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Essential genes in the hDp16/hDp19 region of chromosome I in Caenorhabditis elegans McDowall, Jennifer Susan 1990

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E S S E N T I A L G E N E S I N T H E hDpl6/hDP19 R E G I O N O F C H R O M O S O M E I I N CAENORHABDITIS ELEGANS By JENNIFER SUSAN McDOWALL B.Sc, Edinburgh University, 1983 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES GENETICS PROGRAMME We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1990 © Jennifer Susan McDowall, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. The University of British Columbra Vancouver, Canada Department DE-6 (2/88) i i A B S T R A C T This thesis describes the genetic analysis of a small region of the Caenorhabditis elegans genome. The region analyzed was defined b}' the 0.5 map unit interval between the breakpoints of the duplications hDpl6 and hDpl9, which lies within the dpy-5 unc-13 region on chromosome I. The analysis consisted of the identification and characterization of essential genes in this region. A l l the lethal mutations analyzed came from a set of 495 EMS-induced, sDp£-rescued lethals described in Howell (1989). The lethal mutations have been maintained as homozygotes, made viable by the presence of a wild-type allele on the sDp2 duplication. I used a combination of mapping techniques to analyze over 200 EMS-induced lethal mutations. A total of 189 new lethal mutations were positioned within the dpy-5 unc-13 interval. Three methods were used for mapping: recombination analysis, lethal rescue using duplications, and deficiency mapping. Duplication mapping was found to be the fastest and most precise method used. 178 of the new lethal mutations were mapped relative to the duplication breakpoints of hDplS, hDpl6, and hDpl9. These three duplications divided the dpy-5 unc-13 region into three approximately equal-sized zones. This study completes the mapping of the 495 lethals in the sDp2 set. In addition, thirty-three previously identified essential genes lying between dpy-5 unc-13 were positioned with respect to the breakpoints of the duplications hDplS, hDplS, hDplS, hDpl6, hDpll, and hDpl9. The dpy-5 unc-13 region carries a relatively large number of loci, therefore, I decided to concentrate on the smaller hDpl6/hDp 19 interval within this region. Complementation analysis was used to define the number of essential genes in the iii hDP16/hDpl9 region. A total of eight new genes were described, six tying in the hDpl6/hDP19 region, two lying just outside this region. This brings the total number of essential genes in the hDP16/hDpl9 region to sixteen. In addition, as a result of my mapping data, the hDpl6/hDpl9 region has been subdivided into six intervals with respect to duplication and deficiency breakpoints. The stage of developmental arrest was determined for both the essential genes, and the new lethal mutations (ie. not yet defined by complementation tests), in the dpy-5 unc-1 S interval. Although the number of genes studied was not great, the data suggests a relationship between map position and time of developmental arrest. The average forward mutation rate for C. elegans genes was determined to be 5.8 X mutations per gene. I have made a comparison of the forward mutation rates of the essential genes in the hDpl6/hDpl9 region, bli-4 was found to be the most mutable target in the region with nine mutant alleles, giving a forward mutation rate six times higher than average. In the hDpl6/hDpl9 region, ten of the sixteen essential genes were represented by more than one allele. The minimum estimate of the number of essential genes in the region using a truncated Poisson calculation was twenty. Therefore, the sixteen genes identified represent. 80% of the essential genes in this region. This data was extrapolated to give a minimum estimate of approximately 225 essential genes in the 15 m.u. sDp2 region, and 4,500 essential genes in the C. elegans genome. This research has established the hDpl6/hDpl9 region as a genetically well-defined system for studying the genetic organization of essential genes, as well as the developmental regulation of gene expression, and the functional relationship between adjacent genes. IV T A B L E O F C O N T E N T S Abstract i i List of Tables vi List of Figures vii I N T R O D U C T I O N 1 M A T E R I A L S A N D M E T H O D S 7 Nomenclature 7 Stock Maintenance and Strains S Chromosomal Rearrangements 12 1) Duplications 12 2) Deficiencies 14 3) Translocations 14 Mapping Genes 16 1) Recombination Mapping 16 2) Mapping by Complementation to Duplications 22 i) Mapping Known Genes 22 ii) Mapping New Mutations 26 iii) Mapping the hDpl6/hDpl9 Region 26 3) Mapping by Complementation to a Deficiency 27 Complementation Analysis of Lethal Strains 29 Determining the Stage of Developmental Arrest 31 Test for Sperm-defective Mutants 34 R E S U L T S 35 Recombination Mapping 35 Mapping by Complementation to Duplications 39 i) Mapping Known Genes 39 ii) Mapping New Mutations iii) Mapping of the h.Dpl6/hDpl9 Region Mapping by Complementation to a Deficiency Complementation Analysis of Lethal Strains i) Recombination Mapped Lethals ii) Duplication Mapped Lethals Stage of Arrest of Lethal Mutations in dpy-5 unc-13 Region Test for Sperm-defective Mutants D I S C U S S I O N Comparison of Mapping Techniques Stage of Developmental Arrest % Saturation for Essential Genes in hDpl6/hDpl9 Forward Mutation Rates Total Number of Genes in C. elegans Genome Summary Proposals for Future Research B I B L I O G R A P H Y A p p e n d i x ^ 1: Strains Used Append ix#2: Strains of New Lethal Mutations Used Appendix#3: Duplication Mapping Results for New Mutations Appendix#4: Complementation Results for Recombination Mapped Mutations Appendix#5: Complementation Results for Duplication Mapped Mutations Appendix#6: Inter se Complementation Results for genes in hDpl6/hDp 19 Region Appendix#7: Truncated Poisson Formula vi LIST OF TABLES #1 Genes Used in this Study 9 #2 Two-factor Mapping Data for New Lethal Mutations 37 #3 Duplication Mapping Results for Essential Genes in dpy-5 unc-13 42 #4 Allocation of New Mutations 48 #5 Results of Fertility Tests for Homozygotes carrying hDpl9 49 #6 Strain Names for putative two-hit lethals 49 #7 Duplication Mapping Results for Essential Genes in hDpl6/hDP19 52 #8 Deficiency Mapping Results for Essential Genes in hDpl6/hDpl9 54 #9 Recombination Mapped New Essential Genes in dpy-5 unc-13 57 #10 Duplication Mapped New Essential Genes in hDpl6/hDpl9 59 #11 Stage of Developmental Arrest for Lethals in hDpl6/hDpl9 62 #12 Chi-square Test for Arrest of Mutations in dpy-5 unc-13 78 #13 Chi-square Test for Arrest of Genes in dpy-5 unc-13 79 #14 Poisson Distribution of Mutations 83 vii LIST OF FIGURES #1 Genetic Map of Essential Genes in sDp2 11 #2 Genetic Map of Duplications 13 #3a Protocol for Recombination Mapping of Lethals Left of dpy-5 19 #3b Protocol for Recombination Mapping of Lethals Right of dpy-5 20 #4 Equations Used for Recombination Mapping 21 #5 Protocol for Duplication Mapping of Lethals 24 #6 Resultant Unc-13s from Duplication Mapping 25 #7 Protocol for Deficiency Mapping of Lethals 28 #8 Protocol for Complementation Analysis 30 #9 unc-13 e51 Homozygote Growth Curve 33 #10 Genetic Map of New Lethal Mutations 38 #11 Duplication Map of Essential Genes in dpy-5 unc-13 Region 45 #12 Duplication Map of New Lethal Mutations 50 #13 Genetic Map of Essential Genes in hDpl6/hDpl 9 Region 55 #14 Stage of Developmental Arrest for Mutations in dpy-5 unc-13 75 #15 Stage of Developmental Arrest for Genes in dpy-5 unc-13 76 #16 Equations Used for Chi-square Test 77 #17 Equations Used for % Saturation Analysis 82 #18 Distribution of Mutations in h,Dp!6/hDpl9 84 #19 Forward Mutation Frequencies for Genes in IiDpl6/hDpl9 87 viii A C K N O W L E D G E M E N T S I would like to thank my research supervisor, Dr. A n n Rose, for her encouragement, support, and invaluable guidance during my research. Many thanks to my colleagues in the lab, Nasrin Mawji , Linda Harris, A n n Marie Howell, Terry Starr, K i m M c K i m , Ken Peters, Joe Babity, Monique Zetka, and Shiv Prasad, for their technical guidance, ideas and moral support. I would also like to thank the members of my supervisory committee, Dr. David Baillie, Dr. Steve Wood, and Dr. Diane Juriloff, for their helpful discussions. Thanks also to Dr. Don Moerman, and Dr. Peter Candido, for reading my thesis. Finally, I would especially like to thank my family, P h i l , Richard, and my parents, for their encouragement, and faith in my abilities. 1 I N T R O D U C T I O N The question of how genes essential for development and fertility are organized at both the genetic and molecular levels in eukaryotic genomes has been the subject of extensive scientific research. Knowledge of the organization of a eukaryotic genome may increase our understanding of the control of gene expression, and the evolutionary history of gene linkage. There could be a selective advantage to linking certain sets of genes. For instance, it is possible that genes grouped together on the chromosome may be required during the same period in development, or may share similar functions. This is true for many eukaryotic genes, which have been shown to be organized into multigene families. These multigene families can include either nearly identical genes in tandem arrays, or loosely clustered genes that have diverged in function. For example, in Caenorhabditis elegans, thirty-seven of the forty major sperm protein genes are organized into six clusters that may be co-ordinately regulated (Ward, 1988). The arrangement of genes along the chromosome may have other consequences as well. The spatial organization of genes may be structurally necessary for certain processes to occur, such as chromosome condensation. To investigate these and other possibilities, one would need to have a complete genetic, and molecular map of the organism, identifying both genes and their regulator}' regions. The nematode C. elegans is an excellent organism for the study of eukaryotic genome organization. C. elegans exists as self-fertilizing hermaphrodites. Males are produced by spontaneous X chromosome nondisjunction, making genetic analysis possible. C. elegans being self-fertilizing is useful in the identification of recessive mutations, because it allows the genetic analysis of severe morphological and behavioural mutants, which would otherwise be difficult to mate. The effects on 2 development of recessive mutations can be studied since development in C. elegans is precise, giving rise to countable sets of cells with strict fates. The relatively small genome size, combined with the ability to store strains almost indefinitely in liquid nitrogen, makes feasible the long-term goal of mutationally identifying virtually every gene essential for development and fertility in this organism. The six chromosomes that make up the C. elegans genome have been the subject of intensive genetic and molecular analysis. The genetic characterization of essential genes in several different, regions of the genome has been done using translocations, duplications and deficiencies, to balance and recover lethal mutations in specific regions. Many research groups have examined the distribution of essential genes over small chromosomal regions, especially on L G I (Rose et al, 1980; Howell et al, 1987), L G II (Sigurdson et al, .1984), L G IV (Rogalski et al, 1982, 1985; Clark et al, 1988), L G V (Rosenbluth et al, 1988), and L G X (Meneely et al, 1979, 1981). This extensive research has resulted in the genetic mapping of almost 800 loci (Edgely et al, 1987), and the physical mapping of almost the entire genome using overlapping cosmid clones (Coulson et al, 1986). In several regions of the genome, the genetic and physical maps have been aligned (Greenwald et al, 1987; Starr et al, 1989). However, the function of at least 80% of the genome still remains unknown. Extensive lethal analysis has been carried out in other eukaryotic organisms as well, most, notably Drosophila m.elanogaster. Many groups have attempted to saturate small regions of the Drosophila genome for mutations in essential genes, in an endeavour to define all the essential genes present in those regions. Hochman (1971) attempted to uncover all the major loci on the small chromosome 4. He noted that the use of chemical mutagens, such as ethyl methanesulphonate (EMS) , substantially increased the number of lethal chromosomes recovered, and raised the number of loci detected, over X-ray-induced mutagenesis. Shannon et al (1972) strove to identify all the essential genes in the zeste white region on the X 3 chromosome. Their aim was to determine the developmental lethality pattern and morphology of the essential genes identified in this region. Leicht and Bonner (1988) tried to isolate all the essential genes surrounding the small heat shock protein gene cluster on chromosome 3. In most studies on Drosophila, deficiencies have been used to recover lethal mutations. These mutations could then be placed over a balancer chromosome, such as a chromosome carrying multiple inversions, which would suppress recombination in the region of interest. One problem with using deficiencies to recover lethal mutations is the recovery of "haplo-specific lethal mutations" (Nash et al, 1983). Nash et al demonstrated that a third of the mutations which appeared to act as lethals in hemizygotes, were viable in homozygotes. They attributed this phenomenon to these mutations being hypomorphs, with activity levels above the threshold level required for survival in homozygotes, but below the threshold level in hemizygotes. They cautioned that the inclusion of these haplo-specific lethals in autosomal complementation tests may lead to false positive results. A second problem with lethal analysis in Drosophila is the maintenance of large numbers of strains, which is difficult because, unlike C. elegans, they do not survive freezing. Lethal and sterile mutations are potentially important, tools in understanding the genetic basis of eukaryotic development and genome organization. The detailed analysis of these mutants, both at the cellular and molecular levels, can provide an important approach to understanding the genetic, programs controlling development. A collection of alleles for each essential gene in a given region can provide information about its pattern of expression in development, and possibly about the functional relationship between adjacent genes in the region. The role of essential genes in normal development can be inferred from an analysis of the difference between mutant and wild-type organisms. In order to identify new essential genes in a large fraction of the genome, Dr. Rose's lab has undertaken the genetic analysis of the left third of L G I, a region of 4 approximately fifteen map units. A region of this size should carry a wide variety of chromosomal loci, representing most classes of genes and regulatory sites. The left third of L G I is balanced by the large chromosomal duplication sDp2. W i t h i n this region visible genes, comprising both morphological and behavioural mutants, are unevenly distributed along the genetic map. Most of the genes from both classes are clustered together near the center of the chromosome around unc-13, while the remainder of the chromosome appears sparsely populated. This uneven distribution of genes is believed to be due to the suppression of recombination in the gene cluster, rather than the physical clustering of genes along the D N A . This hypothesis is supported by K i m et al (1987), who showed an increase in recombination frequency across the L G I gene cluster with the use of gamma radiation. More recently, this question has been addressed by the correlation of genetic and physical maps. Several restriction fragment length polymorphisms ( R F L P s ) have been cloned and mapped to the L G I gene cluster. Using the 1.6 kb transposable element T e l (Rose et al ,1985), and following the protocol of Rose et al (1982), I isolated four R F L P s between Bristol and Bergerac genomes: hP4, hP5. hP6, and hP7. The strain polymorphism hP5 was subsequently mapped to the dpy5 unc-13 interval. A cosmid contig of greater than 1,000 kb of D N A around the hP5 site has been identified by the analysis of J. Sulston and A . Coulson, M R C , Cambridge (personal communication). Subsequently, Starr et al (1989) positioned the 1,000 kb of cloned cosmid D N A around the dpy-5 unc-13region on the genetic map, demonstrating that the amount of D N A per map unit is not constant across the gene cluster, but reaches a peak around unc-13. The dpy-5 unc-13region is known to contain some interesting genes. There are two dpy genes, dpy-5 and dpy-14, three unc genes, unc-13, unc-15, and unc-40, a blistering mutant, bit-4, as well as many genes known to be essential for the development and fertility of the organism. Mutations in dpy-5 cause a morphological 5 change in the organism, causing the animals to be much shorter and fatter than wild-type. However, through the recent cloning of this gene (Babity et al. 1989), unlike most dpy mutations, dpy-5 lias been shown not to be a collagen gene. Mutations in dpy-14 also cause a dumpy phenotype, however, the morphological change is less severe than with dpy-5. dpy-14 mutations are temperature-sensitive, with a less severe phenotype produced at 16°C, than at 20°C. Next to d!py-5there is a putative acetylcholine receptor gene. However, this gene does not confer levamisole resistance, and as such is unlike the three genes to the left of dpy-5 (unc-38, unc-63, and unc-74), which have been proposed to encode for subunits of the acetylcholine