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The role of pleiotropy in the maintenance of sex in yeast Hill, Jessica Anne 2006

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THE ROLE OF PLEIOTROPY IN THE M A I N T E N A N C E OF SEX IN YEAST by JESSICA A N N E HILL B.Sc. Queen's University 2002 B.Sc.H. Queen's University 2003 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E D E G R E E OF MASTER OF SCIENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES (Zoology) T H E UNIVERSITY OF BRITISH COLUMBIA May 2006 © Jessica Anne Hill, 2006 Abstract Sexual reproduction is widespread, yet no comprehensive explanation for its . ubiquity exists, despite a multitude of theories for sex. In order to determine the plausibility of these theories, it would be useful to know how easily sexual function can be lost. We have estimated the total rate of mutations that are deleterious to sexual function in a facultatively sexual organism, the yeast Saccharomyces cerevisiae. We propagated replicate lines of yeast at small population size (SMA) for 800 generations, so that all but the most deleterious of mutations were maintained. We estimated the sexual fitness (sporulation rate) of the evolved and ancestral SMA lines, thus allowing us to apply maximum-likelihood and Bateman-Mukai techniques to estimate the rate and nature of mutations affecting sexual function. The deleterious mutation rate per diploid per genome with respect to sexual function (Usex) was estimated as 2.3 x 10"4, while the average reduction in fitness of heterozygous mutants with respect to sexual function (ssex) was estimated as 0.24, which is approximately double the value of estimates of mutational parameters in S. cerevisiae with respect to asexual growth. In a facultatively sexual organism like yeast, pleiotropy between asexual and sexual function is likely to occur. To determine what effect pleiotropy with asexual function was having on sexual function, we propagated replicate lines of yeast asexually at large population size (LMA). We determined the direction of pleiotropy (positive or negative) between asexual and sexual function by comparing the rate of decline in sexual function in the L M A and SMA lines. We found evidence for positive pleiotropy in our lines. This indicates that sexual function in yeast may be maintained by asexual function. We find that sex is lost at a slow rate in yeast and that the costs of sex are mitigated by pleiotropy with asexual function. In a separate study, I explored the interaction between DNA methylation and associated protein attachment, which is important for proper transcription and cell function. A model that examines the dynamics of DNA methylation and methyl-CpG-binding domain protein attachment in the context of selection at the level of the cell was developed. The approximate equilibrium values of the four possible states of the system were determined, and numerical simulations were performed, using realistic parameter values from prior studies when known. Two general conclusions emerge from this model: 1) selection among cells can alter epigenetic signals such as proteination attachment and methylation status, but 2) the efficacy of selection is dramatically reduced by high transition rates in methylation and proteination status. T a b l e o f C o n t e n t s Abstract ii Table of Contents - iv List of Tables vi List of Figures vii Acknowledgements ix CHAPTER 1: General Introduction 1 Background and Objectives 1 Study systems 6 Summary 7 Literature Cited 9 CHAPTER 2: The role ofpleiotropy in the maintenance of sex in yeast 11 Introduction 11 Methods 15 Results , 22 Discussion 25 Literature Cited 36 CHAPTER 3: The effect of selection at the level of the cell on DNA methylation and methyl-CpG-binding domain protein dynamics in a vertebrate genome 38 Introduction 38 The Model 41 Numerical Analysis 43 Results and Discussion 44 Literature Cited 54 i v CHAPTER 4: General Conclusions Summary of Objectives and Conclusions Summary Literature Cited List of Tables 2.1 Mean and variance values of sexual fitness (sporulation rate) and asexual fitness (growth rate) in L M A evolved, SMA evolved and ancestral strains of Saccharomyces cerevisiae 34 2.2 Maximum likelihood estimates of mutational parameters of Saccharomyces cerevisiae derived from M A experiments on non-mutator strains 35 3.1 Solutions to the first and second order of the equilibrium values (X t) 53 V I List of Figures 2.1 Box plots of the sporulation rates for 128 ancestral (t = 0), 78 SMA evolved (t=800) lines and 50 L M A evolved (t = 800) lines. Each data point represents the mean value of two measurements of the proportion of tetrads per replicate line. Box plots represent median, 10th, 25th, 75th and 90th percentiles. 30 2.2 Box plots of the growth rates for a subset of lines: 40 ancestral (t = 0), 20 SMA evolved (t = 800) lines and 19 L M A evolved (t = 800) lines. Each data point represents the mean value of two measurements of 95th percentile growth rate per replicate line. Box plots represent median, 10th, 25th, 75th and 90th percentiles. 31 2.3 Correlation between sexual fitness on the y-axis and asexual fitness on the x-axis of a randomly selected subset of lines. The correlation is not significant (dashed lines; p = 0.17, P = 0.15) when only the randomly selected lines are examined but is significant when all lines are considered, including the two poorly sporulating lines indicated by the white dots (solid line; p = 0.22, P = 0.05). 32 2.4 Log-likelihood values generated for different values of |3, with maximum likelihood Usex and ssex values associated with that p\ The red dotted line indicates 2 log-likelihood (InL) units (i.e., 95% confidence interval) from the maximum InL at |3 = 1. 33 3.1 The four possible states of a CpG, and their relative frequencies denoted by Xt. The symbols a through d and Sa through cV denote transition rates between states. M = methylated; U = unmethylated; P = proteins attached; N = no proteins attached. , 49 3.2 The cell cycle with respect to selection, protein attachment/unattachment, methylation and replication. 50 vii Exact numerical solutions of the equilibrium frequencies when protein attachment is favoured (a, c) and when no protein attachment is favoured (b, d). The values for a and ft are held constant at 0.96 and 0.17 (a, b), or 0.95 and 0.05 (c, d), respectively. The remaining parameters are set for all graphs as follows: b = 0.05, d = 0.1, 6b = 0.05, -0.05. The effect of the size of transition rate parameters a, b, c and d on selection on proteinated CpGs (Xj + X3) when selection is strong (a; s = 0.1) and when selection is weak (b; s = 0.01). Solid lines indicate <5; = 0; dashed lines indicate dt, = 0.05 and 6j = -0.05. Bold lines indicate that protein attachment is favoured, unbolded lines indicate no protein attachment is favoured. Base parameter values are set at a = 0.02, b = 0.05, c = 0.085 and</=0.1. Acknowledgements I would like to thank my supervisor Sally Otto and my committee members Rosie Redfield and Mike Whitlock for their conscientious comments and approachability. I would especially like to thank Sally for her inspired ideas, guidance, trust and continual support. I am indebted to Otto lab members past and present for their input, advice and support in particular. I would like to thank Aleeza Gerstein, Dilara Ally, Risa Sargent, Aneil Agrawal, Andy Peters, Elizabeth Chun, Crispin Jordan, Leithen M'Gonigle, Rowan Barrett and Chrissy Spencer for letting me pick their knowledgable brains, with special mention to Chrissy and for sharing her experience by lending me advice, particularly concerning lab work. The SOWD lab group here at UBC provided me with sound comments, as well as other commentors Jackie Ngai, Andrew Cameron and Martin Kang. I am appreciative of the solid technical support I have received from undergraduates Laura Glaubach and Patrick Wu. I would also like to thank Sally and my labmates for making this degree a memorable experience academically and otherwise. I would like to thank my supportive officemates Aleeza and Allyson Longmuir, who often bore the brunt of being on the front lines when I was discouraged or dissatisified with my progress, and managed to return my panic to manageable levels. Finally I would like to thank my parents, Anne and Lawrence Hill, and my sister, Kelly Hill, for their unconditional, unwaivering support. ix Chapter One General Introduction This thesis is composed of two chapters of novel research. I examine two evolutionary topics, which can be broadly classified as'related to the evolution of sex (Chapter Two) and to methylation and related protein dynamics (Chapter Three). The methods of employed in these two studies differ: the questions of Chapter Two are addressed by experimental evolution in a laboratory environment, while Chapter Three's questions are addressed by mathematical modeling. These chapters have little in common besides my interest in both subject areas, so that in this introductory chapter, I will address the background and research questions that have driven each study separately. While this thesis is composed of two chapters, these chapters should not be weighted equally in terms of amount of time dedicated to each project. Chapter Two is the main focus of this thesis, as reflected in the title of the thesis, whereas Chapter