which is 14-fold (or more) below that of wild-type cells (Table 3). In other words, centromere-proximal crossover recombination on chromosome II was reduced in those meioses with aberrant segregation. As discussed previously, the heterozygous diploids (9%) could be due to this residual recombination, to a low level of MI NDJ, to a low level of PSS, or to some combination of the three. By any of the models, between 87 and 100% of the rec10 mutant meioses suffer MII NDJ of chromosome II.

Similar observations and conclusions apply to the segregation patterns of chromosome I in the rec10 mutants (Table 2 and Table 3; Figure 2). A reduction of 10-fold (or more) in centromere-proximal recombination was observed in those meioses with aberrant segregation, and between 54 and 100% of the segregation errors are due to MII NDJ.

MII NDJ in rec11 mutants:
The results and conclusions for the rec11 mutants parallel those of the rec10 mutants (Table 2 and Table 3; Figure 2C). Each of the three chromosomes suffered MII NDJ of sister chromatids and centromere-proximal recombination was reduced at least eightfold and at least fivefold on chromosomes I and II, respectively, in those meioses with aberrant segregation. Between 47 and 100% (chromosome I), 66 and 100% (chromosome II), and 61 and 100% (chromosome III) of the segregation errors are due to MII NDJ.

Reduced centromere-proximal recombination in the rec8, rec10, and rec11 mutants:
Reduced centromere-proximal recombination was demonstrated for rec8 (chromosome II), rec10 (chromosomes I, II, and III), and rec11 (chromosomes I and II) mutant meioses with aberrant chromosome segregation (Table 3). Two studies of crossing over between pairs of markers have shown that recombination is reduced markedly near the centromeres of each of the three chromosomes in each of the rec8, rec10, and rec11 mutants, but recombination toward the telomeres occurs at nearly wild-type levels (KRAWCHUK et al. 1999 ; PARISI et al. 1999 ). Because those studies looked at the majority of meioses, and this study examined only those meioses in which the chromosome missegregation could be scored genetically, it is not possible to make a direct comparison. However, centromere-proximal recombination may actually be reduced on each chromosome in each of those rec8, rec10, and rec11 mutant meioses leading to diploidy. The mapping functions reveal the maximum possible genetic distance between a marker and its centromere and therefore probably underestimate the magnitude of the centromere-proximal recombination defects. If, for example, some fraction of rec10 or rec11 mutant meioses suffered MI NDJ, then the amount of centromere-proximal recombination that occurred could actually be considerably lower than calculated based upon the assumption of 100% MII NDJ at the centromeres (e.g., dashed line in Figure 2C). A similar rationale applies to the rec8 mutant meioses, which have predominantly MI NDJ errors.

Cohesion, crossovers, and segregation:
It has been reported that the rec8⁺, rec10⁺, and rec11⁺ genes encode chromosome III-specific activators of recombination (DEVEAUX and SMITH 1994 ; FOX and SMITH 1998 ). That claim seems indefensible in light of the results of this study and others (MOLNAR et al. 1995 ; KRAWCHUK et al. 1999 ; PARISI et al. 1999 ). The rec8⁺ gene actually encodes a sister chromatid cohesion (cohesin) protein required for normal sister chromatid cohesion, homologous chromosome pairing, and MI chromosome segregation. The rec8-110 mutation is epistatic to rec10-109 and to rec11-111, thereby defining a genetic pathway. And the rec10⁺ and rec11⁺ genes are required for proper segregation of sister chromatids during MII. These genes are proposed to encode components of a pathway required to establish, maintain, and appropriately release meiotic interactions between homologous chromosomes (KRAWCHUK et al. 1999 ). Hypotheses of how sister chromatid cohesion and crossover position work synergistically to ensure the fidelity of chromosome segregation in each of the two meiotic divisions can be found in that study.

The utility of the mapping functions:
The new mapping functions permit the simultaneous analysis of centromere-proximal recombination and chromosome segregation defects. There are three principal advantages of these functions. First, it is not necessary for the marker to be tightly linked to the centromere in wild-type cells, nor is it even necessary to know the map distance between the marker and its centromere in wild-type cells. Any significant deviation from 67% heterozygosity in the meiotic aneuploids proves that the locus is linked to its centromere. Thus, one can readily map loci relative to the centromeres in mutant meioses or even in otherwise wild-type meioses with spontaneous nondisjunction events. Second, the frequency of heterozygosity provides a direct readout of the type of meiotic missegregation. Any significant deviation from 67% heterozygosity must be due to either MI NDJ or MII NDJ; the type of error and the lower limit to its magnitude can be read directly from the mapping functions (Figure 2C). And third, these functions may be applied to any organism in which diploid or disomic meiotic products can be studied. While it is easiest to visualize the derivation of the mapping functions for organisms with ordered tetrads (Figure 2), the functions will work equally well for organisms without ordered tetrads.

There are also three limitations to the new mapping functions. First, they only reveal the upper limit to the genetic distance between any given marker and its centromere (Figure 2C). Second, they only reveal the lower limit to the type of NDJ (Figure 2C). And third, it is not possible to map the distance between a marker and the centromere in those meioses that undergo predominantly PSS. Nevertheless, these functions can provide a better understanding of the relationship between meiotic recombination and chromosome segregation.

	ACKNOWLEDGMENTS

We thank Aaron Graff, Jürg Kohli, Ning Kon, Michael Lichten, Gisela Mosig, and Wallace Sharif for helpful suggestions; Calley Hardin and Steve Lindsey for laboratory assistance; and Gerry Smith for providing yeast strains. This work was supported by a grant from the National Institutes of Health (GM54671) and by pilot project funds from the Vanderbilt University Research Council. M.D.K. was supported in part by a training grant from the National Institutes of Health (CA09582) and W.P.W. was a Leukemia Society of America Special Fellow (3021-94) for a portion of this research.

Manuscript received January 14, 1999; Accepted for publication May 27, 1999.

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