receptor. Of the three unc mutations found in this region, only unc-13 has the ability to lay eggs, even though it is contorted and uncoordinated. The other two unc mutations, unc-15 and unc-40, are unable to lay eggs, resulting in internal hatching, unc-15 is also paralyzed, and is known to encode for paramyosin (Waterston et al, 1977). In the center of the dpy-5 unc-13 region lies bli-4, which causes the formation of fluid-filled blisters in the cuticles of homozygous adults, bit-4 is currently being cloned in our lab by K . Peters (personal communication). In addition, there are several genes known to be involved in the fertility and development of the organism. One of the goals of our lab is to saturate the left third of L G I for mutations in essential genes. In an effort to accomplish this, Howell et al (1987) used the duplication sDp'2 to recover 495 EMS-induced lethal mutations on L G I. Through a collaborative effort, including this study, all these lethals have now been mapped. Although most regions in the C. elegans genome have been mapped using deficiencies (Sigurdson et al, 1984), this method was unsuitable for the L G I gene cluster, as this region appeared to be haplo-insufficient, with deficiencies in this region giving poor viability. As an alternative, the sDp2 duplication was broken down using gamma rays ( M c K i m et al, 1988), so as to create a series of overlapping duplications with 6 different breakpoints along the left third of L G I. The use of duplications does not significantly affect the viability of the animals, as do deficiencies. Also, mapping using the duplications is a faster and more precise method than recombination analysis, and as such is more suitable for mapping large numbers of lethal mutations. The purpose of the present study was to identify essential loci in a small, approximately 0.5 map unit, region within the dpy-5 unc-13 interval. This region was defined by the breakpoints of the duplications hDp 16 and hDp!9, surrounding the bli-4 locus. The strain polymorphism hP5 lies near the hDpl6 breakpoint. In this thesis I describe the characterization of a set of EMS-induced lethal mutations balanced by the duplication sDp2. In order to identify and position genetic loci along the chromosome, I used recombination, duplication and deficiency mapping to position recessive lethal mutations, and divided the dpy-5 unc-13 region into three zones by rearrangement breakpoints. I analyzed a total of 189 recessive lethals isolated in our lab. In all , sixteen essential genes were identified in the hDp!6/hDpl9 region. The minimum number of essential loci in this region was estimated to be twenty, based on a truncated Poisson calculation. Therefore, approximately 80% of the essential genes in this 0.5 map unit region of the C. elegans genome have been identified. The goals of this research were: to help describe the distribution of essential loci on L G I, so as to determine whether essential genes followed the same pattern of uneven clustered distribution as do visible genes; to help determine whether genes required during the same time in development are spatially grouped together on the chromosome; and, to address the questions of the different mutabilities of genes, and the total genome size for the organism C. elegans. 7 M A T E R I A L S A N D M E T H O D S Nomenclature This thesis follows the accepted nomenclature system for C. elegans (Horvitz et al, 1979). C. elegans has six chromosomes (linkage groups) designated I, II, III, IV, V and X . As almost all C. elegans mutants have been derived from the Bristol strain, designated N2, this strain is called wild-type (Brenner, 1974). Gene names consist of three italicized lower case letters followed by a number, and refer to a detectable phenotype. For example, the unc mutations cause the animal to be uncoordinated. However, the gene name does not indicate whether particular alleles are dominant or recessive. Mutant alleles are assigned one or two lower case italicized letters, to indicate the lab of origin, followed by a number. The allele name can be used alone, or in parentheses after the gene name, for example bli-4 (h-520). Phenotypes of mutant worms are indicated by using the gene name without italics, with the first, letter in upper case, for example Unc-13s. Strain names consist of two or three non-italicized uppercase letters, to indicate the lab of origin, followed by a number. The designations for A n n Rose's lab are ' K R ' for strains and 'h ' for mutations. Chromosomal rearrangements are abbreviated as follows: ' D f for deficiencies, ' D p ' for duplications, and ' T ' for translocations. Such rearrangements are named by listing the lab mutation name, followed by the abbreviation and a number, for example hDpl6. In this thesis, I refer to mapped loci which have been defined by complementation tests and are essential for the development of the organism as "essential genes", and to EMS-induced mutations not yet assigned to loci as "new lethal mutations". Mutations in essential loci (let- ) result in lethality. Stock Maintenance and Strains Strains were maintained on 35mm petri plates containing ~10ml of nematode growth medium that has been seeded with OP50, a uracil-requiring mutant of E. coli (Brenner, 1974). The limited growth potential of OP50 allows the worms to be readily visible. Stocks of strains can be stored in liquid nitrogen almost indefinitely. Strains are usually maintained as self-fertilizing hermaphrodites ( 5 A A ; X X ) . Males ( 5 A A ; X 0 ) are obtained from such self-crosses at a frequency of approximately 0.1% at 20°C (Rose &i Baillie, 1979), resulting from X chromosome nondisjunction (Hodgkin et al, 1979). Matings were done by placing six to eight mutant hermaphrodites on a petri plate with fifteen to twenty males, which were then left at 20°C for twenty-four hours. After the mating, the individual hermaphrodites were transferred to fresh plates. In C. elegans, male sperm is used preferentially over the hermaphrodite's own sperm. The previously characterized mutants studied in this thesis are listed by their gene name and linkage group (LG) in T a b l e # l , and by their strain name and genotype in Append ix# l . A recombination map of the genes is shown in F igure#l . The 189 new mutations studied are listed by their strain name and genotype in Appendix#2. These new lethal alleles were induced in E M S screens of dpy-5(e61) + unc-13(e450)/dpy-5(e6l) unc-15(e73) +/sDp2 hermaphrodites, and were rescued using the sDp2 lethal rescue system (Howell et al, 1987). B y this method, after treatment with 12mM, 15mM, or 17mM E M S , lethal mutations in genes present in the sDp2 region were isolated and rescued by the wild-type allele on sDp2. In all , 31,600 chromosomes were screened, from which 495 new lethal mutations were generated (Howell et al, 1987). 189 of these new mutations were studied in this thesis. Table#l: Genes used in this Studied Gene L G Allele Phenotype bli-4 I h.42 Developmental arrest hi 99 Developmental arrest h.254 Developmental arrest dpy-5 I e61 Short, dumpy dpy-14 I e!88 Short, swollen medially let-83 I s91 Developmental arrest let- 86 I sl41 Developmental arrest let- 355 I h81 Developmental arrest let-367 I hi 19 Developmental arrest let- 370 I hi 28 Developmental arrest let-376 I hi 30 Developmental arrest let-377 I hi 10 Developmental arrest let-378 I hi 24 Developmental arrest let- 379 I hl27 Developmental arrest let- 380 I h80 Developmental arrest let-381 I hi 07 Developmental arrest let-382 I K82 Developmental arrest let- 383 I hi 15 Developmental arrest-let-384 I h84 Developmental arrest let-385 I h85 Developmental arrest let-386 I h!17 Developmental arrest 10 Tableftl: continued Gene L G Allele Phenotype let-387 1 K87 Developmental arrest let-388 I h88 Developmental arrest-let-389 I hi 06 Developmental arrest let-390 I K44 Developmental arrest let-391 I h91 Developmental arrest-let-392 I h!20 Developmental arrest let- 393 I h225 Developmental arrest let- 394 I h,262 Developmental arrest let-395 I h271 Developmental arrest-let-396 I K211 Developmental arrest. let-397 I h,228 Developmental arrest-let- 398 I h257 Developmental arrest let- 399 I h273 Developmental arrest let-400 I h269 Developmental arrest let- 601 I K281 Developmental arrest let-602 I h283 Developmental arrest unc-11 I e47 Contorted, uncoordinated unc-13 I e51 Contorted, uncoordinated unc- 4 0 I el430 Slow, dumpy, no eggs laid Ion-2 X e678 Long, increase length/width 1 1 0.5 map units I- let-357 sDp2 sDf4 unc-11, lei-351, let-356 Figure#l: Genetic map of previously identified visible and essential genes in sDp2 (Howell, et al, 1987; Pilgrim, et al, 1988). Asterisks denote genes with more than one allele. let-366, let-368, let-369, *let-372. Het-354 - let-353 *him-l let-352, let-359, *let-361, *let-363, let-364 let- 311 dpy-5, lei-355, let-361, let-370 let-376, let-377, *let-378, *let-379, let-388 let-393, let-395 bli-4, let-380, let-384, let-387, let-394, lei-396, let-601, let-602 dpy-14, let-381, let-382, let-383, *lei-3S5, let-386, let-389, let-390, let-391, *let-392, let-397, let-398, let-399, let-400 unc-13 12 Chromosomal Rearrangements 1) Duplications A l l the duplications used in this study are free duplications of the left third of chromosome I. sDp2 was generated in D. Baillie's lab at Simon Fraser University (Rose et al, 1984). The duplications with the 'h ' allele designation were generated and mapped with respect to visible markers by K . M c K i m ( M c K i m &: Rose, 1988 & 1990). They were generated by breaking down sDp2 with gamma rays. These duplications carry wild-type alleles for the farthest left known markers on chromosome I. However, they vary in their right end breakpoints, thereby creating a series of endpoints within the dpy-5 unc-13 region. The breakpoint of sDp2 lies between dpy-14 and unc-13, therefore it carries the wild-type alleles of dpy-5 and. dpy-14, but not of the unc-13 locus (Rose et al, 1984). The breakpoints of hDpl9, hDpSS, hDp35, hDP39. hDp54 and hDp56 were mapped to lie between the visible markers bli-4 and dpy-14- These duplications carry wild-type alleles of bli-4 and the markers to the left of bli-4, u u t not of the dpy-14 locus. The hDpl2, hDP14, hDpl6, hDpll, hDpl8, hDpSl, and hDP32 breakpoints lie between unc-40 and bli-4- The hDplS and hDpl5 breakpoints lie between dpy-5 and unc-40. The extent of all the duplications used are shown in figure#2. I i unc-11 hDpl3, hDpl5 hDpl2, hDpl4, hDpl6, hDpl7, hDpl8, hDp31, hDp32 0.5 map units hDpl9, hDp33, hDp35, hDp39, hDp54, hDp56 sDf4 him-1 sDp2 dpy-5 unc-40 - bli-4 dpy-14 unc-13 Figure#2: unc-11 unc-13 region of chromosome I showing the extents of the deficiencies and duplications before this present study was begun (McKim, et al, 1988). 14 2) Deficiencies The deficiency hDf8 (h572) was generated as a formaldehyde-induced dpy-14 mutation. hDf8 spans the region from unc-37 to dpy-14- Both the right (K. Peters) and left (T. Starr) endpoints of this deficiency have been mapped molecularly to the cosmid contig covering the dpy-5 unc-13 region on chromosome I. However, with both endpoints, cosmid probes used for Southern analysis detected two new bands in the hDf8 lanes as compared to the N2 lanes. These results suggest that hDfSw&s a complex rearrangement, which might involve both deletion and duplication events. Neither endpoint has been mapped genetically, although, the deficiency is known to cover the visible genes unc-37, unc-87 and dpy-14, as well as the lethals let-83, and let-8 6.. The hDf8-carrying chromosome does not carry any visible markers. The hDf8 mutation is a cross-over suppressor, so markers could not be introduced by recombination (A. Rose, unpublished results). This suppression of recombination also suggests that hDf8 is not a simple deficiency. A n attempt made to introduce a dpy-5 or unc-13 marker with E M S failed, because of the poor viability of the animals. The strain used in this study carried the hDf8 chromosome over a chromosome carrying the visible markers dpy-5 and dpy-14, resulting in a Dpy-14 phenotype (see Appendix# l ) . 3) Translocations The translocation szTl (I;X) was induced on a Ion-2 (e678) (X) chromosome using 7000R of X-radiation (Fodor et al, 1985), and was isolated as a dominant X chromosome crossover suppressor. The szTl chromosome is composed of two 15 abnormal chromosomes derived from the normal chromosomes I and X . Animals homozygous for the szTl chromosome arrest as embryos. Fodor showed that when heterozygous hermaphrodites are allowed to self-cross, they produce Lon-2 males at the elevated frequency of 0.08-0.12%, and that recombination was reduced in the dpy-7 unc-3 (X) interval from 19.2 map units to 0.3 map units. The strain of szTl used in this study was obtained from K. McKim, who introduced the markers unc-11 and dpy-14 onto the chromosome I portion of the szTl chromosome (McKim et al, 1988). 16 M a p p i n g Genes Three methods have been used for mapping sDp2-rescued lethal genes: recombination mapping, lethal rescue using duplications, and deficiency mapping. The duplication mapping proved to be the method of choice because of the speed and ease with which it was carried out. 1) Recombination Mapping Recombination mapping was used initially to position the sDp2-rescued new lethal mutations with respect to the dpy-5 and unc-13 markers. Al l recombination mapping was done at 20°C using young adults for crosses. Young adults carry oocytes, but no fertilized eggs, and can be identified by a darkly-pigmented crescent-shaped area at their vulva. The recombination frequency fluctuates with variations in temperature and parental age (Rose & Baillie, 1979), therefore, it is necessary to use standardized conditions. Using the conditions recommended by Rose and Baillie (1979), I attempted to position thirteen new lethal mutations: h286, h,289, h290, h291, K292, h293, h294: h295, h298, h.300, hSll, hSIS, and hSlS. The recombination frequency was determined by scoring all the progeny from a self-cross of a hermaphrodite cis-heterozygous for three linked loci ( e.g. + + +/dpy-5 let-X unc-13 ). The positions for two of the genes, dpy-5 and unc-13, were known, while the position of the lethal was not. In order to generate hermaphrodites heterozygous for the linked markers, N2 wild-type males were crossed to Unc-13 hermaphrodites from each of the lethal-bearing strains. These Unc-13 hermaphrodites were homozygous triple mutants, made viable by the presence of wild-type markers on the sDp2 duplication. Only the Wt heterozygotes which lacked the sDp2 duplication were used for mapping. Since the duplication carrying progeny 17 were slightly longer than those without the duplication, it was possible to select non-duplication carrying progeny. If sDp2 heterozygot.es were accidently set-up, they were easily identified because they segregated approximately 12% Unc-13 progeny, compared to less than 1% Unc-13 progeny (corresponding to recombinants) produced by the non-duplication-carrying heterozygotes. A l l the progeny from twelve non-duplication-carrying hermaphrodites were scored. The hermaphrodites were transfered from the mating plate to fresh plates every twenty-four hours, three times in all . This allowed the expected 150-200 progeny from each hermaphrodite to be spread over three plates, thereby making it easier to count all the progeny. The recombinant F2 Dpy-5s, Unc-13s and Dpy-5 Unc-13s were removed to individual plates to ensure that they were fertile, as only the fertile ones were true recombinants and could be counted in the recombination frequency equation. The presence of Dpy-5 Unc-13 recombinants (Dpy-5 Unc-13 nonrecombinants would be sterile or dead), and Unc-13 recombinants, along with the absence of fertile Dpy-5s, suggested that the lethal mutation lies to the left of dpy-5 (fig.#3a). The number of Dpy-5 Unc-13 recombinants recovered was used to calculate the distance of the lethal mutation from dpy-5. The Unc-13 recombinant class reflected the distance between dpy-5 and unc-13, and was calculated from the Unc-13 recombinants (data not shown) to ensure no anomalies occured. No Dpy-5s were expected to survive as they would be homozygous lethals. The presence of Dpy-5s and Unc-13s, together with the absence of viable Dpy-5 Unc-13s, suggested that the lethal mutation lay between dpy-5 and unc-13. Two types of recombinant events could be observed, as illustrated in figure#3b. The ratio of these two events is proportional to the distance of the lethal mutation from dpy-5, or unc-13. The Dpy-5 recombinant class reflects the distance of the lethal mutation from dpy-5, while the Unc-13 recombinant class reflects the distance of the lethal from unc-13. Therefore, the number of visible recombinants can be used to calculate 18 the recombination frequency (p) using the equation: p = 1 - ( l -2R) 1 / / 2 (Brenner, 1974). The recombination fraction, R, was calculated as (# of recombinants) / (total progeny). The number of recombinants was calculated as two times one recombinant class (e.g. 2 x # of Dpy-5s): the total number of progeny was calculated as 4/3 Wts (Rose & Baillie, 1979), because one expects a ratio of 3:1 for Wts to Dpy-5 Unc-13s, however, the Dpy-5 Unc-13s are homozygous for the lethal mutation and die (fig.