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Corresponding author: Kenneth C. Burtis, 1 Shields Ave., University of California, Davis, CA 95616., kcburtis{at}ucdavis.edu (E-mail)
Communicating editor: K. G. GOLIC
| ABSTRACT |
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In a screen for new DNA repair mutants, we tested 6275 Drosophila strains bearing homozygous mutagenized autosomes (obtained from C. Zuker) for hypersensitivity to methyl methanesulfonate (MMS) and nitrogen mustard (HN2). Testing of 2585 second-chromosome lines resulted in the recovery of 18 mutants, 8 of which were alleles of known genes. The remaining 10 second-chromosome mutants were solely sensitive to MMS and define 8 new mutagen-sensitive genes (mus212mus219). Testing of 3690 third chromosomes led to the identification of 60 third-chromosome mutants, 44 of which were alleles of known genes. The remaining 16 mutants define 14 new mutagen-sensitive genes (mus314mus327). We have initiated efforts to identify these genes at the molecular level and report here the first two identified. The HN2-sensitive mus322 mutant defines the Drosophila ortholog of the yeast snm1 gene, and the MMS- and HN2-sensitive mus301 mutant defines the Drosophila ortholog of the human HEL308 gene. We have also identified a second-chromosome mutant, mus215ZIII-2059, that uniformly reduces the frequency of meiotic recombination to <3% of that observed in wild type and thus defines a function required for both DNA repair and meiotic recombination. At least one allele of each new gene identified in this study is available at the Bloomington Stock Center.
THE ability of cells to reproduce their genome accurately requires both continuous monitoring of the integrity of the DNA complement and efficient repair of damage to the DNA. Coordination of these processes is required for proper completion of DNA replication and cell division, and it is crucial that cells be able to recognize damaged or incompletely replicated DNA to halt the cell cycle while damage is repaired and, most critically, to accurately repair that damage. In higher eukaryotes, impediments to repair can lead to high frequencies of mutation, cancer, and in some cases, cell or organismal death. DNA damage involves a variety of molecular lesions, including double-strand breaks (DSBs) of the DNA duplex, nicks in a single strand, creation of abasic sites, and a plethora of covalent chemical modifications. These modifications include covalent linkage of a variety of large and small adducts to the bases, as well as creation of intra- and interstrand crosslinks between bases. Damage can result both from external causes, including exposure to chemical mutagens and ionizing radiation, and from interaction with reactive species generated through normal cellular oxidative metabolism.
The repair of such disparate types of damage requires the action of a variety of qualitatively different DNA repair systems. To date, there is biochemical and genetic evidence from bacteria, yeast, and other higher eukaryotic systems for >130 distinct proteins involved in recognition and repair of DNA damage (![]()
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Genes that do not actually participate in the physical correction of damaged sequences may nonetheless be considered to be part of the DNA repair machinery of the cell. For example, error-prone DNA polymerases permit trans-lesion synthesis past damaged bases, allowing a cell to complete DNA replication despite the persistence of damage (![]()
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Work on DNA repair in Drosophila began over 2 decades ago with the first screens for repair-deficient mutants (![]()
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Despite the success of these earlier screens, two lines of evidence suggested that there were many more such genes to be identified in Drosophila. First, numerous Drosophila proteins similar in amino acid sequence to known repair proteins from other species, but not associated with a specific mutagen-sensitive mutation, have been predicted through comparative analysis of the Drosophila genome sequence (![]()
We report here a screen of 6275 homozygous viable mutagenized lines (derived from the Zuker collection) for new mutants that were sensitive to methyl methanesulfonate (MMS) and/or nitrogen mustard (HN2). Of the 78 mutants recovered, 52 represent additional alleles of known genes. One of these, mus301, we have identified as the Drosophila ortholog of the human HEL308 gene. The remaining 26 new mutants define 22 new genes. Characterization of the 78 mutants is described below. One of these genes (mus322) has been characterized at the molecular level and shown to encode the Drosophila homolog of the interstrand crosslink repair gene snm1 (![]()
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| MATERIALS AND METHODS |
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Acquisition of stocks:
The Zuker laboratory created a collection composed of 6000 second-chromosome and 6200 third-chromosome lines obtained following mutagenesis with 25 mM EMS (![]()
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At least one allele of each new gene identified in this study is available at the Bloomington Stock Center. The Hawley laboratory in Kansas City maintains all other alleles.