Three is a secondary chapter, an opportunity to explore mathematical modeling. Background and Objectives Chapter Two In Chapter Two, I answer two specific questions regarding the evolution of sex: 1) how easily is sexual function lost in a facultatively sexual organism, Saccharomyces cerevisiae, and 2) does pleiotropy between asexual and sexual growth occur in S. cerevisiae, and if so, what is the effect on sexual reproduction? Chapter Three is motivated by the myriad of diseases related to aberrant gene regulation. The role of 1 selection in the dynamics of DNA methylation and associated protein interaction in relation to transcriptional repression is examined. Chapter Two of this thesis is inspired by the evolutionary conundrum of sexual reproduction. The vast majority of eukaryotic organisms reproduce sexually, yet the origin and maintenance of sexual reproduction is not well understood. Sex is particularly difficult to explain because there are several costs associated with sexual reproduction. We can generally classify these costs as ecological and genetic. Some of the ecological costs include the cost of finding and attracting a mate, sexual reproduction often makes an organism more susceptible to predation through exposure and sexually transmitted disease, and sexual reproduction often takes more time than asexual reproduction (Otto and Lenormand, 2002). For example, Saccharomyces cerevisiae can reproduce asexually in approximately 90 minutes when conditions are suitable, yet sexual reproduction can take days (Rockmill et al, 1991). Some of the genetic costs of sex include the breakdown of beneficial epistatic interactions by recombination (recombination load; Nei, 1967). / Perhaps the most cited cost of sex is known as the two-fold cost of sex. The two-fold cost of sex states that an asexually reproducing population will have twice as many of its alleles present in the next generation as a sexually reproducing population, because the asexual parent acts as both mother and father to the progeny (Maynard Smith, 1978). For sexuality to be maintained within a population, the advantages of sex must overcome this two-fold cost, amongst the other costs listed. Given the many costs of sex, the question naturally arises: why reproduce sexually? Many theories of sex exist, and they can generally be classified in one of two categories, those that posit that sex aids in the spread of advantageous traits, and those 2 that claim that sex efficiently removes deleterious genes (Hurst and Peck, 1996; West et al, 1999). It is, however, difficult to distinguish among many of the predictions made by these models. In order to evaluate the plausibility of different hypotheses, it is important to have an understanding of how often sex may be lost, as this provides an estimate for the time frame over which the advantages of sex must act to maintain sexuality. For example, if selection in novel environments is necessary for sex to be maintained, we can answer how frequently the environment must shift for sex to be maintained by determining how easily sex is lost. Here, I have determined the rate at which sexual function is lost in the facultatively sexual budding yeast S. cerevisiae. Sexual function as a mutational target was also explored in Chapter Two. Mutation, as the progenitor of genetic variation, is essential for the evolutionary process. Despite its apparent importance, little is known about the frequency of mutation and the shape of the mutational distribution. Since the long-term mutation accumulation experiments performed as early as the 1960's (Mukai, 1964; Mukai et al., 1972), experimental evolution has been used to determine the effect of mutations on the fitness of an organism. Indeed, since Mukai's original experiments with Drosophila melanogaster, similar studies have been conducted in a variety of organisms, e.g. Escherichia coli (Kibota and Lynch, 1996), Caenorhabitis elegans (Estes et al., 2005), S. cerevisiae (Zeyl and DeVisser, 2001; Joseph and Hall, 2004). Mutation accumulation studies require a measurement of the change in fitness of a trait of interest, usually some established component of fitness like competitive ability (e.g., Zeyl and DeVisser, 2001) and occasionally several components of fitness (e.g., Estes et al., 2005). Interestingly, the effects of mutation on sexual fitness has only been studied on one occasion, in the fungus 3 Cryptococcus neoformans (Xu, 2002). In order to gain a more comprehensive estimate of the mutation rate and distribution of mutational effects with respect to sexual function, the maximum likelihood values of mutation rate per diploid genome per generation (Usex) and the average effect size per mutation (ssex) were determined in S. cerevisiae. The objectives of Chapter Two can be summarized as follows: 1) Determine how easily sexual function is lost in the facultatively sexual organism S. cerevisiae; 2) Determine the effect of pleiotropy between asexual and sexual function on sexual function; and 3) Estimate the mutational parameters Usex and ssei. Chapter Three Chapter Three was inspired by the fundamental roles that the epigenetic mechanism of methylation, and its associated proteins, play in the maintenance of a cell. Proper gene expression is essential to the normal functioning of an organism. Gene expression is regulated by a suite of transcription factors whose specific binding to DNA dictates whether the gene will be transcribed or not. Gene expression is fine tuned by a secondary level of genetic control, referred to as epigenetics. Particularly, research suggests that the epigenetic phenomenon of DNA methylation is related to gene silencing (Colot and Rossignol, 1999). In mammals, DNA methylation occurs at the 5' cytosine of CpG dyads. Approximately 70-80% of CpG dyads in the human genome are methylated, while the bulk of those CpGs not methylated are usually found in promoter regions of transcribed genes (Bird, 2002). In fact, approximately 60% of human genes are associated with these "CpG islands" (Antequera and Bird, 1993). Aberrant methylation of CpG islands and subsequent transcriptional repression is of clinical importance as it is related to the etiology of a plethora of diseases, including cancer (Robertson, 2005). 4 While the importance of regulated methylation patterns is well documented (Bird, 2002), the direct role of methylation in gene silencing is unclear. Evidence suggests that methylation can directly interfere with transcription but this phenomenon is limited to specific cases; for most genes transcription can occur regardless of methylation status (Bird and Wolffe, 1999). A more plausible hypothesis for a general mechanism of gene repression involves the binding of methyl-CpG-specific proteins to methylated promoter regions, thus inhibiting the attachment of transcription factors and subsequent transcription. These methyl-CpG-binding domain (MBD) proteins comprise a family that includes MeCP2, MBD1, MBD2 and MBD4 (Ballestar and Wolffe, 2001). While the functional significance of these proteins remains to be clarified, their importance is underscored by the fact that their malfunction is known to cause human disease (Robertson and Wolffe, 1999). In Chapter Three of this thesis, the dynamics of methylation and M B D protein attachment are examined in the context of cellular selection. An early model of methylation dynamics was created by Otto and Walbot (1990). This model was hampered by a lack of knowledge of parameter values, such as the rates of maintenance and de novo methylation. Subsequently, Genereux et al. (2005) used hairpin bisulfite PCR to accurately assess frequencies of hemi-, homo- and unmethylated strands of DNA so that methylation parameters could be inferred. However, no model has yet examined the interplay of methyl-bound proteins and methylation status, to my knowledge. The objective of Chapter Three is simply to examine the effect of selection on methylation-MBD protein attachment kinetics in the context of human disease. 