#4). Confidence limits of 95% were determined using the tables of Crow and Gardner (1959). In this way, both right-left positioning relative to dpy-5, and two-factor recombination frequencies were obtained for each of the thirteen new lethal mutations listed above. Figure#3a: Protocol for Recombination Mapping of  Lethal Mutations to the left of dpy-5 19 + + + let-X dpy-5 unc-13 0 let-X dpy-5 unc-13 Unc-13 Diploid individuals let-X dpy-5 unc-13 1 2 + + + "Wild-type" (two recombination events) Q self-cross Nonrecombinants: + + +  + + + Wild-type let-X dpy-5 unc-1; + + + "Wild-type" Cf "Wild-type" sDpS-carrying individuals let-X dpy-5 unc-13 + + + "long" Wild-type let-X dpy-5 unc-13  let-X dpy-5 unc-13 Dead Recombinant progeny (type 1) let-X + + let-X + + + "Wild-type" let-X dpy-5 unc-13 Dead dpy-5 unc-13 + ±_ + "Wild-type' -f dpy-5 unc-13  let-X dpy-5 unc-13 Dpy-5 Unc-13 Recombinant progeny (type 2): let-X dpy-5 + let-X dpy-5 + + + let-X dpy-5 unc-13 "Wild-type" Dead + unc-13 + "Wild-type + unc-13 let-X dpy-5 unc-13 Unc-13 Figure#3b: Protocol for Recombination Mapping of  Lethal Mutations to the Right of dpy-5 + + dpy-5 let-X unc-13 9 dpy-5 let-X unc-13 Unc-13 Diploid individuals dpy-5 let-X unc-13 1 2 + + + X + ±_ cf "Wild-type" (two recombination events) 9 self-cross Nonrecombinants: + 4- +  4 4 4-Wild-type V dpy-5 let-X unc-13 + + + "Wild-type" "Wild-type" sDpi?-carrying individuals + +  dpy-5 let-X unc-13 4 + + 'long" Wild-type dpy-5 let-X unc-13  dpy-5 let-X unc-13 Dead Recombinant progeny (type 1): dpy-5 4- 4- dpy-5 + + + + + dpy-5 let-X unc-13 "Wild-type" Dpy-5 + let-X unc-13 "Wild-type" + let-X unc-13  dpy-5 let.-X unc-13 Dead Recombinant progeny (type 2): dpy-5 let-X + dpy-5 let-X + + + unc-13 4 - 4 4 dpy-5 let-X unc-13 + + + "Wild-type" Dead "Wild-type" + unc-13 dpy-5 let-X unc-13 Unc-13 21 Figure9^4: Equations used for Recombination Mapping Recombination Frequency: p = recombination frequency = 1 - ( 1 - 2R f^2 R = recombination fraction = # observed recombinants total # progeny = 2 X ( # of Dpy-5's ) 4/3 Wild-types 2 2 2) Duplication Mapping Since mapping by recombination was proving to be too time-consuming, duplication mapping was tried as an alternative. Duplications can be used to map genes by determining whether or not a wild-type copy of a given gene exists in a. duplication strain. Using a series of duplications, I was able to subdivide the dpy-5 unc-13 region into smaller regions, as defined by the duplication breakpoints, for the purpose of identifying genes in the region. i) Mapping Known Genes M y initial step in characterizing the dpy-5 unc-13 region was to position the known essential genes lying between these two markers with respect to the breakpoints of the duplications hDpl2, hDpl3, hDplS, hDpl6, KDpll, and hDpl9. Thirty-three existing published genes (Rose & Baillie, 1980; Howell et cd, 1987; Pi lgr im, 1988) were mapped. Duplication mapping was done following the protocol in figure#5. To be able to introduce the new duplications into each lethal-bearing strain, szTl long males were crossed to Unc-13 hermaphrodites from each of the lethal-bearing strains, as described in M c K i m and Rose (1990). The (I;X) translocation in szTl males was useful for producing males of the required genotype to cross to hermaphrodites carrying the new duplication. szTl (I;X) males carry a normal chromosome I, but the only X chromosome is rearranged in a (I;X) translocation. As a result, all the progeny receiving the paternal chromosome I wi l l be male, while those receiving the paternal (I;X) rearrangement wil l be hermaphrodites. A l l the males generated from the szTl cross were irans-heterozygous for the lethal mutation to be tested, which was linked to the marker unc-13, and for another mutation, the 23 marker dpy-14- Half of these males also carried the duplication sDp2, however, sDp2-carrying males are slower at developing, and do not mate (Rose et al, 1984). The W t male progeny from the szTl cross were then mated to the Dpy-14 hermaphrodites which carried the new duplication. These hermaphrodites were homozygous for both dpy-5 a.nd dpy-14, however, all the duplications used in this study carried a W t allele for the locus, resulting in a Dpy-14 phenotype. From this second cross, only the W t progeny would carry both the new duplication and the lethal mutation. Five F2 W t hermaphrodites were picked, and placed individually on clean plates, where their self-cross progenj< could be examined. The presence of fertile Unc-13s among the progeny would suggest that the duplication must cover the lethal mutation (figure#6). However, if the mutation is not covered by the duplication, then the Unc-13 worms wil l arrest in their development. Five Unc-13 progeny from each W t hermaphrodite would be picked and placed individually on clean plates, making a total of twenty-five Unc-13 worms examined for fertility and arrest times for each duplication analyzed. To ensure the fertile Unc-13 worms have not lost the lethal mutation from recombination, their progeny were screened for the presence of fertile Dpy-5 Unc-13s. Since Dpy-5 Unc-13s are homozygous for the lethal mutation, but do not carry the duplication, they should arrest in their development. The presence of fertile Dpy-5 Unc-13s would therefore suggest that the lethal mutation had been lost. 24 Figure#5: Protocol for Duplication Mapping of Lethal Mutations dpy-5 let-X unc-13 / dpy-5 let-X unc-13 / sDp2 O X unc-11 dpy-14 / s z T l o" Unc-13 Lon-2 • V Pick Wild-type males dpy-5 let-X une-13 / unc-11 dpy-14 a" X dpy-5 dpy-14 / dpy-5 dpy-14 / hDpZ 9 Dpy-14 (carrying new duplication) Pick Wild-type hermaphrodites dpy-5 dpy-14 / dpy-5 let-X unc-13 / hDpZ V 9 self-cross Check for presence of Unc-13s; if present, are they fertile Expected Ratio dpy-5 let-X unc-13 / dpy-5 let-X unc-13 dpy-5 let-X unc-13 / dpy-5 let-X unc-13 / hDpZ dpy-5 let-X unc-13 / dpy-5 dpy-14 dpy-5 let-X unc-13 / dpy-5 dpy-14 / h D p Z dpy-5 dpy-14 / dpy-5 dpy-14 dpy-5 dpy-14 / dpy-5 dpy-14 / hDpZ Dead Unc-13 Dpy-5 "Wild-type" Dpy-5 Dpy-14 Dpy-14 25 Figure#6: Resultant Unc-13s from Duplication Mapping dpy-5 let-X unc-13 dpy-5 let-X unc-13 dpy-5 let-X unc-13 dpy-5 let-X unc-13 + + hDpZ + h D p Z Fertile Unc-13 Unc-13 arrests in development 2 6 ii) Mapping New Mutations 495 new lethal mutations have been rescued using the sDpS system in our lab. These mutations were recovered from 31,600 chromosomes mutagenized with 17mm E M S by a number of people in the Rose laboratory (see Appendix#2). I positioned 178 of the new lethals relative to the hDplo, hDpl6, and hDP19 breakpoints. Duplication mapping was done following the protocol in figure#5. ' Initially, each new mutation was crossed to hDplS. If it lay below hDplS, it was then crossed to hDplG. If it lay below hDplS, it was crossed to hDpl9 (see figure#2). iii) Mapping the hDvl6/hDvl9 Region Once the new lethals were mapped relative to the hDplS, hDpl6, and hDpl9 breakpoints, I then concentrated on the hDpl6/hDpl9 region. After complementation analysis (see next section), I crossed each essential gene in the hDpl6/hDpl9 region to nine additional duplications: hDpl4, hDplS, hDpSl. hDpSS, hDpSS, hDpSo, hDpS9, hDp54, and hDP56. The aim was to find new breakpoints within the hDp!6/hDp 19 region, thereby subdividing it further. From mapping experiments using visible markers ( M c K i m and Rose, 1990), hDpl4; hDp!8, hDpSl, and hDp32 were found to map between unc-40 and bli-4, the same as hDpl6. hDp33, hDp35, hDp39, hDp54, and hDp56 were found to map between bli-4 a n d dpy-14, the same as hDp!9. 27 3) Deficiency Mapping A l l the essential genes lying in the hDpl6/hDpl9 region were crossed to the deficiency hDf8, in order to determine if the upper end point of this deficiency lay within this region. In order to introduce the deficiency into each lethal-bearing strain, szTl long males were crossed to Unc-13 hermaphrodites from each of the lethal-bearing strains (figure#7). The W t heterozygous male progeny were then mated to the Dpy-14 hermaphrodites which carried the deficiency, hDf8. Because of the poor viability of these h.DfS-carrying hermaphrodites, ten would be mated to each lethal-bearing strain. Each mated hDf8-carrying hermaphrodite would then be placed on individual plates, and their progeny would be examined. The presence of fertile Wts among the progeny would suggest that the lethal mutation lay outside the deficiency. If the lethal mutation lay inside the deficiency, then the W t worms would arrest in their development, although their arrest times were not recorded, because of the poor viability of hDf8-carrying animals. Five W t progeny from each mated hDf8-carrying hermaphrodite would be picked and placed individually on clean plates, up to a limit of twenty-five W t worms examined for fertility. 28 F i g u r e ^ ? : Protocol for Deficiency Mapping of Lethal Mutations dpy-5 let-X unc-13 / dpy-5 let-X unc-13 / sDp2 Q X unc-11 dpy-14 / s z T l o" Unc-13 Lon-2 Y Pick Wild-type males dpy-5 let-X unc-13 / unc-11 dpy-14 cf X dpy-5 dpy-14 / hDf8 9 Check for presence of Wild-types dpy-5 let-X unc-13 / dpy-5 dpy-14 Dpy-5 dpy-5 let-X unc-13 / hDf8 Wild-type unc-11 dpy-14 / dpy-5 dpy-14 Dpy-14 unc-11 dpy-14 / hDf8 Dpy-14 Y If Wild-types are present, are they fertile? 29 Complementation Analysis of Lethal Strains The recombination-mapped lethal mutations in the dpy-5 unc-13region were tested for complementation to all the known essential genes in the region. In addition, each new lethal mutation in the hDP16/hDpl9 region was tested for complementation to all the known essential genes in the same region. Complementation analysis was carried out in order to identify previously undescribed essential genes, new alleles of existing essential genes, and large deletions (failure to complement more than one gene). To accomplish this, heterozygous male strains of each new lethal mutation were constructed by crossing N2 (Wt) males to each sDp'2 lethal strain. These males were then mated to Unc-13 hermaphrodites from lethal-bearing strains of each essential gene. The presence of fertile Dpy-5 Unc-13 hermaphrodites, and Dpy-5 Unc-13 males, indicates complementation (see figure#8). A total of ten Dpy-5 Unc-13 hermaphrodites were tested for fertility from each of the lethal-bearing strains. Once all the new lethal mutations were assigned to complementation groups, all the alleles within a complementation group (gene) were tested for complementation to each other. This analysis included reciprocal complementation tests. For example, males of the canonical allele were crossed to hermaphrodites of the new allele, as well as males of the new allele being crossed to hermaphrodites of the canonical allele. The reciprocal complementation tests were carried out as a repeated test to check the data was correct, as well as to determine if any of the alleles showed a maternal lethal effect. The presence of fertile Dpy-5 Unc-13 hermaphrodites indicated complementation. 30 F i g u r e # 8 : Protocol for. Complementation analysis + dpy-5 let-X unc-13 dpy-5 let-X unc-13 9 Unc-13 (carrying sDp2) dpy-5 let-X unc-13  dpy-5 let-Y unc-13 Dpy-5 Unc-13 + ±_ X + + Wild-type Y Pick Wild-type males dpy-5 let-X unc-13  + + + X + + dpy-5 let-Y unc-13 dpy-5 let-Y unc-13 Unc-13 (carrying sDp2) V dpy-5 let-X unc-13 + + "Wild-type" 9 o" + + + dpy-5 let-Y unc-13 "Wild-type" + +  dpy-5 let-X unc-13  dpy-5 let-Y unc-13 Unc-13 + dpy-5 let-X unc-13 _± + "Wild-type' + dpy-5 let-Y unc-13 "Wild-type' 31 Determining the Stage of Developmental Arrest The stage of lethal developmental arrest was determined for each of the thirty-three existing published essential genes, as well as for the majority of the 189 new lethal mutations in the dpy-5 unc-13 region. The times of arrest for the mutations were determined using duplications. Among the self-cross progeny from the wild-type hermaphrodite of the genotype dpy-5 dpy-14 / dpy-5 let-X unc-13 / hDpZ, would be Unc-13 worms (figure#5). These Unc-13 hermaphrodites homozygous for the lethal mutation, and carrying one of the new duplications, would survive and be fertile only if the duplication covered the lethal mutation (see figure#6). However, if the duplication did not cover the mutation, then the Unc-13 worms would arrest in their development sometime between the egg and adult stage, depending upon the lethal mutation present. The time of arrest of the Unc-13 worms would indicate the time in development when the gene-product from the lethally-mutated gene is required, assuming no interaction occurs between the unc-13 locus and the lethal mutation. If Unc-13 worms were present, then, in general, twenty-five young (L1-L3) Unc-13 hermaphrodites from each lethal strain ( dpy-5 let-X unc-13 / dpy-5 let-X unc-13 / hDpZ ) were placed individual!}' on clean plates, and allowed to sit at a controlled 20°C for several days to allow the worms to reach their terminal stage of growth. The lengths of the worms were then measured using a micrometer, and their sizes were compared to the growth curve for normal unc-13 (e51) homozygotes (figure#9), as determined by A . Rose (PhD Thesis, 1979). The growth curve enabled an estimate of the larval stages at which the worms arrested to be made from the sizes of the worms, in millimeters. The stages of arrest were classified as egg, early larval, mid larval, late larval, or sterile adult. The early larval stage was comprised of L l and L2 animals, which ranged in size from 0.15 to 0.3 mm. The mid larval stage was comprised of L2 and L3 animals, ranging from 0.3 to 0.4 mm. The 32 late larval stage was comprised of L3 and L4 animals, ranging from 0.4 to 0.6 mm. Adul t sterile animals grew to 0.6 to 0.8 mm, but failed to produce any self-cross progeny. If no Unc-13 worms were found, then the Wts , Dpy-5s, Dpy-14s, and Dpy-5 Dpy-14s were removed from the self-cross progeny of the W t hermaphrodite ( dpy-5 dpy-14 / dpy-5 let-X unc-13 / hDpZ ) (see figure#5), as they reached the late larval stage (L3-L4). A t the late larval stage, these worms wil l not have laid eggs, but they wil l be old enough not to be confused with Unc-13s, which can move fairly well as L i s or L2s. By this, means it can be determined whether the Unc-13s hatched to the L I stage, or arrested as eggs. 33 Figure#9: unc-13 (e5l) homozygote growth curve (A. Rose, PhD Thesis, 1979). Time course for normal Unc-13 from hatching (first circle) to an egg-laying adult (arrow). 34 Tes t for S p e r m - D e f e c t i v e M u t a n t s Several of the lethal mutations which were found to arrest, as sterile adults were crossed to N2 males in an attempt to detect sperm-defective mutants. B y crossing the lethals to W t males, W t sperm is introduced into the hermaphrodite, which would be expected to rescue the sterile phenotype if the lethal mutation caused a defect in spermatogenesis alone. The hermaphrodites used in this cross carried a duplication which covered dpy-5, but did not cover the lethal mutation ( hDpZ / dpy-5 let-X unc-13 / dpy-5 let-X unc-13 ). In this-way, the lethal mutation would be expressed. However, the dpy-5 locus would not be expressed, giving an Unc-13 phenotype, Unc-13s being healthier and easier to mate than Dpy-5 Unc-13s. In all, eleven adult sterile lethals were crossed to N2 males. Ten of these lethals carried the duplication hDplS, while the other carried hDp!5 (as the lethal was covered by hDplS). 35 R E S U L T S Recombination Mapping In order to position lethal mutations lying between dpy-5 and unc-13, an initial set of thirteen EMS-induced sDp2-rescued lethal mutations were mapped by recombination analysis. The two-factor data for these lethals is listed in table#2. A non-lethal strain, BC415, was used as a control to obtain the recombination frequency of the dpy-5 unc-13 interval. The value of 2.0 map units obtained for the dpy-5 unc-13 interval agrees fairly well with expected value of 1.6 map units (Howell et al, 1987). The presence of Dpy-5s and Unc-13s, together with the absence of viable Dpy-5 Unc-13s, indicated that the mutation lay below dpy-5. Five lethal mutations mapped below dpy-5 (section B of table#2). Dpy-5 and Unc-13 recombinant classes were observed for these five mutations. The distance of the lethal mutation from dpy-5 was calculated from the Dpy-5 recombinant class. The distance of the lethal mutation from unc-13 was calculated from the Unc-13 recombinant class. No Dpy-5 Unc-13 recombinants were expected to survive since they would be homozygous for the lethal mutation. However, in two out of five cases Dpy-5 Unc-13s were observed. Both h292 and h293 gave Dpy-5 Unc-13s upon being crossed, however, both these mutations were considered to lie below dpy-5, because six times more Dpy-5s were present than Dpy-5 Unc-13s. These Dpy-5 Unc-13s could arise from a. double cross-over event ( d.py-5 + unc- 13/dpy-5 let-X unc-13 ), from two cross-over events in separate meioses, or from leaky adult steriies. The presence of Dpy-5 Unc-13s and Unc-13s, together with the absence of viable Dpy-5s, indicated that the lethal mutation lay above dpy-5. Six lethal mutations 36 mapped above dpy-5 (section C of table#2). Dpy-5 Unc-13 and Unc-13 recombinant classes were observed for these mutations. The distance of the lethal mutation from was calculated from the Dpy-5 Unc-13 recombinant class. No Dpy-5s were expected to survive as they would be homozygous lethals. However, in four out of six cases, Dpy-5s were observed. h29Jf, h.295, hSOO and h,313 gave Dpy-5s upon being crossed, however, these mutations were considered to be above dpy-5, because about twenty times more Dpy-5 Unc-13s were present than Dpy-5s. These Dpy-5s could arise from, a double cross-over event ( + dpy-5 + / let-X dpy-5 unc-IS ), or from one cross-over chromosome ( let-X dpy-5 + ) fertilizing a second cross-over chromosome ( + dpy-5 unc-13 ). Section D of table#2 lists the two mutant alleles, h298 and hSll, found to be non-lethal. When Dpy-5 Unc-13s ( dpy-5 let-X unc-13 / dpy-5 let-X unc-13 ) from the original sDp2 strains were allowed to self-cross, they produced progeny, indicating no lethal alleles being present. Figure#10 shows the map positions of the new lethal mutations in relation to the map positions of the known essential genes lying between dpy-5 and unc-13. Unfortunately, because of the large number of progeny needed to be counted for mapping, it is quite laborious to count crosses for recombination mapping. Furthermore, with very closely linked mutants, the recombination distances are not very accurate, since only a few recombinants were detected. Fortunately, a better method for positioning lethals became available, that of mapping by complementation to duplications. 