Screening for mutagen sensitivity:
The screen consisted of three consecutive rounds of mutagen-sensitivity testing: In the first round, the 6275 lines from the second (2585) and third (3690) chromosomes were tested with the appropriate concentrations of MMS and HN2 (see above). Young males and females from each line were transferred into a fresh vial and were allowed to lay eggs for 24 hr at room temperature. After 48 hr, these first vials were treated with MMS. At the end of the first 24 hr, the parents were transferred into a second vial and were allowed to lay eggs for an additional 24 hr. After 48 hr, these second vials were treated with HN2. At the end of 24 hr, the second-vial parents were transferred to a third vial and were allowed to lay eggs for 24 hr and then discarded. The third vials were the controls for round 1. All vials were scored on the fifteenth day after the beginning of egg laying. Lines were considered mutagen sensitive if either mutagen-treated vial had a homozygote/balancer heterozygote ratio that was <10% of the homozygote/balancer heterozygote ratio of the untreated control vials.
A total of 1558 balanced lines (681 from the second chromosome and 877 from the third chromosome) entered round 2 of the screen. For round 2, we followed a similar protocol as in round 1, except that all lines went through the screen as paired vials. The mutagen treatments also changed in this round, with lines receiving 0.05 and 0.025% MMS treatments and 0.003 and 0.005% HN2 treatments. During the first half of this round, it was determined that no significant difference in sensitivity occurred between the two concentrations of MMS or HN2; thus, the last half of the round 2 lines were treated with only 0.05% MMS or 0.005% HN2. A total of 507 lines (210 from the second chromosome and 297 from the third chromosome) entered round 3 of the screen. To increase the number of progeny tested, round 3 lines were brooded in bottles. The transfer/treatment protocol was the same as round 1; the mutagen treatments remained at 0.04% MMS and 0.003% HN2 for both second- and third-chromosome lines.
Complementation testing:
We isolated a total of 78 mutagen-sensitive lines: 18 on the second and 60 on the third chromosome. All 78 lines were complementation tested with the following extant mutagen-sensitive mutations: mus201D1, mus202A1, mus204A1, mus205A1, mus206A1, mus207D1, mus209B1, mus210B1, mus211B1, rad2011, grp1, and okrWS for the second-chromosome lines and mus301D4, mus302D5, mus304D1, mus304D3, mus305D2, mus306D1, mus307D1, mus308D16 (mus308 was tested only with HN2-specific lines), mus309D3, mus310D1, mus311D1, and mus312D1 for the third-chromosome lines.
For complementation tests, 48 virgin heterozygotes of mutant line "A" were crossed to 510 male heterozygotes of mutant line "B." All crosses were performed at 25°. The virgins and males were placed in a fresh vial and maintained there for 48 hr. After 48 hr, flies were transferred to a second vial, and the first vial was treated with MMS. After 48 hr, flies were transferred from the second vial to a third vial, and the second vial was treated with HN2. The third vial served as the nonmutagenized control. All vials were scored on day 15. Mutants were arbitrarily defined as "failing to complement" if the ratio of [trans-heterozygote (musA/musB)]/[balancer/mus] in mutagen-treated vials fell between 0 and 30% of the control trans-heterozygote/balancer heterozygote ratios. Two mutants were likewise said to complement each other if the ratio of [trans-heterozygote (musA/musB)]/[balancer/mus] in mutagen-treated vials was at least 50% of the control homozygote/heterozygote ratios. Crosses were retested if they fell between 30 and 50%. In most cases, the profile of mutagen sensitivity observed for one of our newly isolated alleles matched that of other previously studied alleles of that gene.
Mutagen preparation:
All mutagens were diluted to the appropriate concentration with double-deionized water. The MMS mutagen solution was made from a stock of 99.99% MMS. The HN2 mutagen solution was prepared from a stock of 10% HN2 in 0.1 N HCl. Vials (25 mm in diameter) were treated with 250 µl of mutagen solution, while bottles (64 mm in diameter) were treated with 1 ml of mutagen solution.