5 Study Systems To address the research questions I defined in my introduction, I used two different methods of research: experimental work with Saccharomyces cerevisiae in Chapter Two and mathematical modeling in Chapter Three. Chapter Two Saccharomyces cerevisiae, more commonly known as budding yeast, is a single celled eukaryote that has a long history as a study organism in the fields of microbiology and molecular genetics (Sherman, 1991). More recently, evolutionary biologists have adopted 51. cerevisiae as a potent tool for studying the process of evolution. Budding yeast is an excellent evolutionary study organism for several reasons. These reasons include the fact that yeast are easily maintained in a laboratory setting where environmental variables can be controlled; they have a short generation time, allowing evolution to occur relatively rapidly; and they can be frozen and revived, enabling researchers to directly compare evolved yeast to the ancestral state (Zeyl, 2000). Of particular importance to this study, S. cerevisiae is facultatively sexual. While some organisms can be classified as either fully sexual or asexual, many, including several groups of fungi, invertebrates, and protists, are not obligately sexual or asexual but can utilize both modes of reproduction. With budding yeast, it is straightforward to discern when a yeast has reproduced sexually versus asexually. Working with an organism that can lose the ability to engage in sexual reproduction altogether allows important questions to be answered regarding the evolution and maintenance of sex. The life cycle of Saccharomyces cerevisiae is well known. In non-stressful environments, S. cerevisiae typically reproduce asexually in the diploid state. When yeast 6 are nitrogen stressed, they undergo meiosis, forming four haploid spores ("sporulation") (Freese et al, 1982). They then remain in this state until conditions become suitable for the return to vegetative growth. At this point, hapjoid cells of opposite mating type (a versus a) fuse, returning the yeast to the diploid state. In the absence of such stress, yeast can potentially maintain an entirely asexual lifestyle. The ease of manipulation of the yeast life cycle is appealing to researchers as well. Chapter Three The research design of Chapter Three is markedly different from that of Chapter Two. While an experiment designed around a study organism like S. cerevisiae allows a researcher to examine specific questions, it is difficult to make general statements using this design. Mathematical modeling allows a researcher to specify what are factors are important in addressing a question, thus permitting results to be more broadly applied. Modeling can be used to answer broad questions as well as generate empirically testable questions (Levin et al., 1997). Mathematics has a notable history in population genetics, and here I use modeling to answer general questions about the methylation-proteination process across a genome. Summary The two studies in this thesis address vastly different topics: Chapter Two centres around the evolution of sex, while Chapter Three examines questions about DNA methylation and related protein attachment in the context of selection. In addition, the Chapter Two's questions are addressed experimentally, while Chapter Three's questions are examined by mathematical modeling. What they do share is the fact that they 7 examine pervasive biological phenomena. In addition, the subject matter of this thesis represents my interest in both subject matters. 8 Literature Cited Antequera, F., and A. Bird, 1993 Number of CpG island and genes in human and mouse. PNAS 90: 11995-11999. Ballestar, E. and A. P. Wolffe, 2001 Methyl-CpG-binding proteins: targeting specific gene repression. Eur J Biochem 268: 1-6. Bird, A., 2002 DNA methylation patterns and epigenetic memory. Genes Dev. 16: 6-21. Bird, A. and A. P. Wolffe, 1999 Methylation-induced repression - belts, braces and chromatin: Cell 99: 451-454. Colot, V. , and J. L. Rossignol, 1999 Eukaryotic DNA methylation as an evolutionary device. BioEssays 21: 402-411. Estes, S., B. C. Ajie, M . Lynch and P. C. Phillips 2005 Spontaneous mutational correlations for life-history, morphological and behavioral characters in Caenorhabditis elegans. Genetics 170: 645-653. Freese, E. B., Chu, M . I. and E. Freese, 1982 Induction of yeast sporulation by partial carbon, nitrogen, or phosphate deprivation. J Bac 149: 840-851. Genereux, D. P., Miner, B. E., Bergstrom, C. T., and C. D. Laird, 2005 A population-epigenetic model to infer site-specific methylation rates from double-stranded DNA methylation patterns. PNAS 102: 5802-5807. Hurst, L. D., and J. R. Peck, 1996 Recent advances in understanding of the evolution and maintenance of sex. T R E E 11: 46-52. Joseph, S. B., and D. W. Hall, 2004 Spontaneous mutations in diploid Saccharomyces cerevisiae: more beneficial than expected. Genetics 168: 1817-1825. Levin, S. A., Grenfell, B., Hastings, A., and A. S. Perelson, 1997 Mathematical and computational challenges in population biology and ecosystem science. Science 275: 334-343. Kibota, T. T., and M. Lynch, 1996 Estimate of the genomic mutation rate deleterious to overall fitness in E. coli. Nature 381: 694-696. Maynard Smith, J., 1978 The Evolution of Sex. Cambridge University Press, Cambridge. Mukai, T., 1964 The genetic structure of natural populations of Drosophila melanogaster. I. Spontaneous mutation rate of polygenes controlling viability. Genetics 50: 1-19. Mukai, T., S. J. Chigusa, L. E. Mettler, and J. F. Crow, 1972 Mutation rate and dominance of genes affecting viability in Drosophila melanogaster. Genetics 72: 399-355. Nei, M . , 1967 Modification of linkage intensity by natural selection. Genetics 57: 625-641. Otto, S. P., and T. Lenormand, 2002 Resolving the paradox of sex and recombination. Nat Rev Genet 3: 252-261. Otto, S. P. and V. Walbot, 1990 DNA methylation in eukaryhotes: kinetics of demethylation and de novo methylation during the life cycle. Genetics 124: 429-437. Robertson, K. D., 2005 DNA methylation and human disease. Nat Rev Gen 6: 597-610. Robertson, K. D. and A. P. Wolffe, 2000 DNA methylation in health and disease. Nat Rev Gen 1: 11-19. 9 Rockmill, B., Lambie, E. J. and G. S. Roeder, 1991 Spore Enrichment, pp. 146-149 in Methods in Enzymology V. 194: Guide to Yeast Genetics and Molecular Biology, edited by C. Guthrie and G. R. Fink. Academic Press, San Diego, California. Sherman, F., 1991 Getting Started with Yeast, pp. 3-5 in Methods in Enzymology 194: Guide to Yeast Genetics and Molecular Biology, edited by C. Guthrie and G. R. Fink. Academic Press, San Diego, California. West, S. A., Lively, C. M . and A. F. Read, 1999 A pluralist approach to sex and recombination. J Evol Biol 12: 1003-1012. Xu, J., 2002 Estimating the spontaneous mutation rate of loss of sex in the human pathogenic fungus Cryptococcus neoformans. Genetics 162: 1157-1167. Zeyl, C , 2000 Budding yeast as a model organism for population genetics. Yeast 16: 773-784. Zeyl, C , and J. A. G. M . DeVisser, 2001 Estimates of the rate and distribution of fitness effects of spontaneous mutation in Saccharomyces cerevisiae. Genetics 157: 53-61. 10 Chapter Two The role of pleiotropy in the maintenance of sex in yeast Introduction The vast majority of eukaryotic organisms reproduce sexually, yet the origin and maintenance of sexual reproduction is not well understood, particularly in light of the costs of sex including the two-fold cost of sex and the breakdown of favourable genetic combinations (Otto and Lenormand, 2002; Barton and Charlesworth, 1998; Michod and Levin, 1988). For sexuality to be maintained within a population, the advantages of sex must overcome these costs. Several theories of sex exist (Kondrashov, 1993); in order to evaluate the plausibility of different hypotheses, it is useful to estimate the rate at which mutations appear causing sex to be lost. This provides an estimate for the time frame over which the advantages of sex must act to maintain sexuality, which is particularly important for theories that advocate accelerated adaptation of sexual populations to occasional changes in the environment. For example, if sex is advantageous in a new environment, then we need to know how often environments must change to ensure that sex is not lost in intervening periods with a constant environment. We have determined the proportion of mutations that adversely affect sexual function in the facultatively sexual budding yeast Saccharomyces cerevisiae. While some organisms can be classified as either fully sexual or asexual, many, including several groups of fungi, invertebrates, and protists (Bell, 1982), are not obligately sexual or asexual but can utilize both modes of reproduction. 11 In non-stressful environments, budding yeast typically reproduce asexually in the diploid state. When yeast are nitrogen stressed, they undergo meiosis, forming four haploid ascospores (a tetrad) in a process known as sporulation. They remain in this state until conditions become suitable for the return to vegetative growth. At this point, haploid cells of opposite mating type (a and a) fuse, returning the yeast to the diploid state. In the absence of such stress, yeast can propagate asexually indefinitely. There is anecdotal evidence that laboratory yeast strains can lose their ability to reproduce sexually after many generations of asexual reproduction in the lab (e.g., Zeyl, 2005), yet there has been no quantitative assessment of how frequently or easily sexuality can be lost in S. cerevisiae. To estimate the total rate of mutations that are deleterious to sexual function, we performed a mutation accumulation experiment (Small Mutation Accumulation; SMA; as in Kibota and Lynch, 1996). Small, replicate populations of diploid yeast were propagated asexually for 800 generations using regular bottlenecks to single cells to reduce the genetic variance and efficacy of selection within each line. Consequently, all but the most deleterious mutations were maintained in the SMA lines. In a mutation accumulation experiment, two predictions are generally made: 1) if the lines are well adapted to their environment, the mean fitness is expected to decline, and 2) the genetic variance between lines is expected to increase as different mutations accumulate in the various lines (Mukai 1964; Mukai etal. 1972; Bateman 1959). The sexual fitness of the ancestral and evolved SMA lines was assessed so that the rate of decrease in sexual function could be estimated using the Bateman-Mukai calculation (Bateman 1959; Mukai 1964) and a maximum likelihood algorithm (Keightley, 1994). Specifically, we measured 12 sexual fitness