37 Table#2: Two-Factor Mapping Data for New Lethal Mutations Al le le 0 ' N & Progeny c Dpyunc Dpy Unc / (95% C.I.) pe (95% C.I.) A ) Control BC415 dpy-5 unc-13/+ + 8 1653 448 23 B) Lethals below dpy-5: h289 8 1213 0 3 h-290 12 2468 0 1 h292 13 2183 4 23 h293 12 2167 2 12 h.312 12 2382 0 10 C) Lethals abi •ve dpy-5: h286 15 2665 4 0 h291 11 1512 17 0 h294 9 1742 46 2 h.295 12 2540 115 2 hSOO 16 3060 20 1 hSIS 17 2694 25 3 D) Non--lethal alleles: h-298 h.311 18 2.00 (1.37-3.14) 11 0.38 (0.07-0.67) 1.37 (0.63-2.38) 38 0.06 (0.00-0.34) 2.40 (1.64-3.23) 21 *1.59 (1.03-2.20) 1.44 (0.85-2.17) 7 0.83 (0.45-1.38) 0.48 (0.21-0.94) 5 *0.63 (0.31-1.10) 0.31 (0.13-0.69) 39 0.23 (0.08-0.54) 19 1.70 (0.94-2.58) 9 3.96 (2.94-5.18) 25 7.04 (5.56-8.11) 17 1.00 (0.61-1.47) 20 1.39 (0.92-2.01) ^ Lethal strain outcrossed to N2 males " Number of heterozygotes ^Calculated as 4/3 wild-types (see Materials and Methods) d Frequency of recombination with dpy- 5 e Frequency of recombination with unc-13 * two-factor map distance is anomalous h295 h291 h313 h300 h286 T h290 ± h289 T h294 h292 h293 h312 let-357 ± 0.5 maD units unc-11, let-351, lei-356 - let-366, lei-368, let-369, let-312 - let-351, lei-353 - him-1 let-352, let-359, let-361, . let-363, let-364, let-311 dpy-5, lei-355, let-361, let-310 let-316, let-311, let-318, let-319, let-388, lei-393, let-395 - bli-4, let-380, let-384, let-381 lei-394, let-396, let-601, let-6 02 dpy-14, let-381, let-382, let-383, let-385, let-386, let-389, let-390, let-391, let-392, let-391, let-398, let-399, let-400 \- unc-13 Figure#10: Genetic map of the new lethal mutations. The map positions are based on columns #7 and #8 in table#2. B B 39 Duplication Mapping A tremendous advantage to using a series of free duplications for mapping is that their breakpoints allow one to subdivide the region of interest into very precisely defined intervals. Furthermore, mapping using the duplications is much less time-consuming than recombination analysis, and results in fewer complementation tests to define essential genes, and as such is more suitable for mapping large numbers of lethal mutations. i) Mapping Known Genes In order to characterize the dpy-5 unc-13 region, I have positioned all the known essential genes lying between dpy-5 and unc-13, with respect to the breakpoints of the duplications hDplS, hDplS, hDplS, hDpl6, hDpll, and hDpl9. In all, thirty-three existing published genes, as well as the four genes and one mutation described in the previous section, were mapped. Of the three essential genes, let-355, let-367, and let-370, which were previously considered to be inseparable from dpy-5 (Howell et al, 1987), two {let-355 and let-367) were shown to lie below the dpy-5 gene. One of the duplications, hDp!5, did not cover let-355, which was known to map in sDf4, but not known to be separable from dpy- 5. This result placed both let- 355 and the sDf4 breakpoint below dpy- 5 (the position of the sDf4 breakpoint was not previously known because sDf4 was induced on a dpy- 5 chromosome), let- 367 was also separated from dpy-5, since it was covered by neither hDplS, nor hDpl5. However, let-370 remained inseparable from dpy-5, as it was covered by hDpl5. The new mutation, h290, was also covered by hDp!5, and, hence, remained inseparable from dpy-5. Therefore, both let-370 and h290 may lie either above or just below dpy-5. 4 0 The remaining essential genes were split into three almost equal groups by lethal rescue using the hDplS, hDplG, and hDpl9 duplications. As a result, the dpy-5 unc-13 interval was divided into three almost equal zones by the hDplS, hDpl6, and hDpl9 breakpoints. Each zone contains a visible gene, which was useful as a marker: the hDplS/hDp 16 zone contains unc-40, the hDp 16/hDp 19 zone contains bli-4, and the hDp 19/sDp2 zone contains dpy-14- Consequently, these three duplications were chosen for mapping the new EMS-induced lethals rescued by sDp2 (Howell et al, 1987). Table#3 and f igure#l l show a summary of the duplication mapping results. For each duplication, twenty-five Unc-13 progeny were examined for fertility. There were two categories of results: (a) 0/25 Unc-13s producing progeny were considered to be outside the duplication; (b) 25/25 Unc-13s producing progem' were considered to be inside the duplication. Exceptions to (a) above occurred in fifteen cases, where from 1/25 - 5/25 Unc-13s produced progeny. Five Dpy-5 Unc-13 self-cross progeny were tested for fertility from each of these fertile Unc-13s. Since Dpy-5 Unc-13s are homozygous lethal, with no duplication present, they should die. A l l Dpy-5 Unc-13s tested were fertile, indicating that they had lost the lethal mutation, possibly through recombination. Therefore, in all fifteen cases, the lethals were considered to be outside the duplication. Exceptions to (b) above occurred in five cases, where 24/25 Unc-13s gave progeny, and one Unc-13 died. In all cases, the dead Unc-13 was due to transfer error. The time of arrest in development of the Unc-13 worms ( dpy-5 let-X unc-13 / dpy-5 let-X unc-13 / hDpZ) for each of the essential genes is also shown in table#3. The let-X gene product is required at or before the time of developmental arrest. The twenty-five Unc-13 progeny examined for fertility for each duplication, were also examined for their time of developmental arrest. W i t h the exception of recombinants which had lost their lethal mutation, all the worms for a given allele 41 arrested at the same stage, ranging in size within the limits set for that particular stage (see footnote in table#3 for sizes of stages). 4 2 Table#3: Duplication Mapping Results for  Essential Genes in dpy-5 unc-13 Region Duplication (hDp) Gene Allele 15 13 12 11 16 19 A r r e s t a S ize 0 (mm) A) Existing Published Lethals: *let-83 s91 O U T Not determined *let-86 sl41 O U T Not determined let-355 h.8l O U T IN Adult. Sterile 0.6 let-367 hll9 O U T O U T IN Adult. Sterile 0.6 let-370 hi 28 IN IN IN Not determined let-376 hi 30 O U T O U T IN Early larval let-377 hi 10 O U T O U T IN Early larval let-378 hl24 O U T O U T IN Early larval let-379 hl27 O U T O U T IN Early larval let-380 h.80 O U T O U T IN Egg let-381 hl07 O U T IN M i d larval let-382 h82 O U T O U T O U T IN M i d larval 0.5 *let-385 ? h.115 O U T Not determined let-384 h.84 O U T O U T O U T O U T IN IN Adul t Sterile 0.6 *let-385 > h85 O U T Not determined let-386 hi 17 O U T IN Early larval let-387 h87 O U T O U T O U T IN M i d larval let-388 h.88 O U T O U T IN Early larval * let-381 > hi 06 O U T Early larval let-390 h44 O U T IN Early larval 43 Table#3: continued Duplication (hDp) Gene Allele 15 13 12 17 16 19 Arrest ( Size mm) * let- 391 h9l O U T O U T O U T IN IN Adul t Sterile *let-392 hl20 O U T Early larval let-393 h225 O U T O U T IN IN Early larval let-394 h262 O U T O U T O U T O U T O U T Early larval 0.3 -0.35 let-395 K211 O U T O U T IN IN Adul t Sterile 0.6 let-396 h217 O U T O U T O U T O U T O U T IN Early larval *let-S97 h.228 O U T Not determined * let-398 h257 O U T Early larval let-399 h.273 O U T O U T Not determined *let-400 h269 O U T Not determined let-601 h281 O U T O U T O U T O U T O U T IN Egg let-602 h283 O U T O U T O U T O U T O U T IN Early larval B) New Essential G enes c: let-603 h289 O U T O U T IN Adul t Sterile 0.6 let-604 h293 O U T O U T O U T IN Adul t Sterile 0.7 let-605 h.312 O U T O U T O U T O U T Adul t Sterile let-606 K292 O U T O U T O U T IN Adul t Sterile C) New Mutation: h290 IN IN IN Ta'ble#3: continued a Arrest = Stage of lethal developmental arrest ^ Sizes used to determine larval stages, which were measured by a micrometer, as follows (see figure#8): Early larval stage = L 1 / L 2 = 0.15 - 0.3 m m M i d "larval stage = L 2 / L 3 = 0.3 - 0.4 mm Late larval stage = L 3 / L 4 = 0.4 - 0.6 mm Adul t stage = 0.6 - 0.8 m m c = see section on complementation analysis * = Mapped by A . Rose 45 hDp IE hDp 13 hDp 12 hDplT hDp 16 hDpl9 sDf4 sDp2 1- dpy-5, h290, let-370 - let-355 unc-40, let-367, let-376, let-377, let-378, let-379, let-388, let-393, let-395, let-603 let-384, lei-391 bli-4, let-380, let-381, let-382, let-386, let-387, let-390 lei-396, let-601, let-602, let-604, let-606 dpy-14, let-83, let-86, let-383, let-385, let-389, let-392, let-394, let-397, let-398, let-399, let-400. let-605 0.1 map units unc-13 1 Figure#ll: Duplication map of the essential genes in the dpy-5 unc-13 region. 4 6 ii) Mapping New Mutations I have mapped 178 new lethal mutations relative to the hDp 13, hDp 16, and hDpl9 duplication breakpoints. This completes the positioning of the 495 new lethals that have been rescued using the sDp"2 system in our lab. Appendix#3 shows a summary of the duplication mapping results for these new lethals, including their time of developmental arrest. For each duplication, twenty-five Unc-13 progeny were examined for fertility, and their time of developmental arrest. There were two categories of results: (a) 0/25 Unc-13s producing progeny were considered to be outside the duplication; (b) 25/25 Unc-13s producing proge^' were considered to be inside the duplication. There were sixteen exceptions to (a) above, however, in each case the surviving Unc-13s had lost their lethal mutation (i.e., they segregated fertile Dpy-5 Unc-13s). There were thirty-four exceptions to (b) above, in each case the Unc-13s that died were due to transfer error. Figure#12 shows the position of the new lethal mutations relative to the duplication breakpoints. The number of lethal mutations located between the duplication breakpoints may reflect the physical distance between the different breakpoints. This assumption would make the distances between hDpl3/hDp!6, and between hDp 16/hDp 19 similar in length, in comparison to the longer distance between hDpl9/sDp2, which is almost double in length (see table#4). Three of the lethal mutations, hJ,62, h,79l, and h.824, seemed to carry double hits. W i t h h462, sixteen out of twenty-five Unc-13s gave progeny, while the remaining eight died as early larva, when complemented to h.Dpl9. Similarily, with h!91, thirteen out of twenty-two Unc-13s gave progeny, while nine arrested as early larva, when covered by hDpl9. Finally, with h824, thirteen out of eighteen Unc-13s gave progeny, while five arrested as mid-larva, when covered by hDpl9 (see table#5). These results suggest that h462, h!91, and h824, each have two mutations, one lying 47 between hDpl6/hDP19, and the other lying outside hDpl9. When these mutations were crossed to hDpl9, the Unc-13s which arrested would have two mutations, the mutation not covered by hDpl9 causing lethal arrest. The Unc-13s which were fertile carried only the mutation lying between hDpl6 and hDpl9, having lost the mutation lying outside hDP19, perhaps by recombination. I would expect to see more Unc-13s arresting than surviving, as the survivors arise by recombination, and this could have been the case, since most of the Unc-13s which died from the lethal lying outside hDpl9 would have been missed. W i t h all three lethals, the fertile Unc-13s were kept as a new stock: h462/hDpl9, h.79l/hDpl9, and h824/hDpl9. Each of these new stocks were retested against hDpl6, to ensure they were still outside this duplication - all three were not covered by hDplG. These new stocks were frozen in liquid nitrogen, and assigned new strain names (see table#6). These new stocks were used for all subsequent complementation analysis, and not the original stocks over sDp2. 48 Table#4: Allocation of New Mutations Region Number of N ew Mutations hDplS 62 hDpl3/hDpl6 31 hDpl6/hDpl9 30 hDp!9/sDp2 55 Tota l 178 Table#5: Results of Fertility Tests for  Homozygotes carrying hDv!9 for Putative Two-hit Lethals Allele Fertile Unc-13s Sterile Unc-13s Total h462 16 9 25 h.791 13 9 22 h.824 13 5 18 Table#:6: Strain Names for Putative Two-hit Lethals Allele Genotype Strain h462 hl0l4 dpy-5 h462 hl014 unc-13 ; sDp2 KR789 h462 dpy-5 h462 unc-13 ; hDpl9 KR1884 h.791 hl015 dpy-5 h791 hl0l5 unc-13 ; sDp2 KR1434 h791 dpy-5 h.791 unc-13 ; hDpl9 KR1841 K824 hl0l6 dpy-5 h824 hl016 unc-13 ; sDp2 KR1486 h824 dpy-5 h.824 unc-13 ; hDpl9 KR1885 50 6 hDpl3 hDpl6 hDpl9 sDp2 0.2 map units - dpy-5 unc-40 bli-4 dpy-1^ - unc-11 h.314, h356, h.358, h379, h380, hSSl, h382, h381, h393, h396, h391, h398, h403, h4l2, h.413, h415, h425, h.434, h.436, h440, h.443, h.446, h447, h450, h455, h458, h460, h461, h463, h464, h469, h411, h483, h487, h494, h.498, h.500, h.501, h502, h503, h504, h505, h506, h508, h509, ho 12, h5l8, h521, h525, h526, h534, h!28, h!30, h!32, hi43, h!44, h!45, hi55, hi51, h!58, h!59, h869 h351, h359, h362, h315, h388, h401, h408, h416, h433, h431, h454, h415, h510, h611, h!15, hi29, h!33, h.136, hi41, hi52, hi53, h!66, hi61, h!15, h.194, h!91, h805, h8l2, h,S43, h865, h810 h.354, h.369, h314, h.3S4, h402, h421, h462, h416, h490, h495, h491, h520, h538, h615, h618, h695, h699, h.106, hi41, hi49, h!54, h!56, h!91, h822, h824, h83l, h850, h851, h853, hSIS hS50, h351, hS60, h36l, h361, h389, h406, h410, h428, h429, h431, h435, h442, h444, h445, h453, h410, h412, h419, h486, h489, h492, h514, h519, h523, h521, h531, h,680, h686, h681, h.690, h692, h69S, h.104, hi01, hill, hi21, h!35, hi42, hi48, h.151, hi62, hi63, h!69, h!80, hi89, h!92, h.193, A.755, h800, h806, h801, h825, hS36, h842 Figure#12: Duplication map of the new lethal mutations 51 iii) Mapping of the hDp 16/hDp 19 Region I have mapped all sixteen essential genes lying between the hDpld and hDpl9 breakpoints with respect to nine new duplications: hDpl4, hDpl8, hDpSl, hDp32, hDpSS, hDp35, hDp39. hDp54, and hDp56. The aim was to further subdivide the hDp 16/hDp 19 interval into smaller regions. Twenty-five Unc-13 progeny were examined for fertility for each duplication tested; there were no anomalies. Initially, the breakpoints of hDpl4, hDplS, hDpSl, and hDp32 were inseparable from hDpl6, while the breakpoints of hDp33, hDp35, hDp39. hDp54, and hDp56 were inseparable from hDpl9. Following my analysis, the breakpoints of hDpl4, hDplS, and hDP32 remained inseparable from hDp 16, while the breakpoints of hDpSS, and hDp35 remained inseparable from hDpl9. The breakpoints of hDpSl, hDp39, hDp54, and hDp56 were all found to lie below hDp 16. and above hDp 19. Of the sixteen essential genes in the hDp!6/hDp!9 region, three lie between hDp!6 and hDpSl, eight (including bli-4) he between hDpSl and hDP56, two lie between hDP56 and hDp39 . two lie between hDp39 and hDp54, and one lies between hDp54 and hDp 19, as illustrated in figure #13. Table #7 gives a summary of the duplication mapping data. 52 Table^T: Duplication Mapping Results for  Essential Genes in h.Dpl6/hDvl9 Region Duplication (hDp) Gene (Allele) U 18 31 32 33 35 39 54 56 ltt-380 (h80) O U T O U T O U T O U T IN IN IN IN IN let-381 (hlOT) O U T O U T O U T O U T IN IN IN I N IN let-382 (h82) O U T O U T O U T O U T IN IN O U T IN O U T let-386 (hi 17) O U T O U T O U T O U T IN IN IN IN O U T let-387 (h87) O U T O U T O U T O U T IN IN IN I N IN let-390 (h44) O U T O U T O U T O U T IN IN O U T IN O U T let-396 (h217) O U T O U T IN O U T IN IN IN IN IN let-601 (h28l) O U T O U T O U T O U T IN IN IN IN IN let-602 (h-283) O U T O U T IN O U T IN IN IN IN IN let-604 (h293) O U T O U T O U T O U T IN IN IN I N O U T let-606 (h292) O U T O U T O U T IN IN IN IN IN let-607 (h402) O U T O U T O U T IN IN O U T O U T O U T let-608 (h706) O U T O U T O U T I N IN IN IN IN let-610 (h695) O U T O U T O U T IN IN IN IN IN let-611 (h850) O U T IN O U T I N IN IN IN IN bli-4 (h254) O U T O U T O U T IN IN IN IN IN 53 Deficiency Mapping I have mapped fifteen of the sixteen essential genes lying between hDpl6 and hDpl9 with respect to the deficiency hDf8 (figure#13). The aim was to position the upper endpoint of the deficiency on the genetic map. Since both the upper and lower endpoints have been mapped molecularly to the cosmid contig covering the dpy-5 unc-13 region, the positioning of the upper endpoint genetically would help align the genetic and molecular maps in this region. The hDf8 deficiency also proved useful in subdividing the hDp 16/hDpl9 interval into smaller regions. The upper endpoint of hDf8 mapped between the breakpoints of the duplications hDpSl (above), and hDp56 (below). Of the fifteen essential genes in the hDp 16'/hDp 19 region mapped to hDf8, eight (including bli-4) lie above, while seven lie below hDf8, as illustrated in figure#13. Table#8 gives a summary of the deficiency mapping data. Twenty-five wild-type progeny were examined for fertility for each essential gene tested against hDfS. Fertili ty indicated that the essential gene lay outside the deficiency, while sterility or developmental arrest indicated that the essential gene lay inside the deficiency. There were no anomalous results. 54 Table#8: Deficiency Mapping Results for  Essential Genes in hDv 16/hDp 19 Region Gene Allele hDj8 let-380 h80 O U T let-381 hlOl O U T let-382 h82 IN let-386 hi 17 IN let-381 h87 O U T let-390 K44 IN let-396 K217 O U T let-601 K281 O U T let-602 K283 O U T let-604 h293 IN let-606 h292 O U T let-601 h402 IN let-608 h.706 IN let-610 h695 IN let-611 h850 O U T bli-4 h254 O U T h D p 14 h D p l 6 h D p l 8 hDp32 hDp31 hDp56 hDp39 hDp54 0.1 map units h D p 19 hDp33 hDp35 hDf8 let-396, let-602, let-611 bli-4 let-381, let-381, let-380, let-601, let-606 - lei-608, let-610 let-386, let-604 let-382, let-390 let-6 07 Figure#13: Genetic map of the essential genes in the hDpl6/hDp!9 region, showing the duplicat ion and deficiency breakpoints. 