Measurement of meiotic nondisjunction:
Selected homozygous mutagen-sensitive mutants were tested for chiasmate X nondisjunction, including rad201ZII-0670, mus201ZII-1953, mus212ZII-1436, mus212ZII-4368, mus213ZII-6078, mus215ZII-2059, mus217ZII-5470, mus218ZII-5841, mus219ZII-5970, mus302ZIII-1882, mus302ZIII-6004, mus305ZIII-1990, mus305ZIII-2140, mus305ZIII-5909, mus312ZIII-1973, and mus314ZIII-2504. One to three homozygous virgins were crossed to 610 XY,y+ v f B; C(4), ci eyR males at room temperature. Crosses were scored and nondisjunction frequencies calculated as described (![]()
| RESULTS |
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To begin the screen, it was necessary to determine the background sensitivity of the second- and third-chromosome parental flies to both MMS and HN2. For the third chromosome, we transferred the bw/bw; st/st siblings into fresh vials and allowed them to lay eggs for 24 hr at room temperature. The cleared vials were aged for an additional 24 hr to permit all embryos to hatch and then treated with varying concentrations of MMS (0.0250.2%) or HN2 (0.0030.02%). Parents transferred from the first vial were allowed to lay eggs in a second vial for an additional 24 hr and then removed. After an additional 24-hr period, the second vials were treated with water. Concentrations of MMS (0.04%) and HN2 (0.003%) were identified that permitted 5080% survival when comparing the mutagenized bw/bw; st/st flies to unmutagenized bw/bw; st/st flies. These concentrations were used in subsequent studies. On the basis of similar studies using the second-chromosome parental line, the second-chromosome experimental lines were tested using the same dosages (0.04% MMS and 0.003% HN2).
The second chromosome:
After discarding the lines bearing recessive lethal or semilethal mutations, 2585 second chromosomes were tested for mutagen sensitivity. Approximately 0.7% (18/2585) of these lines were shown to be sensitive to MMS. Sensitivity data for these lines are reported in Table 2. Although the frequency with which we recovered mutagen-sensitive mutants was approximately fivefold higher than that previously obtained from EMS-mutagenized second chromosomes (0.1%, or 5/4039; ![]()
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All 18 newly identified second-chromosome mus mutants were tested for the ability to complement known second-chromosome mus mutants mus201D1, mus202A1, mus204A1, mus205A1, mus206A1, mus207D1, mus209B1, mus210B1, mus211B1, rad2011, grp1, and okrWS. As shown in Table 3, of the 18 second-chromosome mutants, 8 are new alleles of existing mutants [mus201 (1), mus205 (4), okra (1), and rad201 (2)]. As shown in Table 4, the remaining 10 mutants were complementation tested in all pairwise combinations and shown to define 8 new mutagen-sensitive genes, all of which were uniquely sensitive to MMS. Two of these genes, mus212 and mus213, are defined by more than one new allele.
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Both alleles of mus212 (mus212ZIII-1436 and mus212ZIII-4368) are female sterile; females homozygous for either of the two mutants fail to lay eggs. When initially analyzed, mus215ZII-2059 females, although fertile, displayed a severe defect in meiotic recombination. Females of the genotype y cv v f car/+; mus215ZII-2059 displayed both very high levels of X chromosome nondisjunction (20.9%, N = 1331) and levels of meiotic recombination that were <3% of those observed in wild type. Curiously, the observed decrease in recombination was not polar, as is observed for most recombination-defective mutants (![]()
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The third chromosome:
After discarding the lines bearing recessive lethal or semilethal mutations, 3690 third chromosomes were tested for mutagen sensitivity. Approximately 1.4% (53/3690) of these lines were shown to be sensitive to MMS. Sensitivity data for these lines are reported in Table 5. Again, the frequency with which we recovered MMS-sensitive mutants was
5-fold higher than the frequency (0.3%, 31/11,334) of MMS-sensitive mutants previously obtained (![]()
10-fold lower dose (3 mM) of EMS.
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All 60 newly identified third-chromosome mus mutants were tested for the ability to complement known third-chromosome mus mutants mus301D4, mus302D5, mus304D1, mus304D3, mus305D2, mus306D1, mus307D1, mus308D16, mus 309D3, mus310D1, mus311D1, and mus312D1. As shown in Table 6, 44 of the 60 third-chromosome mutants were alleles of existing mutants [mus301 (8), mus302 (5), mus304 (2), mus305 (24), mus308 (3), and mus312 (2)]. The identity of the two new alleles of mus312 has been verified by sequence analysis (![]()
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The remaining 16 mutants define 14 new mutagen-sensitive genes (mus314mus327). Mutants in 7 of these genes were hypersensitive only to MMS (mus314mus320), mutants in 3 genes (four total alleles) were hypersensitive only to HN2 (mus321mus323), and mutants in 4 of these genes (five total alleles) displayed sensitivity to both MMS and HN2 (mus324mus327). For the 16 novel third-chromosome mutants, inter se complementation tests were performed within phenotypic groups. Because it is possible that mutants in different phenotypic classes could be allelic, the number of unique new third-chromosome genes identified in this study may be an overestimate; indeed, one example of this was noted after completion of our studies.