by determining the sporulation rate, or proportion of tetrads relative to vegetative cells, obtained in a sporulation medium. When yeast are propagated asexually, mutations that are deleterious only to sexual function are effectively neutral, regardless of the population size. Thus, if mutations affecting sexual function had no effect on asexual growth (no pleiotropy), then the patterns observed in the SMA lines should be similar in populations propagated asexually at large size. To test this, we measured the decline over time in sporulation ability of large, asexually propagated populations (Large Mutation Accumulation; LMA). By comparing the fate of mutations reducing sexual function between the L M A and SMA lines, we were able to assess the extent to which sexual function is maintained by pleiotropic selection on asexual function. In addition to the L M A experiment, we assessed the asexual fitness, measured as the vegetative growth rate, of all lines, as an alternative means of examining the relationship between asexual and sexual function. These data allow us to assess two different ways in which sexual and asexual function are pleiotropically linked. Pleiotropy between sporulation and growth rate among virtually all mutations (excluding near lethals) is assessed by measuring the growth and sporulation rates of the SMA lines. In contrast, pleiotropy among those mutations that are likely to accumulate in large populations (only those beneficial or nearly neutral to asexual growth) is assessed by measuring the growth and sporulation rates of the L M A lines. From our SMA experiment, we have estimated mutational parameters U (deleterious mutation rate per diploid genome per generation) and s (the average reduction in fitness of heterozygous mutants) with respect to sexual function in yeast (Usex 13 and ssex). Previous mutation accumulation studies have determined the genomic mutation rate for mutations affecting maximum growth rate in budding yeast (Korona, 1999; Zeyl and DeVisser, 2001; Joseph and Hall, 2004), yet the proportion of mutations that affect sexual function has not been examined in Saccharomyces cerevisiae. Estimates of mutational parameters with respect to both vegetative and sexual growth (growth rate and sporulation rate, respectively) are underestimates of the total deleterious mutation rate and mutational effect size, as both are only components of total fitness {e.g., approximately 50% of gene disruptions have no apparent growth deficiency (Hampsey, 1997); sporulation rate is a component of sexual fitness that does not include mating ability, for example). By comparing estimates of U and s derived from growth rates with our estimates of Usex and ssac, a more comprehensive picture of mutational parameters can be derived. The rate of loss of sex has been examined in the distantly related fungus Cryptococcus neoformans (Cryptococcus: phylum Basidiomycota, Saccharomyces: phylum Ascomycota) (Xu, 2002). Sexual function in C. neoformans was estimated for two traits, mating ability and filamentation (a precursor to meiosis and spore formation), after 600 generations of SMA. In addition, Zeyl et al. (2005) have examined the relationship between asexual fitness (assayed through competitive experiments) and sexual fitness (sporulation efficiency) in different strains of S. cerevisiae propagated in restrictive environments (minimal media). We can contrast our results with that of a different fungus with respect to different measures of sexual ability (Xu, 2002) as well as with different strains of the same organism propagated in a harsher selective environment (Zeyl et ai, 2005) to speculate on the generality of our findings. 14 Methods Founding strain: The founding strain in this study is a diploid Y55 derivative of genotype leu2A (Zeyl and Devisser, 2001). The ancestral lines for both the replicate SMA and L M A experiments were established from single colonies. Samples from these ancestral lines were frozen in 15% glycerol. Mutation accumulation environment: Strains were propagated in rich media (YPD: 2% yeast extract, 1% peptone, 2% dextrose + 2% agar for solid media). Testing for contamination was conducted by plating yeast on synthetic complete media lacking leucine (SC-leu: 0.67% yeast nitrogen base without amino acids, 2% glucose, 0.2% leucine dropout mix), which prevents growth of leucine deficient strains like the strains used in this study. Tests for contamination sampled at least 20 randomly selected SMA lines and 10 L M A lines at intervals of approximately 2 weeks. When contamination was detected from outside sources (yeast or otherwise), or a compensatory mutation allowing leucine synthesis occurred, (3 times out of about 750), strains were regrown from the most recent uncontaminated culture, or eliminated in the SMA experiment in two instances. Undetected contamination among lines would serve to reduce the variance among lines, and/or increase the mean fitness; the quantitative effects of such contaminants are unknown as is common in such long-term experimental evolution studies. All cultures were maintained at 30°. Liquid cultures were shaken at 200 rpm in 18 mm x 150 mm borosilicate tubes. Small Mutation Accumulation: To perform the SMA, one hundred initially isogenic strains were propagated by single colony transfer for approximately 800 generations. To propagate lines, a colony was randomly selected for transfer by choosing the isolated 15 colony nearest to a previously applied dot on the plate. The selected colony was then streaked on to a new YPD plate with a sterile toothpick. The plates were incubated for 48 h at 30°C, after which the next transfer occurred. The SMA consisted of a total of 35 transfers. A sample colony from each plate was frozen in 15% glycerol at transfers 0, 6, 16, 22, 26 and 35. Before freezing, lines were tested for petite mutations and for contamination. Over the course of the SMA, 20 SMA strains exhibited a petite phenotype. Petites are unable to sporulate due to respiration deficiency caused by mitochondrial mutations that occur at high frequency. As we are concerned primarily with the effects of nuclear mutations on sexual and asexual fitness, we chose to eliminate these lines. Petites were detected by streaking a colony from each SMA line on a medium that does not support anaerobic growth (YPG: 1% yeast extract, 2% peptone, 3% glycerol + 2% agar). Testing for petites occurred at regular intervals (approximately every 100 generations) and before lines were frozen down. The number of generations occurring between transfers was determined by counting the number of cells in a 48h colony using a hemacytometer (Spencer Bright-Line). Six cultures from transfers 0, 6, 16, 22 and 26 were grown from frozen, and single colonies from each culture were randomly selected for counting. On average, each colony contained 9.37 x 106 cells with little heterogeneity. Thus, approximately 23 generations occurred over 48 h (2 2 3 1 5 = 9.37 x 106). The effective population size of each SMA line is thus -16 (Wahl and Gerrish, 2001). Large Mutation Accumulation: The L M A experiment consisted of fifty lines propagated in batch culture. Every 24 h, cultures were vortexed thoroughly and 0.1 ml 16 was transferred to 10 ml of fresh YPD. Approximately 6.64 generations occurred between transfers (2 6 6 4 = 100), so that 800 generations had accumulated after 121 transfers. The mean number of inoculating cells was 1.45 x 106 cells, estimated by counting the number of cells in five 24 h cultures that had evolved for 800 generations with a hemacytometer. Cultures reached stationary phase after about 10 - 11 h. The effective population size of the L M A lines is 6.9 x 106 (Wahl and Gerrish, 2001), over 104 times greater than in the SMA experiment. Lines were frozen at transfers 0, 12, 26, 73, 90 and 121 by adding 0.75 ml of culture to 0.75 ml of 15% glycerol. Strains were tested for contamination by plating on SC - leu plates and tested for petites by plating on YPG before freezing (as described above). Petite mutations are only about 70% as fit as their wild type counterparts (Zeyl and DeVisser, 2001) and were expected to be swiftly eliminated from the L M A lines. As expected, no petite L M A lines were found. Sexual fitness measure: A component of sexual fitness was determined by counting the proportion of tetrads per line, observed after inducing sporulation. Frozen strains of the ancestral and the SMA and L M A evolved lines (t - 800 cell generations) were reacclimated by growing on YPD plates for 24 h, after which a single, randomly selected colony was transferred for growth in 10 ml of liquid YPD for 24 h. To facilitate sporulation, 0.1 ml of culture was added to 10 ml of presporulation media (6% YPD: 1% yeast extract, 2% peptone, 6% dextrose) and grown for 24 h. Subsequently, 1 ml of culture was washed by centrifuging at 6000 rpm, removing the supernatant, adding 1 ml of dH20, repeating these steps, then resuspending in 0.2 ml of dH20. From the washed culture, 0.1 ml was transferred to 10 ml of sporulation media (SPM + leu: 0.3% KAc, 0.02% raffinose, 0.003% leucine) and incubated for 4 days. After 4 days had elapsed, 17 each culture was examined under a light microscope (Zeiss Axioskop) at 400x magnification. A minimum of 200 cells and, when the proportion of tetrads was low, up to 600 cells were