5 6 C o m p l e m e n t a t i o n A n a l y s i s of L e t h a l S t ra ins Complementation analysis was carried out for the recombination mapped lethals lying between dpy-5 and unc-13, as well as for the duplication mapped lethals lying between hDp 16 and hDp 19. i) Complementation Analysis of Recombination Mapped Lethals The five new mutations found to lie below dpy- 5 by recombination analysis, h'289, h.290, h292, h29S, and h312, were tested for complementation to the thirty-three known essential genes in the dpy-5 unc-13interval. Each of the five new mutations was complementation tested to itself as a control. Each of the five new mutations complemented all the known essential genes. Four of the new mutations, h289, h-292, h293, and h3l2, define four newly identified essential genes in this region (see table#9). However, h-290 was not assigned a gene name since it was considered to be inseparable from dpy-5, and, therefore, could lie either above or below the dpy-5 gene, and as such would require further complementation analysis. This decision was made based on the recombination mapping data, which placed h290 below dpy-5 on the recovery of only one dpy-5 mutant, and because the duplication mapping results showed h290 to be covered by hDp 15, which lies extremely close to dpy-5. This data was considered insufficient, to accurately determine the position of h290. Table#9: Recombination Mapped  New Essential Genes in dvy-5 unc-13 Region Allele New Gene Name h-289 let-603 K292 let-606 h.293 let- 604 h312 let-605 58 ii) Complementation Analysis of Duplication Mapped Lethals Once the 178 lethal mutations were assigned to their map positions relative to the duplication breakpoints, the next step was to test them for complementation to the essential genes lying between the same breakpoints. I have concentrated on the h.Dpl6/hDp 19 region, where I have complementation tested thirty new mutations with ten known essential genes, and two new essential genes, let-604 and let-606 (see previous section), identified between the same breakpoints. My results define an additional four essential genes in this region (see table#10), making a total of six newly identified essential genes in the hDp 16'/hDp 19 region. In addition, several new alleles of known essential genes have been identified, including six new alleles of bli-4, f ° u r n ew alleles of let-386, and four new alleles of let-396. There are now a total of sixteen essential genes in the hDp!6/hDp 19 region, including bli-4- Ten of these genes are represented by more than one allele (see tableau). None of the new mutations failed to complement more than one essential gene, suggesting that all the mutations arose from either point mutations, or from very small deletions which do not span more than one essential gene. This is consistent with the type of mutations usually found using EMS mutagenesis (Miller, 1978). Reciprocal complementation tests for each allele within a complementation group (gene) were also carried out. In every case, all the alleles within a given complementation group failed to complement each other. Therefore, no maternal effects were detected. Table#10: Duplication Mapped  New Essential Genes in hDp 16'/hDp 19 Region Allele New Gene Name h(02 let-607 h706 let-608 h.695 let-610 h850 let-611 60 Stage of Arrest of Lethal Mutations in dpy-5 unc-13 Region The stage of lethal developmental arrest was examined for each of the existing published essential genes, as well as for the new lethal mutations in the dpy-5 unc-13 region, by examining the Unc-13s from each arresting strain ( dpy-5 let-X unc-13 / dpy-5 let-X unc-13 / hDpZ ). If the duplication does not cover the lethal mutation, then the Unc-13 worms will arrest in their development sometime between the egg and adult stages, depending upon the lethal mutation present. Twenty-five Unc-13 worms were examined for their time of developmental arrest for each lethal mutation studied, except in cases where no Unc-13 worms were found. W i t h the exception of recombinants which had lost their lethal mutation, for every lethal mutation examined, all the worms for a given allele arrested at the same stage in development, ranging in size within the limits set for that particular stage (see footnote in table#3 for sizes of stages). Table#3 gives a summarj' of the times of arrest for the essential genes, while appendix#3 gives a summary of the times of arrest for the new lethal mutations in the dpy-5 unc-13 region. T a b l e # l l gives a summary of the times of arrest for all the alleles of the essential genes in the hDp 16/hDp 19 region. For three essential genes, let-380, let-601, let- 607, no Unc-13s were found, even when the other phenotypes were removed from the self-cross progeny of the W t hermaphrodite (figure#5). A l l three of these lethals were found to arrest in the egg stage, the eggs turning from colourless to dark brown, collapsing, and the egg shell getting more pliable and spherical as the egg shell broke down. This procedure was also carried out for three of the bli-j alleles, h520, h699, and h754, as they seemed to arrest around the egg or L l stage, and a more accurate timing of their arrest was wanted. W i t h all three of these bli-j alleles, some of the eggs remained unhatched, but were in the late embryonic stage (pretzel shape), then went mushy and died; 61 some Unc-13s hatched just out of the egg shells, but were still folded in the pretzel shape when they died; and, others managed to hatch and unfold before they died. Their arrest stage is recorded as e g g / L l . This same pattern of arresting at or near the time of hatching was seen for all the bli-4 alleles. The lethals which arrested as adult steriles had the same life span as the normal Unc-13s, however, no eggs were laid, and no oocytes were visible inside the worms. A l l the adult steriles grew to the normal length expected for Unc-13 adults (0.6 - 0.8 mm), except for let-604 h490. h.490 was much squatter and fatter (0.45 - 0.5 mm) than expected for an adult Unc-13. However, the canonical allele, let-604 h'293, was the length expected for a normal Unc-13 adult. In the hDp 16'/hDp 19 region, some differences were seen between alleles of a given essential gene, for which multiple alleles existed. For example, two alleles of let- 608 (h369 and h853) arrest at the early larva stage, while the third allele (h706) arrests at the late larva stage. However, there was no variation in arrest stage within one given allele of an essential gene (see tableau). Table^fcll: Stage of Developmental Arrest for  Lethals in hDp 16'/hDp 19 Region Gene Allele Size(mm) Stage of Arrest let-380 h80 1x675 K831 0.2 Egg Early larval Not determined let-381 hi 07 h495 h747 M i d larval Early larval Earfy larval let-382 h82 1x476 0.5 0.35 M i d larval M i d larval let-386 hi 17 h678 h749 h851 h873 0.3-0.35 0.4 Early larval Early larval Not determined M i d larval M i d larval let-387 h87 M i d larval let-390 h.44 Early larval let-396 h217 h354 h462 h538 h.824 Early larval Early larval Early larval Early larval M i d larval let-601 h281 Egg let- 602 h283 h374 K497 Early larval Early larval Early larval let- 604 h.293 h490 0.7 0.45-0.5 Adul t sterile Adul t sterile let-606 h292 Adul t sterile let-607 h402 Egg let-608 h706 h369 1x853 Late larval Early larval Early larval 63 T a b l e # l l : continued Gene Allele Size Stage of Arrest ltt-610 h695 Adul t sterile let-611 h850 0.3 M i d larval h756 0.2 Early larval h822 0.3-0.35 M i d larval bli-4 h42 ' ' E g g / L l hi 99 E g g / L l h.254 E g g / L l h,384 E g g / L l h427 E g g / L l h520 E g g / L l h699 E g g / L l h754 E g g / L l h79l E g g / L l * Sizes used to determine larval stages, which were measured by a micrometer, were as follows (see figure#8): Early larval stage = L 1 / L 2 = 0.15 - 0.3 m m M i d larval stage = L 2 / L 3 = 0.3 - 0.4 mm Late larval stage = L 3 / L 4 = 0.4 - 0.6 mm Adult stage = 0.6 - 0.8 m m 64 Test for Sperm-defective Mutants A l l the sterile adults identified in this thesis were healthy, and lived the normal life-span expected for an Unc-13 worm (approximately two to three weeks), except no progeny were produced. It is possible that the lethal mutations only affected their gonads. Since hermaphrodites produce both egg and sperm, a mutation affecting either of these two processes would cause sterility. A simple test to identify sperm-defective mutants is to mate an adult hermaphrodite homozygous for the lethal mutation to W t males. In this way, if the hermaphrodites are producing normal oocytes, the sperm from the W t males should rescue the sterile phenotype. Eleven adult sterile lethal mutations were crossed to N2 males, in an attempt to rescue the phenotype. One lethal was in the hDp 15'/hDpIS region, let-355 (h8l), and carried the duplication hDp 15. The other ten lethals, listed below, carried the duplication hDplS. Six lethals were in the hDp 13/hDp 16 region: let-367 (hi 19), let-384 (h84), let-395 (h27l), let-603 (h289), h408, and h752. Three lethals were in the hDp 16/hDP 19 region: let-604 (h.293), let-606 (1x292), and let-610 (h.695). One lethal was in the hDPl9/sDp2 region, let-605 (hSl2). None of the adult sterile lethals were rescued by the W t sperm. Therefore, none of these eleven lethal mutations could have affected solely the process of spermatogenesis. Alternatively, these mutations could affect either oogenesis, or possibly cause a gross defect in the gonad itself, such as by affecting the lineage of the gonad, or affecting the distal tip cell. 6 5 D I S C U S S I O N I have analyzed the essential genes in a small region of the C. elegans genome, as defined by the breakpoints of the chromosomal duplications hDp 16 and hDp 19, on chromosome I. I examined 189 from the set of 495 EMS-induced lethal mutations described in Howell (1989) to define the essential genes in this interval, and to identify new alleles of the existing essential genes. A combination of recombination mapping, deficiency mapping, duplication mapping, and complementation analysis were used to analyze the lethal mutations lying between dpy-5 and unc-13, as well as for a saturation analysis of the hDp 16/hDp 19 region. Howell et al (1987) demonstrated that the large chromosomal duplication sDp°2 could be used to isolate EMS-induced lethal mutations on Linkage Group I. McKim (McKim et al, 1990) broke down the sDp2 duplication, using gamma rays, to create a series of overlapping duplications with different breakpoints within the dpy-5 unc-13 interval. Using these new duplications, the dpy-5 unc-13interval was divided into three almost equal zones, which are defined by the breakpoints of three overlapping duplications, hDplS, hDp 16 and hDp!9. These three duplications were used to map thirty-three previously identified essential genes known to lie between dpy-5 and unc-13, as well as to map 178 new mutations from the sDp2 set of lethals. 116 of these new mutations were found to map within the dpy-5 unc-13 interval. I then concentrated on the small, approximately 0.5 map unit, region as defined by the breakpoints of the duplications hDp16 and hDp!9. I mapped ten known essential genes, and thirty-two new lethal mutations to this region, using nine new duplications and one deficiency. These new lethal mutations were assigned to complementation groups, thereby identifying six new essential genes. This increased 66 the number of existing genes in the hDp 16/hDp 19 region by 60%, bringing the total number of essential genes to sixteen. Ten of these genes have more then one allele. As a result of my analysis, six newly defined regions were established, wTith breakpoints approximately every 1/10 of a map unit, in the hDpl6/hDpl9 region. This gave a resolution of one breakpoint for every approximately three genes. Comparison.of Mapping Techniques The 189 sDprescued lethals analyzed in this study spanned the left third of chromosome I, about seventeen map units. A n efficient mapping technique was needed, which would be suitable for mapping large numbers of lethal mutations quickly, and precisely. Three different, mapping techniques were employed to map the lethal mutations: recombination mapping, deficiency mapping, and duplication mapping. Recombination mapping is a simple, straightforward method using sDp2 as a balancer. To obtain the heterozygous hermaphrodites to use in recombination mapping, the sDp2-rescued lethal-bearing Unc-13s are simply mated to W t males. sDp2-carrying progeny can easily be selected against, because of their slower development and different appearance. The two-factor mapping made use of the visible markers dpy-5 and unc-13, which were linked to the lethal mutations. Both of these markers are easily visible, which increases the accuracy of the mapping, as recombinants are easily detected. 6 7 Usually, over a thousand worms are counted in such crosses, removing the animals from the plates as they are counted. It is quite labour intensive to count such crosses. Furthermore, with mutants very closely linked to dpy-5, the recombination distances are not likely to be very accurate, since only a few recombinants are detected. The distances of more distant mutants are less subject to statistical fluctuation. The recombination distances estimated from two-factor crosses can often be insufficient to establish the map order of mutants, as demonstrated by my results in figure#10. To order the genes unambiguously, three-factor crosses need to be carried out. Even then, recombination mapping gives a right-left position of the mutant with respect to the marker, but the distance of the mutant from the marker is not precisely determined unless a large number of recombinants are scored. Deficiency mapping has been used to map large numbers of lethal mutations on Linkage Group IV (Clark et al, 1988), Linkage Group V (Rosenbluth et al, 1988), as well as for other chromosomes in C. elegans. Deficiency mapping is easier than recombination mapping, because it is not necessary to score progeny. Unfortunately, attempts in our lab to construct a series of overlapping deficiencies to span the gene cluster on L G I have failed. Deficiencies generated in this gene cluster generally lead to poorly viable worms, and the strains die out. It is possible that portions of the gene cluster on L G I is haplo-insufficient. However, a few deficiencies for this region do exist. hDf8 is one such deficiency, which proved useful for the analysis of the dpy-5 unc-13 region. Strains carrying hDf8 were sickly, and the brood sizes were low, but mapping using this deficiency was still possible. A comparison of hemizygotes to homozygotes for the lethal mutations would have given useful information on the developmental arrest stages. In general, a lethal mutation which displays a more severe phenotype in the hemizygote is likely to be a hypomorphic 68 mutation. However, because of the lower viability of the animals carrying hDf8, lethal arrest times were considered unreliable, and were not recorded. A n y variation in lethal arrest stages could be due to the poor viability of hDf8-carrying strains, rather than to the lethal mutation being hemizygous. A second problem with hDf8 is that it does not carry any marker genes. Attempts in our lab to introduce dpy-5, or mic-13, markers onto the hDf8-carrying chromosome were unsuccessful, as it is a cross-over suppressor (A. Rose, personal communication). This cross-over suppression suggests that hDf8 is not a simple deficiency, but involves a more complex rearrangement (Starr, P h D Thesis, 1989). The problem of the lack of markers was circumvented by using a protocol involving screening for Wts , which carried the deficiency, and the lethal mutation. Since there are no other deficiencies which overlap h.Df8, the positioning of lethals with respect to hDf8 alone can be ambiguous. If a lethal mutation lies within hDf8, its position is well defined. However, if it lies outside of hDf8, it could lie either to the left or to the right of hDf8. Duplication mapping has been the most effective way to position large numbers of lethal mutations for chromosome I. Duplications are easier to recover than deficiencies for chromosome I. Animals carrying duplications are much healthier, and have larger brood sizes, than animals carrying deficiencies, making them easier to work with, and, as such, more useful for mapping genes. M c K i m ( M c K i m & Rose, 1990) generated a series of duplications by breaking down the duplication sDp2 with gamma rays. These duplications have one fixed end, while the other end forms a series of overlapping breakpoints between dpy-5 said unc-13, giving a right-left positioning of the lethal mutations with respect to one another. 