All pairwise combinations of the seven MMS-sensitive mutants displayed full complementation, thus defining seven new genes. Among the five mutants that were sensitive to both MMS and HN2, one gene (mus324) was defined by two alleles. The remaining three mutants define novel genes. Finally, all three novel mutants that were solely sensitive to HN2 fully complemented each other in all pairwise combinations and also complemented an allele of the mus308 gene. These three genes thus provide a substantial increase in the number of Drosophila genes whose products might function specifically in interstrand crosslink repair. As described below, one of these three genes was examined at the molecular level and shown to define the fly ortholog of the crosslink repair gene snm1, first characterized in S. cerevisiae (![]()
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Identification of snm1:
As noted above, our screen identified only seven lines that were uniquely hypersensitive to HN2. Of the seven new mutants, three were determined to be alleles of mus308, the only previously characterized Drosophila gene whose mutant phenotype included hypersensitivity only to agents capable of creating DNA interstrand crosslinks (![]()
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Both ZIII-4709 and ZIII-2589 possess mutations not present in the ZIII-0708 sequence or in the sequence of the CG10018 gene from GenBank (Fig 1A). The sequence of CG10018 in mus322ZIII-2589 flies revealed a missense mutation resulting in substitution of an evolutionarily conserved cysteine residue (Cys357 in the Drosophila sequence) by tyrosine, while the sequence in mus322ZIII-4709 flies revealed a missense mutation resulting in substitution of an evolutionarily conserved glycine residue (Gly377) by glutamic acid (Fig 1B). Drosophila SNM1 is a member of a large superfamily of proteins that include the metallo-ß-lactamase fold domain (![]()
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3' exonuclease activity as well as endonucleolytic activity in complex with DNA-PK (![]()
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The mus301/spnC gene corresponds to the Drosophila gene CG7972 and is the Drosophila ortholog of the human gene HEL308:
The Drosophila gene CG7972 encodes a polypeptide (CG7972-PA) very similar (29% identity) to the helicase domain of the interstrand crosslink repair gene mus308. The orthologous polypeptide encoded by the human gene HEL308 (41% identical to CG7972-PA) has been demonstrated to possess 3'-5' DNA helicase and DNA-dependent ATPase activities in vitro (![]()
The discovery that an allele of CG7972 was mutagen sensitive led us to question whether it might correspond to any previously discovered mus genes not yet characterized at the molecular level. CG7972 maps to cytological location 66B8 (![]()
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The P-element-induced CG7972 mutant allele was tested for its ability to complement the mutagen sensitivity of three alleles of mus301, using 0.08% MMS as a mutagen. Alleles tested included one previously isolated allele (mus301D5; ![]()
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The identification of the Drosophila ortholog of the human HEL308 gene as mus301/spn-C provides the first evidence suggesting that the HEL308 protein may function in recombinational repair of DNA DSBs. Other members of the "spindle" class of female-sterile mutations in Drosophila have been identified as mutations in okra, the Drosophila ortholog of the S. cerevisiae RAD54 gene (![]()
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| DISCUSSION |
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Mutagen sensitivity and DNA repair pathways:
There is a complex relationship between the specific hypersensitivity displayed by each mus mutant (MMS only, HN2 only, or both mutagens) and the repair pathway defined by that mutant.