counted per culture to determine the proportion of tetrads relative to vegetative cells. Two replicate measurements were conducted, with cultures randomized with respect to time and experiment type to minimize block effects. The second replicate measurement was conducted blindly. Results for both replicates were similar (see Table A l in Appendix). Asexual fitness measure: A component of sexual fitness of strains was estimated by determining the growth rates using the microbiology workstation Bioscreen C (ThermoLabsystems), which samples the optical density of cultures over time. Lines were grown from frozen culture on YPD plates for 24 hours, after which a single colony was transferred to 10 ml liquid YPD for 24 hours. From these stationary phase cultures, with cell densities of approximately 108 cells/ml, 1.5 uf of culture was added to 150 [i\ YPD in a 100-well Bioscreen plate. Within the Bioscreen plate, evolved cultures were grown next to their ancestors, and these "culture pairs" were randomly assigned to the wells of the plate, excluding the outer perimeter as controls. Cultures were grown for 48 h in the Bioscreen, while continuously shaking at 30°C. Optical density of cultures was automatically measured every 30 minutes. Growth curves were created by plotting OD measurements. A sliding window program was created in Mathematica 5.0 (Wolfram, 2003) to estimate growth rate from log-transformed data. The sliding window program calculates the least squares regression for a set of OD measurements within a set window length. Several different sliding window lengths were tested (60, 120, 140, 160 minutes). The 140 min window was selected for analysis because it minimized the variance within 18 replicates relative to the variance between replicates. Across the 48 hours over which the cultures grew, the slopes were calculated for each window, and the 95th percentile slope was used as the measure of growth rate. We used the 95th percentile slope rather than the maximum growth rate to avoid the influence of outliers. We found that this sliding window program gave growth rate estimates that had lower variance within replicates than fitting either a logistic growth curve or a compound logistic growth curve that can fit a diauxic shift. Consequently, these other fitting procedures were not pursued further. Asexual fitness measurements were conducted on a subset of M A lines, with two replicates per line. By running a representative subset of cultures we were able to conduct all measurements at once, thus minimizing block effects. Eighty lines, 20 per type (LMA t = 0, 800; SMA t = 0, 800), were randomly selected. This random selection included one of the three strains that greatly lost their ability to sporulate; we also added the other two poorly sporulating strains to provide a comprehensive picture of the worst performing lines. Analyses were then conducted with and without the three low sporulating lines. One of the L M A t = 800 lines selected did not grow and therefore was not included in the analyses. Previous attempts to grow this culture and measure its growth rate with the Bioscreen in a pilot study had been successful, and it displayed no apparent reduction in its growth rate (data not shown), so it was eliminated from analysis without further consideration. A n a l y s i s o f f i t n e s s m e a s u r e s : Differences in sexual and asexual fitness were tested using /-tests for three cases: 1) between SMA evolved lines and ancestral lines, 2) between L M A evolved lines and ancestral lines, and 3) between SMA evolved and L M A evolved lines. In addition, we tested for correlations between vegetative and sexual fitness of 19 lines. As expected, no difference was found between the L M A and SMA ancestral lines with respect to sexual or asexual fitness (/-tests, ?0.o5(2),ii3 = 0.43, P = 0.66; ? 0 . o 5 ( 2 ) , 7 6 = 0.21, P = 0.42), so they were grouped for comparisons. Correlations between replicate measurements with respect to sexual and asexual fitness were significant and positive in all cases (sporulation rate p = 0.32, P < 0.01; growth rate p = 0.40, P < 0.01). All data was normally distributed, with the exception of the SMA t = 800 lines with respect to sexual function (Shapiro-Wilk, W= 941, P = 0.03). Despite this departure from normality, we used parametric tests to compare population means because Mes t s are robust to departures from normality (non-parametric test results were similar). All statistics were performed in Mathematica 5.0 and/or JMP IN 5.1 (SAS Institute Inc.). Mutational parameter estimates: The mutation rate per diploid genome per generation (60 and the heterozygous mean effect on fitness per mutation (s) were estimated using two methods: Bateman-Mukai (BM) calculation and Keightley's maximum likelihood (ML) algorithm. B M (Bateman, 1959; Mukai, 1964) provides a minimum point estimate of U (Umi„) and a maximum point estimate of s (smax) and is straightforward to calculate when equal effects of mutations on fitness is assumed. B M assumes that mutations have a deleterious fitness effect so that evolved lines are expected to have a lower mean fitness than ancestral lines. B M uses the extent of fitness decline plus the increase in variance between lines over time (as different mutations accumulate in replicate lines) to estimate Umin and smca. The M L program was written and provided by Peter Keightley (Keightley, 1994). The M L algorithm assumes a Poisson distribution of the number of mutations and a gamma distribution of mutational effects. The gamma distribution requires values for (3 and a, the shape and scale parameters, where the mean mutational effect is equal to pVcx. 20 The M L program generates the log-likelihood values of the data given the mutational parameters. A profile likelihood for the shape parameter (3 was generated by searching over a wide parameter space, using starting values of U = 10"5, 10"3, 10"2, 1 0 1 , 10 and s = 0.003, 0.03, 0.3. Confidence intervals (95%) were generated for U and 5 by fixing (3 at its M L value and determining values for U and 5 where the log-likelihood decreased by two units (Keightley, 1994). Including a proportion, P, of mutations that increased sporulation was explored, but the likelihood of explaining the data was not improved by the inclusion so we disregarded it. M L is thought to provide a more accurate estimate of mutational parameters than B M because it estimates the variability in the fitness effects of mutations (Keightley, 1998). 21 Results Sexual fitness: The change in mean number of tetrads (sporulation rate or "sexual fitness") in both mutation accumulation experiments was determined by comparing the sexual fitness of each type of evolved strain to the ancestral lines (Table 1). The distributions of the 128 ancestral, 78 SMA evolved lines, and 50 L M A evolved lines are displayed in Figure 1. The mean sporulation rate of the SMA evolved lines is significantly lower than that of the ancestral lines (t-test: f0.05(2),86 = 3.02, P < 0.01). Indeed, three SMA lines lost the ability to sporulate almost entirely. Even when the three non-sporulating lines are removed, the sporulation rate of the SMA evolved lines remains significantly lower than that of the ancestral lines (r-test, ?0.o5(2),io6 = 2.73, P < 0.01). The mean sporulation rate of the L M A evolved lines is significantly greater than the ancestral lines (Mest , ^0.05<2).ii3 = 1L37, P < 0.01), as well as significantly greater than the SMA evolved lines (Mest , t005{2)9X = 7.22, P< 0.01). The data were arcsine square root transformed to examine differences in variance. This transformation was used because the data are confined between 0 and 1 as proportions, which underrepresents variance differences. The variance among the SMA evolved lines is significantly greater than the variance among ancestral lines (Levene's test, Fli204 = 18.31, P < 0.01), even when the three non-sporulating lines are removed from the dataset (Levene's test, F 1 2 0 1 = 11.42, P < 0.01). In addition, there is a significantly higher variance among the SMA evolved lines than among the L M A evolved lines (Levene's test, Fll26 = 9.56, P < 0.01). The variance among the evolved L M A strains is not significantly different from the variance among ancestral lines (Levene's test, F l i l 7 6 = 1.47, P = 0.23). 22 Asexual fitness: Growth rate measurements were conducted on a randomly selected subset of ancestral, SMA and LMA lines (Table 1 and Figure 2). The growth rate of the SMA lines is slightly lower but not significantly different from the ancestral lines (Mest, ^ o . o 5 ( 2 ) , 2 4 = 0.19, P = 0.85), or from the L M A lines (/-test, / 0 . o 5 ( 2 ) , 3 o =1.46, P = 0.15). (Including the additional two lines that lost the ability to sporulate in the SMA estimate, lowers the average growth rate of the SMA lines, but the differences are still not significant). The growth rate of the LMA lines is marginally significantly greater than the ancestors (Mest, / 0 . 