6 9 One problem encountered with the use of duplications is the increased expression of genes located outside the duplication, which could result in the rescue of hypomorphic mutations (Meneely & Nordstrom, 1988). However, this problem has only been found to occur with X chromosome duplications. It has not been studied with chromosome I duplications. Duplication mapping was found to be a faster and a more precise method than recombination analysis. Also, the duplications were easier to generate and work with than deficiencies for chromosome I. As a result, mapping using the duplications is the method of choice for positioning large numbers of lethal mutations on chromosome I. S tage of D e v e l o p m e n t a l A r r e s t The stage of developmental arrest was determined for the majority of the 178 new lethal mutations lying between dpy-5 and unc-13 (Appendix#3). The new lethal mutations have been grouped into three zones, as defined by the duplication breakpoints of hDplS, hDplS, hDp 19, and sDp2. a) hDp 13/hDp 16 region, b) hDp 16/hDp 19 region, and c) hDp!9/sDp2 region (figure#14). There seemed to be a correlation between the map position of the lethal mutations and the time in development at which they block. Wi th in each region, many of the lethal mutations appeared to arrest at the same stage, this stage differing from region to region. Overall, there seemed to be a gradation in blocking time, with the hDp 13/hDp 16 region carrying more late blocking mutations, the hDp 16/hDp 19 region being more or 70 less evenly distributed, and the hDpl9/sDp'2 region carrying mostly early larval blocking mutations. To determine whether such a pattern of lethal distribution exists, a chi-square test was applied to the data (table#12). The. chi-square test looks at the deviation between the observed number of mutations within a class and the expected values (figure#16). The value of chi-square was then converted into the probability that the deviation from the expected values were due to chance, using the tables of Fisher and Yates (Stansfield 1983). When the chi-square test was applied to the data, the egg, early larval and adult stages showed statistically significant deviations from the number of lethal mutations expected to arrest in each region (table#12). However, any conclusions drawn from this data could only be tentative, since some of the lethal mutations could be alleles of the same essential genes. If some of the essential genes have received multiple hits, then an overemphasis would have been placed on these genes, distorting the results. To determine the distribution of essential loci along the chromosome would be biologically more meaningful. Therefore, the stage of developmental arrest was determined for the majority of the thirty-three existing published essential genes lying between dpy-5 &nd unc-13 (table#3). When grouped within the breakpoints of the duplications hDplS, hDpld, hDp 19 and sDp2, the essential genes seemed to follow a gradation in blocking times, with late blocking mutations close to dpy-5, and early blocking mutations near unc-13 (figure#15). When the chi-square test was applied to the data, the only stage of arrest which showed any significant difference between the number of essential genes arresting was the egg stage (table#13). The deviation from the expected values for the remaining stages of arrest could have been due to chance. Therefore, my data does not show a statistically significant association of the regions with the times of arrest. However, the problem with applying such a statistical test to this data is the small sample size available to work with. The chi-71 square test cannot be properly used for experiments where the expected frequency within a phenotypic class is so small, even when the Yates correction for small samples is applied (figure#16). To determine whether regions do vary in the arrest times of their essential loci, a larger sample size would be needed to work with. Hopefully, the work presented in this thesis might encourage other scientists to look at the distribution of lethal arrest times along small regions of the chromosomes. As more regions are studied for developmental arrest, more data will become available for this type of analysis. This type of analysis is important, because a distinct pattern of lethal developmental arrest might suggest that the genes required during the same period in development may be spatially clustered together on the chromosomes. In all three zones, the majority of essential genes and new lethal mutations arrest at the early larva stage. This result is not surprizing, as most housekeeping genes would fall into this class of early arrest genes. C. elegans embryonic development is strongly maternally influenced, so most of these mutants would survive the egg stage, then die as they enter the first larval stage. For example, Rogalski et al (1988) showed that mutants homozygous for null lethal mutations in ama-1 IV, encoding the largest subunit of RNA polymerase II, an enzyme required for transcription, are able to survive the egg stage, before dying as early larvals. The stage of lethal arrest for the sixteen essential genes in the hDpl6/hDpl9 region was examined more closely. For the essential genes which had more than one allele, most of the alleles of a given gene arrested at approximately the same stage in development (table#ll). For a given allele, there was no variability in the time of lethal arrest; for each lethal, all the worms examined (twenty-five in each case) arrested at exactly the same stage, ranging in size within the limits set for each stage 72 (table#3). Therefore, there was some variability in the time of developmental arrest between different alleles within a given complementation group, but there was no variation within a given allele. One might have expected to see a background "noise" of lethality due to other causes, such as nondisjunction, which would give a low frequency of lethality at other stages. Such a background "noise" would probably be missed, since the majority of mutations in C. elegans would arrest at the early L l stage, which is the stage that most of the mutations that I examined arrested. Furthermore, I only examined a random sample of twenty-five Unc-13s for each lethal, therefore, I could have missed any Unc-13s which arrested earlier. Other researchers have also found such a consistency within complementation groups (Rosenbluth et al, 1988; Rogalski, 1982). However, Clark et al (1988) observed interallelic variation in developmental arrest between homozygotes and hemizygotes. They showed that when variability existed, the hemizygote always exhibited the more severe phenotype, indicating l^pomorphic mutations (Muller, 1932). Hypomorphic mutations result in a reduced amount of gene product being produced. Two copies of a hypomorphic allele (homozygote) would be less severe than only one copy (hemizygote), because the two copies could produce more gene product, thereby getting closer to wildtype levels. In contrast, a hypermorphic mutation, which results in the overproduction of the gene product, would be more severe in a homozygote, than in a hemizygote. A n amorphic, or null allele, would be as severe in a homozygote as in a hemizygote, since in each case no gene product would be made. A comparison of the time of arrest for the lethal mutations in homozygotes and hemizygotes would, therefore, give valuable information on the type of mutation involved. Unfortunately, the difference in arrest stages between homozygotes and hemizygotes could not be examined in this study, because the hemizygotes carrying the deficiency hDf8 were sickly animals, so any variation in 73 developmental arrest could be due to hDf8, and not to the lethal mutation itself. Liecht and Bonner (1988) also found interallelic variation, which they attributed to linked second site mutations, which had earlier lethal blocking times. The small variation in lethal arrest stages between alleles at essential genes in the hDpl6/hDpl9 region could be due to leakiness of later arresting lethal mutations, or to a difference in severity of the mutant alleles. The essential genes in the hDpl6/hDpl9 region show considerable variability between their developmental arrest stages. If the earliest blocking allele is taken for genes with more than one allele, then three genes are required for development past the egg stage, eight genes are required for development past the first larval stage, two genes are required for development past the mid-larval stage, and three genes are required for fertility of adult hermaphrodites. Two classes of early larval blocking lethals were found: those which reached the earfy larva stage, and then soon died; and those which reached the early larva stage, and lived for at least a further two weeks without developing past the first larval stage. Seven out of eight of the essential genes in the hDp 16/hDp 19 region died after reaching the first larval stage. This class of genes probably carries the housekeeping genes necessary for the worm to survive. Maternal influence, common in C. elegans, is probably responsible for these mutants developing past the egg stage. However, once they hatch, they can no longer survive. The second class of mutants, those which live for at least two weeks as early larva, is represented by only one essential gene, let-608, in the hDp 16/hDp 19 region. This mutant seems to live the normal life-span for C. elegans worms, which is two to three weeks from egg to adulthood, however, they are "trapped" as early larva ( L l ) , not being able to molt to the mid-larval stage (L2). let-608 could, therefore, be a gene required for the molting process from the L l to the L2 stage. One would expect many more housekeeping genes than 74 genes required specifically for molting, and this was indeed found. Other lethal mutants were also found to live for at least one week as early larva. K360, h361. h^29 and h445 (appendix#3) did not develop past the first larval stage, but were still alive after one week. A l l four of these new mutations mapped to the hDpl9/sDp2 region. A l l of the adult sterile lethals that were identified had a normal life-span (approximately two weeks), and grew to the size expected for Unc-13 worms (0.6 -0.8 mm), with the exception of let-604 h-490, which was much more squat and fatter (0.45 -0.5 mm) than usual. The other allele of let-604, namely h293, grew to the normal length for Unc-13s. let-604 h293may have a less severe phenotype than let-604 h490. a) hDp13/hDp16 region; U of mutat ions r e p r e s e n t e d b) hDp16/hDp19 reg i on; Egg Ear ly larval Mid larval Late larval Adul t s ter i le Time of arrest # of mutations represented Egg Ear ly larval Mid larval Late larval Adul t ster i le Time of arrest c) hDp19/sDp2 reg ion: * of mutations represented Ear ly larval Mid larval Late larval Adult ster i le Time of arrest F i g u r e # 1 4 : A comparison ot the stages ot developmental arrest for new lethal mutations in the dpy-5 unc-13 region a) hDp13/hDpl6 # of genes represented 7 reg ion : - n - n m • Wk Egg Early larval Mid larval Late larval Adult sterile Time of arrest b) hDp16/hDpl9 reg i on : of genes represented c) hDpl9/sDp2 reg i on : Egg Early larval Mid larval Late larval Adult sterile Time of arrest # of genes represented Egg Early larval Mid larval Late larval Adult sterile Time of arrest Figure#15: A c o m p a r i s o n of the s t a g e s of d e v e l o p m e n t a l a r r e s t for e s s e n t i a l g e n e s in the dpy-5 unc-13 r e g i o n F i g u r e ^ l G : Equations used for Chi-Square Tests 77 Chi-Square Test: o ? % 3 (o.-ej)2 ( o i - e i ) 2 ( o 2 - e 2 ) 2 (03 - e 3 ) 2 A - 1 = = -f- - f i=l ei e l E2 E3 Yates Correction for Small Samples: r 2 *'=3 [(Oi-ei)-0.5]2 [(oj - ej) - 0.5]2 [(o2 - e 2 ) - 0.5]2 [(03 - e 3) - 0.5]2 X — /_/ _ 1 1 7=1 e i e l E2 E3 where, A ' 2 = probability that deviation is due to chance •1 = number of classes increasing from 1 to n n = 3 regions (hDplS/hDpl6, hDpl6/hDpl9, hDpl9/sDp2) o = number of observed genes within a region e = number of expected genes within a region degrees of freedom = n - 1 = 2 78 Table#12: Chi-Square Test for the Developmental Arrest of the  New Lethal Mutations lying between dpy-5 and unc-13 Stage of Developmental Arrest Egg Early larval M i d larval Late larval Adult, sterile Total % of lethals represented # of Lethal Mutations observed, arresting a) hDplS/hDpl6region 0 9 5 1 7 22 21% b) hDp 16'/hDp 19 region 7 11 5 3 2 28 27% c) hDpl9/sDp2 region 3 41 3 2 5 54 52% Total # of Mutations 10 61 13 6 14 104 100% # of Lethal Mutations expected to arrest 0 a) hDp 13/hDp 16 region 2 13 3 1 3 22 b) hDp 16'/hDp 19 region 3 16 3 2 4 28 c) hDp 19/sDp2 region 5 32 7 3 7 54 A * 8.10 5.3 4.9 0.8 6.9 Ar2 (Yates correction) 8.35 5.7 4.4 1.1 6.6 For 2 degrees of freedom S* S N S C NS S °; calculated from (total # of observed mutations x % of mutations represented) S = significant difference (i.e. probably not due to chance) c NS = not significant difference (i.e. probably due to chance) 79 Table#13: Cm-Square Test for the Developmental Arrest of the  Essential Genes lying between dpy-5 and unc-13 Stage of Developmental Arrest Egg Early larval M i d larval Late larval Adult, sterile Total % of genes represented # of Essential Genes observed arresting a) hDpl3/hDpl6region 0 6 0 0 4 10 29% b) hDp 16/hDp 19 region 4 7 2 0 3 16 46% c) hDp 19/sDp2 region 0 7 1 0 1 9 26% Tota l # of essential genes 4 20 3 0 8 35 100% # of Essential Genes expected to arrest a a) hDpl3/hDp 16 region 1 6 1 0 2 10 b) hDp 16/hDp 19 region 2 9 1 0 4 16 c) hDp 19/sDp2 region 1 5 1 0 2 9 A3 4.0 1.2 2.0 0 2.75 A r2 (Yates correction) 5.6 1.2 2.5 0 2.80 For 2 degrees of freedom N S C NS NS NS ?• calculated from (total # of observed genes x % of genes represented) ° S = significant difference ( i . e . probably not due to chance) c NS = not significant difference (i.e. probably due to chance) 8 0 % S a t u r a t i o n for E s s e n t i a l Genes i n hDpl6/hDpl9 The completion of the lethal analysis has resulted in eight newly identified essential genes, six within hDp 16/hDp 19. This brings the total number of essential genes in the hDp!6/hDpl9 region to sixteen. Ten of these genes have more than one allele. These lethal mutations were identified from a screen of 31,600 E M S -mutagenized chromosomes. The minimum number of essential genes in the hDp 16/hDp 19 region can be calculated using the truncated Poisson formula of Meneely and Herman (1979), f = (1 - em - m e " m ) / (1 - e m ) , where T is the fraction of genes with more than one allele, 'm ' is the average number of alleles, and 'e' is the base of the natural logarithm. For the hDp 16/hDp 19 region, ten of the sixteen genes were represented by more than one allele, giving a value for ' f of 10/16 = 0.625 B y calculation from the above formula (see appendix#7), m = 1.65 The fraction of genes with no mutational hits, P ° , is equal to e" m . The proportion of genes in the hDp 16/hDp 19 region with no alleles is P ° = 0.20 Therefore, a maximum of 80% of the essential genes in this region have been identified. From these calculations, I predict that there are four genes yet to be identified, giving a total minimum estimate of twenty essential genes in the hDp 16/hDp 19 region. The truncated Poisson formula was used because it places less emphasis on the highly mutable genes than the regular Poisson formula. This is necessary because the Poisson distribution assumes that all the essential genes are equally mutable, and that all the mutants are equally detectable. If these assumptions are not met, the data wil l not fit a Poisson distribution. Studies with Drosophila. melanogaster have shown that these assumptions do not hold, because they do not take into account loci having extremely low mutabilities, or loci with undetectable phenotypes (Lefevre, 1986). The mutability of the essential genes in the hDp 16/hDp 19 region are clearly unequal. Some genes are obviouly hotspots for E M S mutagenesis, either because of 81 their size or their sensitivity to mutation. This is true for the bli-4 locus, which has nine alleles, when the average allele frequency was calculated as 1.65 Figure#18 shows a comparison of the observed distribution of mutations in the JiDpl6/hDpl9 region to that predicted by the truncated Poisson formula. The data clearly shows that the number of alleles found at different loci does not fit a Poisson distribution exactly, even when the truncated nature of the data is accommodated. There are more, genes with multiple alleles than expected. Because the mutability of the genes is unequal, my estimate of the number of genes in this region is only a minimum one. Furthermore, it is only an estimate of the total number of essential genes in the region, as I cannot estimate the total number of non-essential genes. The frequency of mutational hits should be the same across the entire sDp2 region, since the screen was unbiased in regards to the position of the lethal mutations recovered. Therefore, the degree of saturation of essential genes in any other interval of the sDp2 region should be the same as that obtained for the hDp 16/hDp 19 region. M y results are similar to those obtained by A . M . Howell (PhD Thesis, 1989). Analyzing lethal mutations in the hDf6 region from the same sDp2 screen of 31,600 mutagenized chromosomes, Howell predicted that she had identified 75% of the essential genes in that region. This result is comparable to that I obtained for the hDp16/hDp 19 region, as would be expected. Figure^lT: Equations used for % Saturation Analysis 1) Truncated Poisson Analysis: / = ( 1 - e " m - m e ' m ) ( 1 - e " m ) where, / = fraction of genes with more than one allele m = average number of alleles per gene e ' m = proportion of genes with no alleles e = base of the natural logarithm = 2.71828 2) Poisson Formula (used in figure#16): p i = m t e - m i ! for, i = 1 - 5 alleles where, P = probability of a rare event, e.g. a specific mutation 83 T a b l e ^ l 4 : Distribution of Alleles Compared to Truncated Poisson Distribution Number of Alleles Observed Number Expected Number 0 4 1 6 7 2 2 5 3 5 3 4 0 1 5 2 0 9 1 0 84 F i g u r e # 1 8 ; O b s e r v e d d i s t r i b u t i o n o f l e t h a l m u t a t i o n s in t h e hDpW/hDpW r e g i o n , c o m p a r e d to t h a t p r e d i c t e d by t h e P o i s s o n f o r m u l a , p ' = m ' e~m/ i I , w h e r e t h e v a l u e o f ' m ' w a s d e t e r m i n e d u s i n g t h e t r u n c a t e d P o i s s o n f o r m u l a . 