The most abundant products of MMS treatment are 7-methyl guanine (7MeG) and 3-methyl adenine (3MeA) residues, which are nonbulky adducts classically repaired by the base excision repair (BER) pathway (![]()
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The most frequent class of mutants obtained in the screen reported here were those uniquely sensitive to MMS. The genes identified presumably encode functions not required for repair of types of damage either unique to HN2, such as interstrand crosslinks, or common to both mutagens, such as DSBs. The one known example found in this screen was new alleles of mus205, which encodes the catalytic subunit of DNA polymerase
. This polymerase is capable of trans-lesion synthesis across damaged bases on the template strand and is critical for survival of MMS-treated cells (damage tolerance). However, the lack of sensitivity to HN2 indicates that mus205 is not essential for repair of the bulky adducts, interstrand crosslinks, and DSBs likely created by HN2 at the concentration tested. The S. cerevisiae homolog of mus205, rev3, is likewise not essential for DSB repair (![]()
The second class of mutants identified was that sensitive to both mutagens. Although fewer of these were found in the screen reported here, this class is equal in abundance to the MMS-specific class among the entire set of Drosophila mutagen-sensitive mutants found to date. Examples of this class include components of the NER pathway, including mus201 (XPG; ![]()
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An intriguing result of our screen is the identification of two new mutants, in addition to mus308 and snm1, displaying specific hypersensitivity to HN2. Mapping and characterization of these genes is in progress, and preliminary results suggest the existence of at least two pathways as defined by epistatic interactions (L. CHANG and K. C. BURTIS, unpublished data). Although previous studies have indicated the importance of components of multiple pathways, including NER, recombinational repair, and damage tolerance, in repair of interstrand crosslinks, these pathways are also known to be involved in the repair of damage created by MMS (![]()
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To what degree have this and previous screens saturated the autosomes for mus genes?
Two alternative approaches were used to estimate the degree to which saturation has been achieved in the screens to date for autosomal genes that can be mutated to produce alleles that are both homozygous viable and mutagen sensitive. Both estimatesone derived by comparison with the number of known DNA repair functions identified to date in other organisms and the other derived from a statistical approach based on the number of alleles recovered for each complementation groupsimilarly conclude that mutations have been recovered in
50% of mutable loci.
An analysis of the human genome suggests the presence of
130 genes involved in DNA repair (![]()
The traditional method of approximating the number of "hit-able" genes in Drosophila relies on the use of the Poisson distribution. This method assumes that all genes are mutable with an equal frequency and allows one to estimate the number of "un-hit" genes by the equation P(0) = em on the basis of the average number of alleles per mutable locus (m). Using this method, previous workers have estimated that the Drosophila genome might contain some 5560 genes capable of mutating to mutagen sensitivity (![]()
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Unfortunately, the method in which the Poisson has classically been applied has two major problems. The first problem inherent in the application of the Poisson to estimate the number of target loci is that not all genes are equally mutable. The total collection of mus mutants in Drosophila and our own set of newly isolated mutants clearly contain a substantial number of hypermutable or "jackpot" loci. For example, while only 1 or 2 alleles were recovered for most loci, 8 alleles were recovered for mus301 and 27 alleles were recovered for mus305. Inclusion of such loci would invalidate any estimate of saturation using a Poisson distribution, because it would artificially increase the mean number of alleles per locus. Although others have addressed this difficulty by simply excluding these types of outliers from the calculation of m, it is not clear where to draw the line when considering such loci as mus205, with six alleles.
The second difficulty in the use of the Poisson distribution lies in the method by which m is calculated. Traditionally, m has been determined simply by dividing the number of mutations recovered by the total number of loci they define. The problem is that an accurate estimation of the mean requires knowing the answer that one is trying to obtain, namely the number of un-hit loci. When a screen is approaching saturation, the difference between total loci and loci for which mutant alleles have been recovered may become small enough that ignoring this difference will not greatly affect the result. However, when saturation is low or moderate, ignoring this difference will cause the degree of saturation to be drastically overestimated. These difficulties were anticipated by T. H. Morgan and H. J. Muller (![]()
One effective method, first used by COHEN (1960), gives a maximum-likelihood estimate of m by simply taking the mean number of alleles per gene from the sample mean (alleles/identified locus) and then looking up m from a table. Again, this method requires the investigator to determine where to draw the line between what is an outlier and what is to be included in the calculation. We propose an alternative approach that does not require a subjective decision with respect to outliers. This method is derived from a comparison of the first few classes of the Poisson distribution itself: namely P(0) = em, P(1) = mem, and P(2) = m2/2 em [where P(X) is the proportion of loci with X alleles]. Dividing P(1) by P(2) gives you 2/m. Note that although P(1) and P(2) are both proportions, and thus are dependent upon the size of all of the other classes, their ratio is independent of these classes. Thus, P(1)/P(2) = N(1)/N(2), where N(X) is the total number of loci recovered with X alleles, and m is easily calculated as:

As shown in Fig 2, the percentage of saturation follows directly from the Poisson distribution as 100 (1 em). We favor this method, because not only does it allow for calculation of m without assuming that the P(0) class is small, but also it eliminates the need for the investigator to determine where the line should be drawn as to what is an outlier and what is not. Although we believe this approach to be preferable to a traditional use of the Poisson distribution, it is not without its problems: when either or both N(1) and N(2) are very small, the calculation of m is subject to large fluctuations as a result of sampling error.