0 5 ( 2 ) , 3 4 = 1.93, P = 0.06). The differences in variance between the randomly selected SMA evolved, LMA evolved and ancestral lines were compared There is a marginally significant increase in variance among the SMA lines when compared to the ancestral lines (Levene's test, F l 5 6 = 3.43, P = 0.06) but no significant difference when compared with the variance among LMA lines (Levene's test, F135 = 2.50, P = 0.12). Neither is there a significant difference in among-line variance between the LMA lines and the ancestral lines (Levene's test, F, 5 7 = 0.21, P = 0.65). (Including the additional two lines that lost the ability to sporulate caused the SMA lines to exhibit significantly more variance than either the ancestral (Levene's test, F154 = 6.81, P = 0.01) or LMA lines (Levene's test, F137 = 4.13, P = 0.04). Note that including these additional lines should have had no effect in the absence of pleiotropy between asexual and sexual function.) Correlations between sexual and asexual function: The correlation between the mean number of tetrads and the growth rate was positive, but not significantly so, among the random sample of lines (Figure 3; Spearman rank-order correlation p = 0.17, P = 0.15). This is due, in part, to the lack of variability in growth rate exhibited by the data; 23 including the two additional lines with poor sporulation ability improves the correlation (p = 0.22, P = 0.05). Estimates of mutational parameters: Using the Bateman-Mukai method, the mutation rate affecting sporulation rate, Uminsex, was estimated as 1.6 x 10"4, and sminsex was estimated to be 0.38. The M L estimates with 95% confidence intervals were estimated as Usex = 2.3 x 10'4 (9.37 x 10'5, 4.93 x 10"4), ssa = 0.24 (0.121, 0.542) when (3 was set at its M L value of 1 (-oo, 8), corresponding to an exponential distribution of selection coefficients (see Figure 4). The M L equal effects model provided a significantly poorer fit to the data by approximately five log likelihood units. Estimates of mutational parameters were created for growth rate data although results are not significant. These estimates of Usex and ssex are similar to other estimates of U and s (Table 2). 24 Discussion To date, no comprehensive explanation for the near ubiquity of sex exists. Many theories have been proposed (Kondrashov, 1993), the relevance of which can be'evaluated by knowing the time frame over which sexual function can be lost. We have determined the rate at which sporulation rate (an essential component of sexual viability) changes in a facultatively sexual organism, Saccharomyces cerevisiae, in the presence and absence of effective selection on asexual function. Over a period of 800 generations at low population size so that selection was ineffective (SMA lines), sporulation rate decreased significantly and the variance in sporulation ability increased significantly (Figure 1). Three out of 78 SMA lines completely lost the ability to sporulate, while the remaining lines had sporulation rates slightly but significantly lower than the ancestral lines. This distribution is consistent with a low mutation rate, a large average effect size per mutation, and a broad c distribution of effect sizes (Table 2). On average, sexual ability decreased at a rate of 8% over 800 generations. At this rate, it would take ~42000 generations for the frequency of sex to drop to 1%. If environmental shifts are required for the maintenance of sex, they need occur only once every 42000 generations (ignoring, for the moment, pleiotropy with asexual function). This estimate does not take into account other components of sexual function like spore viability, mating ability or pheromone production, which would likely increase the estimated rate of loss of sex. The maximum likelihood estimate of Usex and ssex is greater than previous estimates of U and s in S. cerevisiae (see Table 2). It may be more advantageous to use Usex rather than U for estimating the overall deleterious mutation rate for two reasons. 25 First, Usex is less likely to be underestimated than U due to selection against low growth rate mutants, because low growth mutants will be eliminated more readily by selection than low sporulating mutants. Second, sporulation might be a greater mutational target than growth rate if many of the genes transcribed during cell growth are also transcribed during meiosis, along with meiosis-specific genes. With respect to our SMA experiments, the results of our experiments are similar to those of Xu (2002). Xu propagated the haploid fungus Cryptococcus neoformans for 600 generations at small population size and measured the rate of decrease in sexual function for two traits: mating (a general sexual trait) and filamentation (a specific sexual trait). As in our study, Xu found a significant decrease in sexual fitness for both traits measured. The amount of decrease, however, was much greater than was found in our study: 67% in mating ability and 24% in filamentation over 600 generations versus the 8% decline in sporulation ability over 800 generations in our SMA lines. Using the Bateman-Mukai method, Xu estimated a much higher genome-wide mutation rate (2 x 0.0472 for mating efficiency and 2 x0.0134 for filamentation, averaged across strains and doubled to give diploid estimates) than observed in the mutation-accumulation experiments in S. cerevisiae (Table 2). Xu's mutation parameter estimates are more similar to the diploid genome-wide mutation rate of 0.0011 reported by Wloch et al. (2001) based on tetrad analysis in S. cerevisiae. These higher mutation rate estimates are based on fitness measures in haploids, suggesting that the rate of partially or fully recessive mutations is underestimated in the diploid mutation-accumulation experiments reported in Table 2. 26 When maintained at a large population size, the lines evolved to become significantly better sporulators (Figure 1). Unlike the distribution of phenotypes in the SMA experiment, nearly all of the L M A evolved lines have increased sporulation ability relative to their ancestors, suggesting that selection, not mutation, is driving the upward bias. Another possibility is that sporulation was inadvertently selected for directly in the L M A experiment. This is unlikely, however, for a couple of reasons. Firstly, sporulation is induced mainly by nitrogen starvation (specifically, a lack of GTPs), not by the growth conditions experienced in this study (Varma et al., 1985). Indeed, it is often difficult to induce sporulation even when sporulation conditions are favourable (Codon et al., 1995). Secondly, when random examinations of L M A cultures by microscopy occurred, no spores were ever found. We argue that the rise in sporulation rate in the L M A lines was an indirect response to selection on asexual fitness. The significantly higher sporulation rates in the evolved L M A lines than in the SMA evolved lines strongly indicates that there is, on average, positive pleiotropy between sexual and asexual growth (see a l s o Figure 3). This positive pleiotropy is confirmed by the observation that the three worst sporulators also had (marginally) significantly lower growth rates than the remaining SMA lines ( M e s t , * 0 . o 5 ( 2 ) , 2 = 2.16, P = 0.0621). That pleiotropy occurs between sexual and asexual fitness is not unexpected. Using a comprehensive library of single gene deletion mutants of S. cerevisiae, Enyenihi and Saunders (2003) found that only 17% of genes deemed necessary for full sporulation were sporulation specific genes, the remainder being genes involved in some aspect of vegetative growth. Positive pleiotropic effects of mutations on fitness related traits have 27 been found in previous experiments (Keightley et al., 2000; Estes et al., 2005). For example, Estes et al. (2005) performed an SMA experiment with selfing lines of Caenorhabditis elegans and found positive mutational correlations between all pairs of life history traits examined. These results indicate that positive pleiotropy is an important factor in the maintenance of sexual function in yeast. The costs of sex alone are abated by selection on asexual fitness and its indirect selection on sexual fitness. It is also not too surprising that lines with low sporulation ability exhibited lower growth rates, as positive pleiotropy among deleterious mutations might simply reflect disruption of genes fundamental to normal cellular functioning during both mitosis and meiosis. What is surprising is the observation that the adaptive changes occurring in the L M A lines exhibited positive pleiotropy between asexual growth and sporulation rate. This result suggests that sexual reproduction can be maintained, in part, by asexual reproduction. That is, purely asexual growth can improve sexual fitness even in the absence of sex. There are several caveats to this study. First, previous studies have found negative pleiotropy between sexual and asexual fitness. In C. neoformans, Xu (2002) found a significant negative correlation between growth rate and mating efficiency, although this result was driven by one data point (no significant correlation was observed between growth rate and filamentation). Similarly, Zeyl et al. (2005) found that increases in asexual fitness in L M A experiments were typically accompanied by decreased sexual fitness, both in haploid mating efficiency and in diploid sporulation rates. These experiments in S. cerevisiae were conducted, however, under different environmental conditions (in minimal media or in mice rather than under permissive conditions) and 28 using different yeast strains (the 875 lab strain derived from S288c and a pathogenic strain isolated from humans) than our experiments. Second, it is