85 Forward Mutation Rates I have made an estimate of the average forward mutation rate per gene in C. elegans using the data obtained from both the hDpl6/hDpl9 region analyzed in this thesis, and the hDf6 region analyzed by A . M . Howell (PhD Thesis, 1989). A combination of our results to give a more accurate estimate of the forward mutation rate was possible, since the same set of 31,600 chromosomes have been used in the saturation analyses of both regions. The mutability was calculated by dividing the average number of mutational hits a gene would receive, by the number of chromosomes screened. Since bli-4 hi the hDp 16/hDp 19 region, and let-354 m t , n e hDf6 region, both have many more alleles than the average gene in their regions, they have been omitted from the calculation. In the hDp!6/hDp!9 region, forty-four lethal mutations have been recovered. The target was the twenty genes predicted to be present in this region. From the work done by A . M . Howell, the hDf6 region has a predicted target of twenty-four genes, thirty-seven lethal mutations having been isolated. This gives a total of eight-one lethal mutations recovered from 31,600 mutagenized chromosomes, with a predicted target of forty-four genes. Using these values, the average forward mutation rate per gene is 5.8 X 10"'-1, using 17mM E M S . This value is almost ten-fold lower than that obtained by Brenner (1974). Brenner estimated that the average forward mutation rate induced by 50mM E M S is about 5 X 10"4 per gene. This difference is not accountable by E M S dose alone. B y examining the dose-response curve for E M S mutagenesis (Rosenbluth et al, 1983), such a difference in E M S dose would only produce a two-fold decrease in induction frequency. Brenner based his estimate on the identification of visible mutations, which could involve some inaccuracy, since the more subtle phenotypes may be missed. His sample size of approximately 800 mutagenized chromosomes was quite small. Also, since only the minority of genes in C. elegans mutate to visible 86 phenotypes, this estimate may reflect the forward mutation rate for visible genes, rather than for the average gene. For these reasons, I consider Brenner's estimate of the average forward mutation rate to be too high. I have made a comparison of the forward mutation rates for the EMS-induced essential genes in the hDp 16/hDp 19 region, which were screened from 31,600 chromosomes. The mutability for a given gene was calculated by dividing the number of mutational hits the gene received, by the number of chromosomes screened. The mutability of the genes in this region is not equal. The most mutable targets are bli-4 with nine alleles (2.9 X 10 "^mutations/gene), let-386 with five alleles (1.6 X 10"^ mutations/gene), and let- 396 with five alleles (1.6 X 10 mutations/gene). Their forward mutation rates are, respectively, 6X, 3X, and 3X higher than the average forward mutation rate for C. elegans genes (5.8 X 10"^ mutations/gene), as calculated above. In contrast, the remaining thirteen genes in the hDp 16/hDp 19 region are represented by only one to three alleles each. This makes their forward mutation rates similar to the average value for C. elegans genes (figure#19). The high mutability of bli-4, a n d to a lesser extent let-386 and let-396, could either be due to the size of these loci, or to their sensitivity to E M S mutagenesis. Two other highly mutable targets in C. elegans, unc-22 and unc-54, have been shown to be large genes (Moerman et al, 1988; McLeod, 1987). However, bli-4 is n ° t unusual when compared to other genes in the L G I gene cluster. For example, in the hDpl9/sDp2 region, let-385 has a total of eighteen alleles, giving a mutation frequency (5.8 X 10"^ mutations) eleven times higher than the average rate, and twice as high as bli-4 (A. Rose, personal communication). Also, in the sDf6 region, which is covered by the duplication hDplS, let-354 is represented by seventeen alleles, making its mutation frequency (5.4 X 10"^ mutations) similar to that of let-385. Therefore, although bli-4 is a highly mutable gene, there seems to be more mutable targets within the gene cluster on L G I. 87 F i g u r e # 1 9 F o r w a r d m u t a t i o n f r e q u e n c i e s f o r t h e e s s e n t i a l g e n e s in t h e hDpW/hDpW r e g i o n . 88 Tota l Number of Genes in C. elegans Genome A method for estimating the total number of genes in the genome, is to make an estimate of the number of genes in the sDp2 region by comparing the number of lethal mutations obtained in the sDp2 region to that in the hDp 16/hDp 19 region. This estimate can then be extended to an estimate of the number of genes in the entire genome. This calculation does not depend on a uniform distribution of essential genes in the sDp2 region, since the frequency of recovery of mutations should be the same across the entire sDp2 region. There is an estimate of twenty essential genes in the hDp 16/hDp 19 region, and forty-four chromosomes carrying lethal mutations in the hDp 16/hDp 19 region were isolated in the sDp2 screen. Since 495 lethal mutations were isolated in the sDp2 balanced region, there must be a minimum of 225 essential genes in the fifteen map unit sDp2 region, which is approximately 1/20 of the genome (300 map units)(Edgely et al, 1987). From this value it can be estimated that there is a minimum of 4,500 essential genes in the C. elegans genome. Since the sDp2 region covers half of the five gene clusters, this estimate is possibly an overestimate. The amount of D N A per map unit in the L G I gene cluster has been shown to be higher than for the rest of the chromosome. T . Starr et al (1989) showed that the amount of D N A per map unit across this gene cluster was not constant, but reached a peak around unc-13, with a D N A / m a p unit value 4.5 times the genomic average. This result is supported by K i m and Rose (1987), who showed that recombination in the same region increased four-fold after radiation treatment. Since sDp2 covers this gene cluster, the average essential gene density for the sDp2 region is probably higher than for the overall genome. Therefore, it is reasonable to assume that the fifteen map units making up sDp2 represent more than 1/20 of the genome. For this reason, 89 this estimate of the total number of essential genes in the C. elegans genome may be an overestimate. However, this estimate is still quite close to those obtained by other researchers, who used different methods to reach their estimates. The original estimate for the total gene number in C. elegans (Brenner, 1974) was 2,000 genes, based on the induction of X-l inked recessive mutations. Clark et al (1988) estimated there to be 3,500 essential genes, by extending an estimate of the number of genes in the region covered by the translocation nTl to the entire genome. Most recently, Howell (1989) obtained an estimate of 4,000 essential genes based on the saturation analysis of the region covered by the deficiency hDf6 on L G I. Originally, Howell arrived at an estimate of 6,000 genes, which was then corrected by the increased gene density of the hDf6 region, which was known to be 1.5 the genomic average. Unfortunately, the average gene density for the sDp2 region is not known, but it is probably higher than average, making my estimate an overestimate. 90 Summary In summary, I have carried out a genetic analysis of a small region of the C. elegans genome, as defined by the breakpoints of the duplications hDp 16 and hDp 19, on chromosome I. Below is a summary of the findings of this thesis. 1) The lower endpoint of the deficiency sDf4 was positioned with respect to dpy- 5 and the lethal mutations around dpy- 5. 2) The upper endpoint of the deficiency hDf8 was positioned with respect to the lethal mutations in the region. 3) The lower breakpoints of the duplications hDp 12, hDplS, hDplS, hDpl6, hDp 17, hDp 19, hDpSl, hDp39. hDp54, and hDp56 were positioned with respect to the essential genes lying between dpy-5 a,nd unc-13. 4) B y positioning the breakpoints of hDf8, hDpSl, hDp39, hDp54, and hDp56, six newly defined regions were established, with breakpoints every approximately 1/10 of a map unit in the hDp 16/hDp 19 region. This gives a resolution of one breakpoint every approximately three genes. 5) 189 new lethal mutations were mapped: eleven by recombination analysis, and 178 by complementation to the duplications hDp 13, hDp 16, and hDp 19. 6) Eight previously unidentified essential genes were identified, six lying in the hDpl6/hDp!9 region, thereby increasing the number of existing genes in the hDpl6/hDpl9 region by 60%. 7) I identified new alleles for ten of the sixteen essential genes in the hDpl6/hDp!9 region. In all, twenty-six new alleles of essential genes were identified, including six new alleles of bli-4-8) Truncated Poisson analysis was used to show the hDp 16/hDp 19 region to be 80% saturated for essential genes. Extrapolation lead to a minimum estimate of 91 approximately 225 genes in the sDp2 region, and 4,500 essential genes in the C. elegans genome. 9) The average forward mutation rate per gene in C. elegans was estimated to be 5.8 X 10" 5 per gene. 10) The stage of developmental arrest was determined for most of the essential genes in the dpy-5 unc-IS region, as well as for many of the 178 new mutations. Proposals for Future Research Below is a list of experiments that could be done to further investigate the work in this thesis. 1) A set of overlapping cosmid clones covers most of the dpy-5 unc-13 interval. Once the position of the duplication breakpoints of hDp 16 and hDp 19 have been determined with respect to the cosmid contig, the cosmids can be aligned to the genetic map. One approach would involve the cosmid rescue of the sixteen essential genes which lie between the hDp!6 and hDp!9 breakpoints. 2) The tissue-specific expression of the essential genes in the hDpl6/hDpl9 region could be investigated by genetic mosaic, analysis. Such a study would be especially interesting with the adult steriles, since mutants in the gonad, spermatogenesis and oogenesis have been well studied in C. elegans (Austin, 1987; Hodgkin, 1987; Miller, 1988) 3) To determine whether any of the lethal alleles cause mutation in a protein coding region, amber suppressor t R N A mutants such as sup-5 (Waterson, 1978) could be used, which is believed to be specific for amber null alleles. The identification of amber nul l alleles of essential genes wil l establish the phenotype of 92 the genes resulting from the complete absence of gene activity, and could be useful for detecting the missing gene product. 4) The identification of the site canying the T e l transposon in the Bergerac chromosome, which gave rise to the hP5 polymorphism, could be investigated. 5) The analysis of the hDp 16/hDp 19 region could be extended to the hDpl3/hDpl6, and hDp 19/sDp2 regions. Since the set of 495 sDp2- res cued lethals have all been positioned with respect to the hDplS, hDp!6, and hDpl9 breakpoints, the next step would be to further subdivide these regions with new duplication breakpoints, then to carry out complementation analysis to identify new essential genes. 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Mutants affecting paramyosin in C. elegans. J. Mol. Biol. 117: 679-698. APPENDIX#1: Strains Used Strain0 Genotype Origin BC149 dpy-5 let-83 (s91) unc-13 ; sDp2 A. Rose BC244 dpy-5 let-86 (sl41) unc-13 ; sDp2 A. Rose BC415 dpy-5 unc-13 / + + A. Rose KR281 dpy-5 let-390 (h44) unc-13 ; sDpS A. M. Howel KR290 dpy-5 bit-4 (h42) unc-13 ; sDp2 A. M. Howel KR350 dpy-5 let-391 (h9l) unc-13 ; sDp2 A. M. Howel KR354 dpy-5 let-385 (h85) unc-13 ; sDp2 A. M. Howel KR355 dpy-5 let-384 (h84) unc-13 ; sDp2 A. M. Howel KR357 dpy-5 let-382 (h82) unc-13 ; sDp2 A. M. Howel KR358 dpy-5 let-355 (h.8l) unc-13 ; sDp2 A. M. Howel KR359 dpy-5 let-380 (h80) unc-13 ; sDp2 A. M. Howel KR362 dpy-5 let-388 (h88) unc-13 ; sDp2 A. M. Howel KR363 dpy-5 let-387 (h87) unc-13 ; sDp2 A. M. Howel KR424 dpy-5 let-383 (hi 15) unc-13 ; sDp2 A. M. Howel KR426 dpy-5 let-370 (hl28) unc-13 ; sDp2 A. M. Howel KR429 dpy-5 let-381 (h!07) unc-13 ; sDp2 A. M. Howel KR430 dpy-5 let-377 (hi 10) unc-13 ; sDP2 A. M. Howel KR431 dpy-5 let-392 (h!20) unc-13 ; sDp2 A. M. Howel KR432 dpy-5 let-386 (hi 17) unc-13 : sDp2 A. M. Howel KR434 dpy-5 let-367 (hi 19) unc-13 ; sDp2 A. M. Howel KR440 dpy-5 let-389 (h!06) unc-13 ; sDp2 A. M. Howel KR444 d,py-5 let-378 (h!24) unc-13 ; sDp2 A. M. Howel 98 Appendix^!: continued Gene Genotype Origin KR446 dpy-5 let-376 (hi30) unc-13 ; sDp2 A. M. Howell KR454 dpy-5 let-379 (hi£7) unc-13 ; sDP2 A. M. Howell KR513 dpy-5 bli-4 (hi99) unc-13 ; sDP2 A. M. Howell KR531 dpy-5 let-396 (h217) unc-13 ; sDp2 A. M. Howell KR539 dpy-5 let-393 (h-225) unc-13 ; sDp2 A. M. Howell KR542 dpy-5 let-397 (h228) unc-13 ; sDp2 A. M. Howell KR595 dpy-5 bli-4 (h254) unc-13 ; sDp2 A. M. Howell KR598 dpy-5 let-398 (h257) unc-13 ; sDp2 A. M. Howell KR603 dpy-5 let-394 (h262) unc-13 ; sDp2 A. M. Howell KR610 dpy-5 let-400 (h269) unc-13 ; sDp2 A. M. Howell KR612 dpy-5 let-395 (h271) unc-13 ; sDP2 A. M. Howell KR614 dpy-5 let-399 (h273) unc-13 ; sDp2 A. M. Howell KR621 dpy-5 let-601 (h28l) unc-13 ; sDp2 A. M. Howell KR623 dpy-5 let-602 (h283) unc-13 ; sDp2 A. M. Howell KR1279 dpy-5 dpy-14 / hDp 19 K. McKim KR1280 dpy-5 dpy-14 ', hDp 13 K. McKim KR1282 dpy-5 dpy-14 i hDp 16 K. McKim KR1284 dpy-5 dpy-14 i hDplS K. McKim KR1293 dpy-5 dpy-14 i hDp 12 K. McKim KR1294 dpy-5 dpy-14 > hDp 17 K. McKim KR1304 dpy-5 dpy-14 > hDp 18 K. McKim KR1305 dpy-5 dpy-14 > hDp!4 K. McKim KR1458 unc-11 dpy-14 / + / szTl [+ + ; lon-2] K. McKim 99 Appendix^l: continued Gene Genotype Origin KR1743 dpy-5 dpy-14 ; ; hDp39 K. McKim KR1746 dpy-5 dpy-L{ , ; hDp56 K. McKim KR1770 dpy-5 dpy-14 ; ; hDpSS K. McKim KR1771 dpy-5 dpy-14 ; hDp 3 5 K. McKim KR1773 dpy-5 dpy-14 . ; hDpSl K. McKim KR1783 dpy-5 dpy-14 . ; hDpSS K. McKim KR1794 dpy-5 dpy-L{ ; hDp54 K. McKim KR1877 dpy-5 dpy-14 , ; hDf8 K. McKim The strain names indicate the lab of origin: BC = D.BailhVs lab, Burnaby, B. C. KR = A.Rose's lab, Vancouver, B. C. APPENDIX#2: Strains of New Lethal Mutations Used Strain Genotype Origin KR632 dpy-5 h286 unc- 13 ; sDp2 *A . Rose Lab KR633 dpy-5 h289 unc- 13 ; sDp2 A. Rose Lab KR634 dpy-5 h.290 unc- 13 ; sDp2 A. Rose Lab KR635 dpy-5 h291 unc- 13 ; sDp2 A. Rose Lab KR636 dpy-5 h292 unc-•13 ; sDp2 A. Rose Lab KR637 dpy-5 h293 unc-•13 ; sDp2 A. Rose Lab KR638 dpy-5 h294 unc-•13 ; sDp2 A. Rose Lab KR639 dpy-5 h.295 unc-•13 ; sDp2 A. Rose Lab KR640 dpy-5 h298 unc-•13 ; sDp2 A. Rose Lab KR641 dpy-5 h.300 unc-•13 ; sDp2 A. Rose Lab KR645 dpy-5 hSll UllC- •13 ; sDp2 A. Rose Lab KR646 dpy-5 h312 unc-•13 ; sDP2 A. Rose Lab KR647 dpy-5 h.313 unc--IS ; sDp2 A. Rose Lab KR648 dpy-5 hS14 unc--13 ; sDp2 A. Rose Lab KR671 dpy-5 h350 unc--13 ; sDp2 A. Rose Lab KR672 dpy-5 h351 unc--13 ; sDp2 A. Rose. Lab KR675 dpy-5 h.354 unc-•13 ; sDp2 A. Rose Lab KR677 dpy-5 h356 unc-•13 ; sDp2 A. Rose Lab KR678 dpy-5 h357 unc--13 ; sDp2 A. Rose Lab KR679 dpy-5 hS58 unc--13 ; sDp2 A. Rose Lab KR680 dpy-5 h359 unc--13 ; sDp2 A. Rose Lab 101 Appendix#2: continued Strain Genotype Origin KR681 dpy-5 h360 unc- lo , sDp2 A. Rose Lab KR682 dpy-5 h361 unc-13 ; sDp2 A. Rose Lab KR683 dpy-5 h.362 unc-13 ; • sDp2 A. Rose Lab KR687 dpy-5 K361 unc- 13; • sDp2 A. Rose Lab KR689 dpy-5 h369 unc- 13 ; • sDp2 A. Rose Lab KR694 dpy-5 h374 unc- 13, • sDp2 A. Rose Lab KR695 • dpy-5 h375 unc-•13 , • sDp2 A. Rose Lab KR704 dpy-5 h379 unc-•lo , • sDp2 A. Rose Lab KR705 dpy-5 h380 unc-•13, • sDp2 A. Rose Lab KR706 dpy-5 h381 unc-•13, • sDp2 A. Rose Lab KR707 dpy-5 K382 unc-•lo , • sDp2 A. Rose Lab KR709 dpy-5 K384 unc-•13, : sDp2 A. Rose Lab KR712 dpy-5 h.387 unc-•13 ; sDp2 A. Rose Lab KR713 dpy-5 h.388 unc-•13 , ; sDp2 A. Rose Lab KR714 dpy-5 h389 unc-•13 , ; sDp2 A. Rose Lab KR718 dpy-5 h.393 unc-•13 . ; sDp2 A. Rose Lab KR721 dpy-5 h396 unc--13 . ; sDp2 A.Rose Lab KR722 dpy-5 h397 unc-13 . ; sDp2 ' A . Rose Lab KR723 dpy-5 h398 unc-•13 , ; sDp2 A. Rose Lab KR726 dpy-5 h40l unc--13 ; sDp2 A. Rose Lab KR727 dpy-5 h.402 unc--13 . ; sDp2 A. Rose Lab KR728 dpy-5 h/OS unc-13 . ; sDp2 A. Rose Lab KR731 dpy-5 h406 unc-•13 . ; sDp2 A. Rose Lab 102 Appendix#2: continued Strain Genotype Origin KR733 dpy-5 hJf08 unc-13 ; sDp2 A. Rose Lab KR735 d,py-5 hJflO unc-•13; sDp2 A. Rose Lab KR737 dpy-5 h^l2 unc-•13 ; sDp2 A. Rose Lab KR738 dpy-5 h413 unc-•13 ; sDp2 A. Rose Lab KR740 dpy-5 h415 unc-•13 : sDp2 A. Rose Lab KR741 dpy-5 h416 unc-•13 ; sDp2 A. Rose Lab KR750 dpy-5 h425 unc-•13; sDp2 A. Rose Lab KR752 dpy-5 h427 unc-•13; sDp2 A. Rose Lab KR753 dpy-5 h-428 unc-•13; sDp2 A. Rose Lab KR754 dpy-5 h429 unc-•13; sDp2 A. Rose Lab KR755 dpy-5 h431 unc-•13 : sDp2 A. Rose Lab KR757 dpy-5 h433 unc-•13; sDp2 A. Rose Lab KR758 dpy-5 h.434 unc-•13 : sDp2 A. Rose Lab KR759 dpy-5 h435 unc-•13 : sDp2 A. Rose Lab KR760 dpy-5 h436 unc-•13 : sDp2 A. Rose Lab KR761 dpy-5 K437 unc-13 ; sDp2 A. Rose Lab KR764 dpy-5 h-440 unc--13; sDp2 A. Rose Lab KR766 dpy-5 h442 unc--13; sDP2 A. Rose Lab KR767 dpy-5 h443 unc-•13; sDp2 A. Rose Lab KR768 dpy-5 h444 unc~ -13; sDp2 A. Rose Lab KR769 dpy-5 h445 unc-•13; sDp2 A. Rose Lab KR770 dpy-5 h-446 unc--13 ; sDp2 A. Rose Lab KR771 dpy-5 h447 unc-•13; sDp2 A. Rose Lab Appendix#2: continued Strain Genotype Origin KR774 dpy-5 h450 unc-13 ; sDp2 A. Rose Lab KR777 dpy-5 h^SS unc-13 ; sDp2 A. Rose Lab KR77S dpy-5 h^54 unc-13 ; sDp2 A. Rose Lab KR782 dpy-5 h455 unc-13 ; sDP2 A. Rose Lab KR785 dpy-5 h458 unc-13 ; sDp2 A. Rose Lab KR787 dpy-5 J146O unc-13 ; sDp2 A. Rose Lab KR788 dpy-5 h.461 unc-13 ; sDp2 A. Rose Lab KR789 dpy-5 h.462 hi014 unc-13 ; sDp2 A. Rose Lab KR790 dpy-5 h463 unc-13 ; sDp2 A. Rose Lab KR791 dpy-5 h464 unc-13 ; sDp2 A. Rose Lab KR796 dpy-5 h4&9 unc-13 ; sDp2 A. Rose Lab KR801 dpy-5 h470 unc-13 ; sDp2 A. Rose Lab KR802 dpy-5 h411 unc-13 ; sDp2 