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The use of this method to estimate the degree of saturation for the second chromosome provides an answer that is pleasingly consistent with the estimate initially described above, which was based on genomic comparisons. For the second chromosome, 10 loci were defined by one allele and 6 loci were defined by two alleles. By using Fig 2, we can estimate that the second chromosome is 70% saturated and that the total number of mus loci on chromosome 2 may lie somewhere in the vicinity of 40. Application of the methods described by ![]()
50% saturation. On the basis of these estimates, one would predict that there are
3550 genes on the second chromosome that can mutate to a mus phenotype, a number in reasonable agreement with the estimate of some 50 DNA repair genes obtained by genomic analysis.
The analysis of the third chromosome is substantially more complicated for two reasons (Table 7). First, statistically, the estimation is made less useful because the number of genes defined by only two alleles is only 2. Given that the number of genes defined by a single allele (16) is large, it is very difficult to accurately assess the degree of saturation. The second problem lies in our suspicion that the excess of single-hit loci on chromosome 3 reflects a substantial number of genes that we would classify as hypo-mutable, either because only very rare changes produce a mutagen-sensitive phenotype or because that phenotype is exhibited only under certain treatment conditions or genetic backgrounds and not in others. We note, for example, that none of the new third-chromosome mus mutants reported here were allelic to the three previously characterized loci that had been defined by single alleles (mus306, mus307, and mus310). In all cases where new alleles of extant genes were obtained, they fell in genes already defined by two or more alleles. Similarly, among the 14 new third-chromosome genes identified in our screen only 2 were defined by two or more alleles. We imagine that, had we continued our screens for third-chromosome mus mutants, the result would have been more alleles of already well-represented genes and a large population of new single-hit loci, rather than a further population of the class of existing loci defined by single mutants.
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While we believe that the use of N(1) and N(2) to estimate saturation (when both are reasonably large) is an improvement over the classical method of estimation, because of its intuitive and practical simplicity, we anticipate that further progress in identifying repair-deficient loci in Drosophila will not be limited to screens such as the one described. Rather, we suspect that mus mutants will also be obtained by the use of reverse genetics to create mutants in genes defined by sequence homology or by the demonstration of a repair-deficient phenotype for mutants initially defined by other means. The rad54 mutants created by Eeken and collaborators (![]()
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The continued acquisition of mus mutants by all of these means will further complete the genetic tool box for the analysis of DNA repair in Drosophila. As the remaining repair-deficient genes are identified and the biochemical functions of their protein products are elucidated, we will begin to address the variety of roles these proteins play not just in repair, but also in normal cellular processes, such as the control of meiotic and mitotic cell cycles, the coupling of replication to cell division induction, the facilitation of meiotic recombination, and the maintenance of active or inactive states of chromatin. The multiple roles played by some of the existing mutants in processes such as heterochromatic condensation and control of chorion gene amplification serve to remind us that the functions once thought of solely as "repair proteins" may indeed play much wider roles in the developmental process (![]()
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| FOOTNOTES |
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1 These authors contributed equally to this work. ![]()
| ACKNOWLEDGMENTS |
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We thank Ed VanVeen for help in coping with the estimates of saturation, as well as Bill Gilliland, Arcady Mushegian, and Galina Glazko for their valuable insights into this matter. We acknowledge Li-Ping Chang, Josh Deignan, Katie Hollis, Dawn Milliken, Valerie Jackson, Coleen O'Neil, Heidi Schoenhard, Jim Ward, Sarah Wayson, Brian Williams, and David Yao for their help with this project at the University of California at Davis. R.S.H. and K.C.B. gratefully acknowledge the participation of Gerry Rubin during the early stages of this project and acknowledge Jeff Sekelsky and Michael Brodsky for stimulating discussion. The influence of the late Professor James Boyd, our friend and colleague for many years, was felt throughout this project. This research was supported by the Department of Energy (grant DE-FG03-99ER62722 to R.S.H. and KCB) and the National Science Foundation (grant MCB-0111011 to K.C.B.).
Manuscript received June 21, 2003; Accepted for publication January 22, 2004.
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