possible that some mutations with negative pleiotropy did arise in our experiment but were masked by more numerous or more pleiotropic mutations exhibiting positive pleiotropy (Baatz and Wagner, 1997). Third, our lines might not yet have accumulated mutations that disrupt genes essential for meiosis; such mutations might exhibit especially strong negative pleiotropy. Whether one observes positive or negative pleiotropy between asexual and sexual fitness in an L M A experiment might well depend on the time frame, with positive pleiotropy being more likely to be observed early when few mutations have accumulated (most of which affect general cell functioning) and negative pleiotropy being more likely to be observed later after the accumulation of several mutations (some of which disrupt genes essential to meiosis). Indeed, Zeyl et al. (2005) observed just such a temporal trend in one of their experiments. Because multiple mutations can accumulate in an L M A line obscuring the nature of pleiotropy, future studies would do well to isolate single mutations increasing asexual fitness and to assess the distribution of pleiotropic effects on sexual fitness. Further studies might also explore the temporal changes in sexual ability in L M A experiments across a range of environments, as the form of pleiotropy might depend strongly on the nature of mutations that improve growth in a particular environment. 29 1.0 S M A LMA 0.8 H 0.6 T t 0.4 4 0.2 H 0.0 800 Figure 2.1. Box plots of the sporulation rates for 128 ancestral (t = 0), 78 S M A evolved (t = 800) lines and 50 LMA evolved (t = 800) lines. Each data point represents the mean value of two measurements of the proportion of tetrads per replicate line. Box plots represent median, 10th, 25th, 75th and 90th percentiles. 0.30 0.25 0.20 Figure 2.2. Box plots of the growth rates for a subset of lines: 40 ancestral (t = 0), 20 SMA evolved (t = 800) lines and 19 LMA evolved (t = 800) lines. Each data point represents the mean value of two measurements of 95th quantile growth rate per replicate line. Box plots represent median, 10th, 25th, 75th and 90th percentiles. 1.0 0.8 B 0.6 H _ c o '•a 0.4 0.2 0.0 o o 0.24 0.25 0.26 0.27 0.28 0.29 0.30 growth rate Figure 2.3. Correlation between sexual fitness on the y-axis and asexual fitness on the x-axis of a randomly selected subset of lines. The correlation is not significant (dashed line; rho = 0.17, P = 0.15) when only the randomly selected lines are examined but is significant when all lines are considered, including the two poorly sporulating lines indicated by the white dots (solid line; rho = 0.22, P = 0.05). 32 Figure 2.4. L o g - l i k e l i h o o d v a l u e s g e n e r a t e d f o r d i f f e r e n t v a l u e s o f |3, w i t h m a x i m u m l i k e l i h o o d Usex a n d ssex v a l u e s a s s o c i a t e d w i t h t h a t p \ T h e r e d d o t t e d l i n e i n d i c a t e s 2 l o g l i k e l i h o o d ( I n L ) u n i t s (i.e. 95% c o n f i d e n c e i n t e r v a l ) f r o m t h e m a x i m u m I n L a t |3 = 1. 33 Table 2.1. Mean and variance values of sexual fitness (sporulation rate) and asexual fitness (growth rate) in L M A evolved, SMA evolved and ancestral strains of Saccharomyces cerevisiae Sexual Asexual Mean Variance* Mean Variance t = 0 0.67543 1.26 x 10"3a 0.2792a 2.18 x 10"5a SMA t = 800 0.6245" 2.1 x 10"2b 0.2772a 7.78 x 10 s b L M A t = 800 0.7484c 2.1 x 10"3a 0.28185a' 2.44 x 10"5a * arcsine transformed data a, b, c indicates significant differences between types ' indicates marginally significant (0.04 < P < 0.05) 4 34 Table 2.2. M a x i m u m l i k e l i h o o d e s t i m a t e s o f m u t a t i o n a l p a r a m e t e r s o f Saccharomyces cerevisiae d e r i v e d f r o m M A e x p e r i m e n t s o n n o n - m u t a t o r s t r a i n s U e s t i m a t e (95% CI) s e s t i m a t e (95% CI) F i t n e s s t r a i t r e f e r e n c e 9.46 x 10 5 (3.45 x 10"5, 1.5 x 10"4)a 0.217 (0.208, 0.236)a G r o w t h r a t e v i a c o m p e t i t i o n e x p e r i m e n t s Z e y l a n d D e v i s s e r , 2001 6.3 x 10"5 (4.6 x 10"5, oo j " * " 0.061 (0, 0.077)bcd M a x i m u m g r o w t h r a t e v i a s l i d i n g w i n d o w p r o g r a m J o s e p h a n d H a l l , * 2004 2.3 x 10"4 (9.37 x 10"5, 4.93 x 10"4)ae; (7.11 x 10"5, a»)be 0.23 (0.12, 0.54)a'e; (0, 0.56)be S p o r u l a t i o n r a t e v i a t h e p r o p o r t i o n o f t e t r a d s H i l l a n d O t t o , ( t h i s s t u d y ) a e s t i m a t e d w i t i (3 s e t a t a f i x e d v a l u e b e s t i m a t e d w i t h (3 p e r m i t t e d t o v a r y 0 p e r h a p l o i d g e n o m e d i n c l u d e s petite m u t a t i o n s eUsex a n d ssex e s t i m a t e s 35 Literature Cited Baatz, M . , and G. 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Genetics 157: 53-61. 3 7 Chapter Three The effect of selection at the level of the cell on DNA methylation and methyl-CpG-binding domain protein dynamics in a vertebrate genome Introduction How a cell functions is shaped by its gene expression pattern. A key control of expression levels occurs through transcriptional silencing, which has been associated with the stable epigenetic process of DNA methylation (Bird, 2002). In most eukaryotes, DNA methylation occurs by the addition of a methyl group to a 5' cytosine, and in vertebrates CpG dyads are the primary targets of methylation. DNA methylation occurs broadly across eukaryotes, but the frequency of DNA methylation varies widely (e.g., no methylation is found in Saccharomyces cerevisiae or Caenorhabditis elegans, while methylation is present throughout vertebrate genomes (Colot and Rossignol, 1999)). In this paper, we consider vertebrate genomes only. The importance of DNA methylation to appropriate expression and development is underscored by the plethora of abnormalities caused by either over- or undermethylation of CpGs in a prompter region. For example, cancer can result from both hypo- and hypermethylation of promoter regions (Robertson, 2005). Hypomethylation of the promoter region of the cell-growth regulating gene IGF2 in humans is associated with a number of cancers like colorectal cancer (Cui et al, 2003). In contrast, hypermethylation of the promoter region of certain genes is also related to cancer, such as hypermethylation of BRCA1 being associated with 10-15% of cases of non-familial breast cancer (Jones and Baylin, 2002). Methylation is not conserved during DNA replication. Thus for patterns of methylation to be maintained, active methylation of daughter strands must occur. DNA 38 methylation is administered by two processes: maintenance methylation, which involves copying the methylation pattern of a daughter strand from the parental strand's pattern, and de novo methylation, which refers to the methylation of a daughter strand without regard for the methylation pattern of the parental strand (Bestor, 1992). DNA methylation itself, however, does not appear to have a major, negative impact on gene expression; for several genes, it has been shown that methylation alone does not greatly reduce levels of transcription (Bird and Wolffe, 1999). Instead, DNA methylation appears to signal for the attachment of methyl-CpG-binding domain proteins (MBD proteins) (Hendrich and Bird, 1998), which physically interfere with the binding of transcription factors, thus inhibiting gene transcription (Nan et al, 1998; Ballestar et al., 2003). While methylation of a CpG provides the target for M B D protein binding, it is the proteins themselves that are directly related to transcriptional silencing. Our research questions are motivated by the dynamics of DNA methylation and MBD protein interaction. In particular, we attempt to answer two questions: what level of fidelity in the processes of DNA methylation and in M B D protein attachment is necessary for transcriptional repression to occur? and, What effect does selection have on these dynamics? We consider these questions in the context of human disease related to epigenetic malfunction, especially cancer. Mounting evidence supports the notion that abherrant methylation and MBD protein attachment are associated with cancer, such that novel cancer-associated genes are identified by their association with M B D proteins (Ballestar et al., 2003). Indeed, cancer is a particularly relevant disease to consider with this model, as the model incorporates selection at the level of the cell, and cancer is characterized by the contrast between selection at the level of cells (cancer is favoured) 39 and selection at the level of the individual (cancer is not favoured). In examining the dynamics of M B D protein attachment and the effects of selection on this process, we hope to add to add insight into the conditions under which inappropriate transcriptional silencing will occur. Previous models have considered the kinetics of DNA methylation (Otto and Walbot, 1990; Pfeifer et al, 1990; Genereux et al, 2005). Most recently, Genereux et al., (2005) have combined empirical work and modeling to determine site-specific values for maintenance and de novo methylation. They used hairpin bisulfite PCR to determine site-specific values for maintenance and de novo methylation. They determined the frequencies of the homo-, hemi- and unmethylated CpG dyads and used mathematical modeling to infer a range of methylation values, 0.90 to 0.98 for