A. Rose Lab KR803 dpy-5 h412 unc-13 ; sDp2 A. Rose Lab KR806 dpy-5 h475 unc-13 ; sDp2 A. Rose Lab KR807 dpy-5 h416 unc-13 ; sDp2 A. Rose Lab KR810 dpy-5 h479 unc-13 ; sDp2 A. Rose Lab KR814 dpy-5 h483 unc-13 ; sDp2 A. Rose Lab KR817 dpy-5 h.486 unc-13 ; sDp2 A. Rose Lab KR818 dpy-5 h489 unc-13 ; sDp2 A. Rose Lab KR819 dpy-5 h490 unc-13 ; sDp2 A. Rose Lab KR824 dpy-5 h492 unc-13 ; sDp2 A. Rose Lab KR825 dpy-5 h494 unc-13 ; sDp2 A. Rose Lab 104 Appendix#2: continued Strain Genotype Origin KR826 dpy-5 M97 unc-13 ; sDp2 A. Rose Lab KR827 dpy-5 h502 unc-13 ; sDp2 A. Rose Lab KR828 dpy-5 h503 unc-IS ; sDp2 A. Rose Lab KR829 dpy-5 h.506 unc-Jj ; sDp2 A. Rose Lab KR831 dpy-5 h50S unc-•lo ; sDp2 A. Rose Lab KR833 dpy-5 h512 unc-•lo ; sDp2 A. Rose Lab KR835 dpy-5 h514 unc-•13 ; sDp2 A. Rose Lab KR839 dpy-5 h518 unc-•13 ; sDp2 A. Rose Lab KR840 dpy-5 h519 unc-•lo ; sDp2 A. Rose Lab KR841 dpy-5 h520 unc-•lo ; sDp2 A. Rose Lab KR842 dpy-5 h.521 unc-•lo ; sDp2 A. Rose Lab KR844 dpy-5 h.523 unc-•lo ; sDp2 A. Rose Lab KR846 dpy-5 h525 unc-•lo ; sDp2 A. Rose Lab KR847 dpy-5 h526 unc-•lo ; sDp2 A. Rose Lab KR848 dpy-5 h.521 unc-•13 ; sDp2 A. Rose Lab KR856 dpy-5 h531 unc-•13 ; sDp2 A. Rose Lab KR857 dpy-5 h.538 unc-•13 ; sDp2 A. Rose Lab KR876 dpy-5 h481 unc-•13 ; sDp2 A. Rose Lab KR877 dpy-5 h498 unc-13 ; sDp2 A. Rose Lab KR878 dpy-5 h500 unc-•13 ; sDp2 A. Rose Lab KR879 dpy-5 h50l unc-13 ; sDp2 A. Rose Lab KR880 dpy-5 h504 unc-•13 ; sDp2 A. Rose Lab KR881 dpy-5 h.505 unc-IS ; sDp2 A. Rose Lab 105 Appendix#2: continued Strain Genotype Origin KR882 dpy-5 h509 unc- 13 ; sDp2 A. Rose Lab KR887 dpy-5 h495 unc- 13; sDp2 A. Rose Lab KR889 dpy-5 h534 unc- 13; sDp2 A. Rose Lab KR890 dpy-5 h5l0 unc- 13 ; sDp2 A. Rose Lab KR1314 dpy-5 K615 unc- 13; sDp2 A. Rose Lab KR1316 dpy-5 h-677 unc-•13 ; sDp2 A. Rose Lab KR1317 dpy-5 h678 unc-•13; sDp2 A. Rose Lab KR1319 dpy-5 h,680 unc-•13; sDp2 A. Rose Lab KR1325 dpy-5 h.686 unc-•13; sDp2 A. Rose Lab KR1326 dpy-5 h687 unc-•13; sDp2 A. Rose Lab KR1329 dpy-5 h690 unc-•13; sDp2 A. Rose Lab KR1331 dpy-5 h692 unc-•13; sDp2 A. Rose Lab KR1334 dpy-5 h695 unc-•13; sDp2 A. Rose Lab KR1337 dpy-5 h698 unc-•13; sDp2 A. Rose Lab KR1339 dpy-5 h715 unc-•13; sDp2 A. Rose Lab KR1340 dpy-5 h699 unc-•13; sDp2 A. Rose Lab KR1345 dpy-5 hi04 unc-•13 ; sDp2 A. . Rose Lab KR1347 dpy-5 h706 unc--13 ; sDp2 A. , Rose Lab KR1348 dpy-5 h707 unc--13; sDp2 A. , Rose Lab KR1356 dpy-5 h7l7 unc--13; sDp2 A. . Rose Lab KR1368 dpy-5 h727 unc--13; sDp2 A. . Rose Lab KR1369 dpy-5 h728 unc-•13 ; sDp2 A. Rose Lab KR1370 dpy-5 h729 unc-•13; sDp2 A. Rose Lab Appendix#2: continued Strain Genotype Origin KR1371 dpy-5 h!30 unc-•13 ; sDp2 A. Rose Lab KR1373 dpy-5 hi32 unc-•13 : sDp2 A. Rose Lab KR1374 dpy-5 hlSS unc-•13 ; sDP2 A. Rose Lab KR1376 dpy-5 hi35 unc-•13 ; sDp2 A. Rose Lab KR1377 dpy-5 h,136 unc-•13 ; sDp2 A. Rose Lab KR1382 dpy-5 hi'41 unc-•13 ; sDp2 A. Rose Lab KR1383 dpy-5 hi42 unc-•13 ; sDpS A. Rose Lab KR1384 dpy-5 hi43 unc-•13 ; sDp2 A. Rose Lab KR1385 dpy-5 hi44 unc-•13 ; sDp2 A. Rose Lab KR1386 dpy-5 h!45 unc-•13 ; sDp2 A. Rose Lab KR1388 dpy-5 hi41 unc-•13 ; sDp2 A. Rose Lab KR1389 dpy-5 hl48 unc-•13 ; sDp2 A. Rose Lab KR1390 dpy-5 hi49 unc-•13 ; sDp2 A. Rose Lab KR1392 dpy-5 hi51 unc-•13 ; sDp2 A. Rose Lab KR1393 dpy-5 hi52 unc--13 : sDp2 A. Rose Lab KR1394 dpy-5 hi53 unc--13 ; sDp2 A. Rose Lab KR1395 dpy-5 hi54 unc--13 ; sDp2 A. Rose Lab KR1396 dpy-5 h.155 unc--13 ; sDp2 A. . Rose Lab KR1397 dpy-5 hi56 unc--13 ; sDp2 A. Rose Lab KR1398 dpy-5 hi51 unc-•13 ; sDp2 A. . Rose Lab KR1399 dpy-5 hi58 unc-13 ; sDp2 A. Rose Lab KR1400 dpy-5 h!59 unc-13 ; sDp2 A. : Rose Lab KR1405 dpy-5 h.162 unc-13 ; sDp2 A. : Rose Lab 107 Appendix#2: continued Strain Genotype Origin KR1406 dpy-5 hl63 unc-13 ; sDp2 A . Rose Lab KR1409 dpy-5 h766 unc-13 ; sDp2 A . Rose Lab KR1410 dpy-5 h767 unc-13 ; sDp2 A . Rose Lab KR1412 dpy-5 h769 unc-13 ; sDp2 A . Rose Lab KR1418 dpy-5 h775 unc-13 ; sDp2 A . Rose Lab KR1423 dpy-5 h780 unc-13 ; sDp2 A . Rose Lab KR1432 dpy-5 h789 unc-13 ; sDp2 A . Rose Lab KR1434 dpy-5 h.791 hi 015 unc-13 ; sDp2 A . Rose Lab KR1435 dpy-5 h.792 unc-13 ; sDp2 A . Rose Lab KR1436 dpy-5 h.793 unc-13 ; sDp2 A . Rose Lab KR1437 dpy-5 h,79Jf unc-13 ; sDp2 A . Rose Lab KR1438 dpy-5 h795 unc-13 ; sDp2 A . Rose Lab KR1440 dpy-5 h.797 unc-13 ; sDp2 A . Rose Lab KR1443 dpy-5 h800 unc-13 ; sDp2 A . Rose Lab KR1448 dpy-5 h805 unc-13 ; sDp2 A . Rose Lab KR1449 dpy-5 h806 unc-13 ; sDp2 A. Rose Lab KR1450 dpy-5 h.807 unc-13 ; sDp2 A. Rose Lab KR1455 dpy-5 h812 unc-13 ; sDp2 A. Rose Lab KR1484 dpy-5 h.822 unc-13 ; sDp2 A. Rose Lab KR1486 dpy-5 h.824 hi016 unc-13 ; sDp2 A. Rose Lab KR1487 dpy-5 h825 unc-13 ; sDp2 A. Rose Lab KR1493 dpy-5 h.83l unc-13 ; sDp2 A. Rose Lab o KR1498 ' dpy-5 h836 unc-13 ; sDp2 A. Rose Lab 108 Appendix#2: continued Strain Genotype Origin KR1504 dpy-5 h842 unc-•13 , • sDp2 A. Rose Lab KR1505 dpy-5 h843 unc-•13, • sDp2 A. Rose Lab KR1512 dpy-5 h850 unc-•13 , • sDp2 A. Rose Lab KR1513 dpy-5 K851 unc-•13 , • sDp2 A. Rose Lab KR1515 dpy-5 h,853 unc-•13, ; sDp2 A. Rose Lab KR1518 dpy-5 h865 unc-•13 , ; sDp2 A. Rose Lab KR1522 dpy-5 h869 unc-•13 , ; sDp2 A. Rose Lab KR1523 dpy-5 h.870 unc-•13 . ; sDp2 A. Rose Lab KR1526 dpy-5 h.873 unc--13 , : sDp2 A. Rose Lab * A. Rose lab participants = J. Babity. G. Gilmour, L. Harris, A. M. Howell, J. S. Kim, N. Mawji, J. McDowall, K. McKim, K. McNeil, K. Peters, T. Starr, B. Rattray, A. Rose, and M. Zetka. 109 APPENDIX#3: Duplication Mapping Results for New EMS-induced Mutations Allele. hDp 13 hDp 16 hDp 19 Size (mm) Stage of Arrest A) In hDylS Region: hSU IN Not determined h,356 IN IN Not determined h358 IN IN Not determined hS79 IN IN Not determined h380 IN IN IN Not determined h,381 IN IN Not determined h382 IN IN Not determined h387 IN IN IN Not determined h393 IN IN IN Not determined h396 IN IN Not determined h397 IN Not determined h398 IN IN IN Not determined h40S IN Not determined h412 IN IN Not determined h413 IN IN Not determined hi 15 IN IN Not determined h425 IN IN Not determined h434 IN IN IN Not determined h436 IN IN IN Not determined h440 IN IN IN Not determined h443 IN IN Not determined 110 Appendix#3: continued Allele hDplS hDp 16 hDp 19 Size (mm) Stage of Arrest h446 IN IN IN Not determined h44i IN IN IN Not determined h450 IN IN IN Not determined h455 IN IN IN Not determined h458 IN IN IN Not determined h460 IN IN Not determined h461 IN IN IN Not determined h463 IN IN Not determined h464 IN IN IN Not determined h469 IN IN IN Not determined h411 IN IN Not determined h483 IN IN Not determined h481 IN Not determined h494 IN Not determined h498 IN IN IN Not determined h500 IN IN IN Not determined h501 IN IN IN Not determined h502 IN IN IN Not determined h503 IN IN IN Not determined h504 IN IN IN Not. determined h.505 IN IN Not determined h506 IN IN IN Not determined h508 IN IN IN Not determined I l l Appendix#3: continued Allele hDplS hDp!6 hDpl9 Size (mm) Stage of Arrest h509 IN IN Not determined h512 IN IN Not determined h,518 IN IN Not determined h521 IN IN Not determined h.525 IN Not determined h526 IN IN IN Not determined h534 IN IN IN Not determined hi28 IN IN IN Not determined h.730 IN IN IN Not determined hi 32 IN IN Not determined hi4 3 IN IN Not determined h744 IN IN IN Not determined hi4 5 IN IN IN Not determined hi5 5 IN IN IN Not determined hi51 IN Not determined hi58 IN IN IN Not determined hi59 IN IN IN Not determined h.869 IN IN Not determined B) In hDv!3/hDvl6 Region h351 OUT IN 0.35 Mid larval h,359 OUT IN Early larval h362 OUT IN IN 0.4 Mid larval h375 OUT IN IN Early larval 112 Appendix#3: continued Allele hDp 13 hDp 16 hDp 19 Size (mm) Stage of Arrest h388 OUT IN IN Adult sterile hJ,01 OUT IN IN Early larval h408 OUT IN IN Adult sterile h416 OUT IN IN Early larval hi S3 OUT IN IN Early larval hJ,31 OUT IN IN Adult sterile I1454 OUT IN IN Adult sterile h475 OUT IN IN Early larval h510 OUT IN IN 0.4 Mid larval h.677 OUT IN IN Not determined hi 15 OUT IN IN Not determined h729 OUT IN IN Not determined h733 OUT IN IN Not determined h,736 OUT IN IN Early larval h741 OUT IN IN 0.35 Mid larval h.75'2 OUT IN IN Adult sterile h753 OUT IN IN Early larval h766 OUT IN Not determined h.767 OUT IN IN Adult sterile h.775 OUT IN Not determined hi94 OUT IN IN Not determined h797 OUT IN IN Mid larval h805 OUT IN IN Not determined Appendix#3: continued Allele hDp IS hDpl6 hDp 19 Size (mm) Stage of Arrest h812 OUT IN IN Adult sterile h843 OUT IN IN Not determined h865 OUT IN IN Late larval h810 OUT IN IN Early larval C) In hDv 16/hDp 19 Region: h354 OUT OUT IN Early larval h.369 OUT OUT IN Early larval (lives hS14 OUT OUT IN Early larval h384 OUT OUT IN Early larval h402 OUT OUT IN Egg h421 OUT OUT IN Egg h462 OUT OUT IN Early larval hi 76 OUT OUT IN 0.35 Mid larval h490 OUT OUT IN 0.45-0.5 Adult sterile h495 OUT OUT IN Early larval h497 OUT OUT IN Early larval h520 OUT OUT IN Egg/Ll h538 OUT IN Early larval h675 OUT IN 0.2 Early larval h678 OUT OUT IN 0.3-0.35 Mid larval h695 OUT OUT IN Adult sterile h699 OUT IN Egg/Ll h706 OUT IN Late larval 114 Appendixes: continued Allele hDp 13 hDp 16 hDp 19 Size (mm) Stage of Arrest h747 OUT OUT IN Early larval h.749 OUT OUT IN Not determined h754 OUT OUT IN Egg/Ll h756 OUT OUT IN 0.2 Early larval h.791 OUT OUT IN Early larval h822 OUT IN 0.3-0.35 Mid larval h824 OUT IN Late larval h.831 OUT OUT IN Not determined h850 OUT IN 0.3 Mid larval h851 OUT OUT IN Mid larval h853 OUT OUT IN Early larval (lives h873 OUT IN 0.4 Late larval D) In hDpl9/sDv2 Region: h350 OUT OUT OUT Early larval h.357 OUT OUT Adult, sterile h360 OUT OUT OUT Early larval (lives h36l OUT OUT OUT Early larval (lives h367 OUT OUT OUT Early larval h389 OUT OUT OUT 0.25 Early larval h406 OUT OUT OUT Early larval h4io OUT OUT 0.3-0.35 Mid larval h428 OUT OUT OUT Early larval h429 OUT OUT OUT Early larval (lives 1 week) 1 week) 1 week) 115 Appendix#3: continued Allele hDp 13 hDp 16 hDp 19 Size (mm) Stage of Arrest h43l OUT OUT OUT Early larval h-435 OUT OUT OUT Early larval h442 OUT OUT Earfy larval h444 OUT OUT OUT Early larval K445 OUT OUT OUT Early larval (lives 1 week h453 OUT OUT OUT Early larval h470 OUT OUT Early larval h.472 OUT OUT OUT Early larval h479 OUT OUT OUT Egg/Ll h486 OUT OUT Adult sterile h489 OUT OUT Early larval h492 OUT OUT OUT Early larval h514 OUT OUT OUT Early larval h.519 OUT OUT OUT Egg h523 OUT OUT OUT Early larval h527 OUT OUT OUT 0.25 Early larval h5S7 OUT OUT OUT Adult sterile h680 OUT OUT 0.2 Early larval h686 OUT OUT OUT 0.15-0.2 Early larval h687 OUT OUT OUT Earl}'' larval h690 OUT 0.3 Early larval h692 OUT OUT Adult sterile h.698 OUT OUT 0.35-0.4 Mid larval Appendix#3: continued Allele hDp 13 hDp 16 hDp 19 hi 04 OUT OUT hi 01 OUT OUT hill OUT hT21 OUT hi3 5 OUT OUT hi4 2 OUT OUT OUT h!4S OUT OUT OUT hi51 OUT OUT OUT hi 62 OUT hi 63 OUT OUT hi69 OUT h!80 OUT hi 89 OUT OUT hi92 OUT OUT hi93 OUT hi9 5 OUT h800 OUT OUT 1x806 OUT h801 OUT h825 OUT h.836 OUT OUT OUT h842 OUT Size (mm) Stage of Arrest 0.6 Adult sterile 0.5 Late larval 0.2 Early larval Early larval Early larval Early larval 0.35-0.4 Mid larval Early larval 0.2 Early larval Early larval Early larval 0.2 Early larval Early larval 0.5 Late larval 0.2 Early larval 0.2 Early larval Egg 0.3 Early larval 0.2 Early larval Early larval 0.2 Early larval Not determined Appendix#3: continued *The sizes used to determine larval stages, which were measured by micrometer, were as follows (see figure#8): Early larval stage = L1/L2 = 0.15 - 0.3 mm Mid larval stage = L2/L3 = 0.3 - 0.4 mm Late larval stage — L3/L4 = 0.4 - 0.6 mm Adult stage = 0.6 - 0.8 mm 118 A P P E N D I X#4: Complementation Results for  Recombination Mapped New EMS-induced Mutations Below is the complementation table summarizing the data used to assign gene names to the new essential genes in the hDp 16/hDp 19 region. In the table below, a indicates complementation, and a '-' indicates failure to complement. Heterozygous lethal-bearing males are listed across the top of the table, and homozygous sUpf-rescued lethal-bearing hermaphrodites are listed down the side. h289 h290 h292 h293 h3. let-355 (h.8l) -r let-367 (hi 19) + + let-370 (hl28) -r + let-376 (hi30) + + + + let-377 (hi 10) + + + let-378 (h!24) + + + + + let-379 (hl27) + + + let-380 (h80) + T + let-381 (hlOT) + -4-! + let-382 (h82) + + + + let-383 (hi 15) + + + let-384 (h84) + i _L let-385 (h85) + + + + let-386 (hi 17) + + + let-387 (h87) + + let-388 (h88) + + + 119 Appendix#4: continued h289 1x290 h292 h293 h312 let-389 (hi 06) + + -L + + let-390 (h44) + + + + let-391 (h9l) + + + + + let-392 (hi 20) + + let-393 (h225) + + let-394 (h262) + + + + let-395 (h211) + + + + let-396 (hi 30) + + + + + let-397 (h228) + + + let-398 (257) + + + + let-399 (h273) + + + + + let-400 (h269) + + + + let-601 (h28l) + + + + let-602 (h283) + + + + bli-4 (h42) + bli-4 (h254) + + h289 -h290 + -h.292 + + - + + h293 + -h312 + + + -120 APPENDIX#5: Complementation Results for  Duplication Mapped New EMS-induced Mutations  lying in the hDp 16/hDp 19 Region Below is the complementation table summarizing the data used to assign gene names to the new essential genes in the dpy-5 unc-13 region. In the tables below, a indicates complementation, and a '-' indicates failure to complement. Heterozj'gous lethal-bearing males are listed across the top of the table, and homozygous sDp2-iescued lethal-bearing hermaphrodites are listed down the side. h354 hS69 let-380 (h80) + + let-381 (hi 07) + + let-382 (h82) + + let-386 (hi 17) + + let-387 (h87) + let-390 (h44) + + let-396 (h217) - + let-601 (h281) + + let-602 (h283) + + let-604 (h293) + + let-606 (h292) + + bli-4 (h254) + + h402 + + h.695 + hl06 + -h850 -f + h.374 h384 h402 h/27 h4 + + + + + i T + + + + + 4-+ + + + + + + + + + + + + + + -+ + + + + - + + + + + + + + + + + + + - + - + + + + + + + + + + + + + + + + + Appendix#5: continued h476 h490 let-380 (h80) + + let-381 (hi 07) + + let-382 (h82) - + let-386 (hi 17) + + let-387 (h87) + let-390 (h.44) -r + let-396 (h217) + + let-601 (h28l) + + let-602 (h283) + + let-604 (h293) + -let-606 (h292) + _j_ bh-4 (h254) + + h402 + h695 + + h706 + + h850 + + h495 h497 h520 h538 hi + + 4- + -- + + + + + + + + + + + + + + + + + - j -+ + + + + + + + - + + + + " T + - + + i + + + + + + + + + + + + - + + + + + + + + + + + + + + + + + + + + Appendix#5: continued let-380 (h80) let-381 (hlOl) let-382 (h.82) let-386 (hi 17) let-387 (h87) let-390 (h44) let-396 (h217) let-601 (h.28l) let-602 (h283) let-604 (h-293) let-606 (h292) bli-4 (h254) h402 h.695 h.706 h850 h678 h695 h699 h\ + + + + + + + + T + + - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - + + + + + + + + + + + + + hi41 h749 h754 h756 + + + + - + + + + + + + - + + + + + + + + + + + + + + + + + + + + + + + + + + + 4-i + + + + + + + + + + + + + + + _ Appendix#5: continued let-380 (h80) let-381 (hi 07) let-382 (h82) let-386 (hi 17) let-387 (h87) let-390 (h44) let-396 (h217) let-601 (h281) let-602 (h283) let-604 (h293) let-606 (h292) bli-4 (h254) h402 h695 h706 h.850 h.791 h822 h.824 hi + + 4- -+ + + 4- - j - + + + - f + -L + + + + + + 4- - T + + - + + + + + 4- + 4- + + + + + + + + + - + + + + 4- + + + + + l 4" i 4- + h850 h851 h853 h873 + + + + + + + 4- + + + - + -+ + + + + + + + + + + + 4- + - j . + + + 4-+ + + 4-+ + + 4-_ l _ + + 4-i i + f + + " T + i i + + 4-APPENDIX#6: Inter se Complementation Results for  Essential Genes in the hDp 16/hDp 19 Region Below are the complementation tables summarizing the reciprocal complementation tests for each allele within a complementation group (gene). In each table, a '+' indicates complementation, and a '-' indicates failure to complement. Heterozygous lethal-bearing males are listed across the top of the table, and homozygous sDpS-rescued lethal-bearing hermaphrodites are listed down the side. let-380 (h80) (h675) (h83l) let-380 (h80) (h675) (h8Sl) let-381 (hlOT) (hi 95) (h7.{7) let-381 (hlOT) (hi95) (h.747) let-382 (h82) (hi 76) let-382 (h82) (h476) let-386 (hi 17) (h678) (hi49) (h85i (h873 let-386 (hi 17) (h618) (h749) (h85l) (h873) 125 Appendix#6: continued let-396 (h£17) (h354) (h462) (h.538) (h824) let-39 6 (Mil) (h.354) (h462) (h538) (h,824) let-602 (h,283) (kS74) (h497) let-602 (h283) (h.314) (h497) let-604 (h293) (h490) let-604 (h293) (h490) let-608 (h706) (h369) (h853) let-611 (h850) (h.756) (K822) bli-4 (h42) (hi 99) (h254) (h384) (h427) (h520) (h.699) (h754) (h.79l) let-608 (h706) (h369) (h853) let-611 (h,850) (h.756) (h822) bh-4 (h42) (h!99) (h254) (h384) (h427) (h520) (h699) (h754) (h.79l) A P P E N D I X # 7 : Truncated Poisson Formula Truncated Poisson formula: 1 - e ' m - me ,-m / = Equation 1 - e ,-m Unfortunately, where / is known, this equation is insoluble for m. Therefore, one must use the Newtonian Method to solve for rn. This method allows one to make an educated guess at the value of m, then, using equation#2, will correct for that estimate. Newtonian Method: Equation m n + l = m n " where 1 - e' ,-m - me ,-m g(m) = - f Equation #3 g'(m) can then be derived from equation#3: Append ix^? : continued g'(m) 1 . e - m [e^ 1 - (e*™ - me" m )] - [1 - e m - m e - m ( e - m ) ] ( 1 - e - m ) 2 1 - e m ( m e m ) - ( e" m - e " 2 m - m e 2 m ) m = ( 1 - e - m \2 g'(m) m e m - me" 2 1 1 1 - em + e'2m + m e " 2 ™ ( 1 - e •m \2 g'(m) = m e - m . e - m , e - 2 m ( 1 - e ,-m E q u a t i o n 128 Appendix#7: continued For example, where / = 0.63, take an educated guess of m = 1 1 - e"1 - e'1 equation #3 g(m) = - 0.63 1 - e 1 1 - 0.37 - 0.37 = - 0.63 1 - 0.37 = -0.22 ^ . e - i + e-2 equation #4 g'(m ) = — ( 1 - e-1 )2 = 0.135 0.397 = 0.34 equation #2 m ^ = 1 - (-0.22 / 0.34) = 1.65 Therefore, where / = 0.63, m must be 1.65 To test if this value of m is correct, it can be put into the truncated Poisson formula (equation#l), and one should get a value for /of 0.63 

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