maintenance methylation and from 0.02 to 1 for de novo methylation. This range of de novo methylation values reflects the range of different genes examined and assumes that methylation occurs on only one strand at a time. In contrast, a broad scale estimate of methylation rates was created by Laird et al. (2004) using hairpin bisulfite PCR. They estimated the maintenance and de novo methylation rates to be 0.96 and 0.17, respectively. While estimates of methylation parameters have been generated empirically and by modeling, no model to date has incorporated the dynamics of M B D protein binding to methylated DNA. We have created an analytical model and used numerical simulations to examine the interactions between methylation status at CpGs and the attachment of M B D proteins while incorporating selection at the level of the cell. 40 The Model Here we consider a particular CpG methylation substrate site in a large population of cells. Each cell has this CpG in one of four possible states: methylated with MBD proteins attached (frequency X,), methylated with no M B D proteins attached (X2), unmethylated with M B D proteins attached (X3), unmethylated with no M B D proteins attached (X4), where X, + X2 + X3 + X4 = 1. Figure 1 displays the four states and the rates of transition among them. The life cycle of the cell is given in Figure 2. From this cell cycle, recursion equations were developed to describe the change in frequency of the states with respect to selection, protein attachment/unattachment, methylation and replication. Each event in the life cycle of the cell applies to the double stranded CpG/CpG dyad. We make the simplifying assumption that methylation occurs only on one strand (see Genereux et al. (2005) for a model that allows one or both strands to become methylated). At time t, the frequencies of the CpG dyads in each state are given by X,. The following equations relate each stage of the life cycle detailed in Figure 2 to the change in these frequencies. The frequency of each state following selection is described by: XW Z,'=^-=^ (la) W X W W X w Y ' = ^ _ _ A (lc) w X w X ' - ± £ Z L (id) 4 W 41 where W = XiWl + X2W2 + X3W3 + X4W4 represents the mean fitness of cells. Subsequent protein attachment/unattachment alters the frequencies of the states by: X:<=X;+dX:-bX: (2a) x2"=x:+bx:-dx: (2b) x;<=x:+(d+5d)x;-(b + db)x: (2c) X4"=X4'+(b + 6b)X3'-(d + Sd)X4' (Id) where b, d,(b + 5b) and (d + 6J are the transition rates (Figure 1), and X,' are substituted from (1). Finally, the processes of methylation and DNA replication are described as follows: X 1 ,"=X 1"+cX 3"-aX 1" (3a) X2'"=X2"+(c + 6c)X4"-(a + 5a)X2" (3b) X3"'=X3"+aXl"-cX3" (3c) X/"= X4"+(a + da)X2"-(c + <5JX4" (3d) where a, c, (a + 6a) and (c + 5C) are the transition rates (Figure 1), and X." are substituted from (2). It is assumed that following DNA replication, M B D proteins reattach immediately so that proteination status is maintained. The methylation parameters in Equations (3) can be related to the processes of maintenance and de novo methylation. Borrowing the terminology of Otto and Walbot (1990), we let a be the rate of maintenance methylation and let B be the rate of de novo methylation. Methylation parameters can be rewritten as: a - - H I - a , ) (3Ma) c - i f l (3Mb) a + 8a=\(\-a2) (3Mc) 42 c + dc=^2 (3Md) where a, (/?,) and a2 {B2) are the maintenance {de novo) rates of methylation when the CpG is proteinated and unproteinated, respectively. While methylation status is an important signal for the transcriptionally repressive MBD proteins to bind to DNA, methylation itself appears to have little regulatory effect on gene transcription (Bird and Wolffe, 1999). We therefore consider selection to occur only with respect to protein status. Specifically, we assume that proteinated states (X, and X3) have a fitness of 1 + s relative to unproteinated states (X2 and X4), where s, the selection coefficient, is positive when protein attachment is favoured and negative when no protein attachment is favoured at this site. In order to determine what affects the relative proportions of the X„ we solved for the equilibrium values (X.). The equilibrium solutions were intractable, however, thus requiring us to make two simplying adjustments. First, we disregarded all rate modifying terms (6, = 0) for the analytical solution, leaving their exploration for the numerical solutions. We also assumed that selection is weak (of order e). Having made these adjustments, we were able to determine equilibrium values. Numerical analysis To better understand the dynamics of the recursion equations, we performed numerical simulations. We investigated cases where it is favourable for the gene to be silenced and therefore for MBD proteins to be attached to CpGs (s > 0; Figure 3a, c) and when gene expression is favoured, with no MBD proteins attached (s < 0; Figure 3b, d). We assigned biologically realistic values to the parameters based on data previously collected. Methylation rates are held constant at 0.96 (a) and 0.17 (ft) (Figure 3a, b) or 43 0.96 (a) and 0.05 (ft) (Figure 3c, d). These values reflect upper and lower estimates of the range of possible de novo methylation rates, with the estimate for the upper bound from Laird et al, (2004) and for the lower bound from Pfeifer et al, (1990). We also examined the effect of the magnitude of transition rate parameters on the efficacy of selection (Figure 4). Again, we consider selection to occur only with respect to protein status, not methylation. Results and Discussion To determine the dominant factors affecting the equilibrium proportions of X-„ we solved for the first and second order terms of the recursion equation (see Table 1). The equilibrium values to the first order are simplistic because they neglect and selection (s). To determine the impact of selection on the equilibrium values, we found solutions for the Xt to linear order in s (Table 1). The impact of selection is proportional to the level of variability in protein attachment status, as measured by prot * (1 - prot), as well as the strength of selection, s. The impact of selection affects both methylated and unmethylated sites in proportion to their frequency. The efficacy of selection is weakened, however, by a factor (1 - b - d)/(b + d), as transitions between unattached and attached proteins erase the effects of selection. Interestingly, this indicates that selection at the cellular level is most effective at altering equilibrium frequencies when there is high fidelity in protein attachment. We examined the effect of the magnitude of selection on equilibrium frequencies (Figure 3) and the effect of increasing the overall transitioning (Figure 4). As selection favouring gene repression and therefore the attachment of M B D proteins increases (Figure 3a, c), the equilibrium frequency of CpGs with proteins attached (Xy and X3) 44 increases. When gene activation (no M B D protein attachment) is favoured, the equilibrium frequency of CpGs with no proteins attached (X2 and X4) increases (Figure 3b, d). This pattern arises regardless of whether de novo methylation is relatively high (Figure 3a, b) or low (Figure 3c, d). When the rate of de novo methylation is high, there is a greater proportion of methylated, proteinated CpGs than unmethylated, proteinated CpGs (X; > X3), while the difference is not as great when de novo methylation occurs at a low rate, reflecting the fact that more CpGs will be methylated when the de novo methylation rate is high. A similar pattern applies to the equilibrium frequencies of the unproteinated states when no proteination is favoured, where unmethylated, non-proteinated (X4) CpGs are dominant when Bis low, while methylated, non-proteinated (X2) CpGs are dominant when B is high. The overall proportion of proteinated or unproteinated CpGs is therefore not greatly affected by the rate of de novo methylation. While selection is able to influence the equilibrium frequencies of the four different states, the effect is not very pronounced even when strong selection is applied (s = 0.2). These results are a straightforward demonstration that the effect of selection is muted by the continual transitions in state. To examine the degree to which the effects of selection were mitigated by transition rates, as implied by Figure 3, we scaled all transition rates by the same factor, which was varied from 0 to 1 in Figure 4. We compared the effect of transition rate magnitude when selection was strong (s = 0.1; Figure 4a) to when selection was weak (s = 0.01; Figure 4b). As expected, when protein attachment was favoured, the frequency of proteinated CpGs approached one when the magnitude of transition parameters was small, for both strong and weak selection. As the magnitude of the transition rate 45 parameters increased, the impact of selection decreased. As transition rates increased, the frequencies of the proteinated states approached their (non-selective) equilibrium values, as given in the first terms of the equations in Table 1. The range of transition rate values over which selection was able to influence the frequencies of CpGs was dependent on the strength of selection. For example, when selection is 0.01, its effects are apparent only when transition rate parameters are quite low (< 0.2). This underscores the fact that selection is only effective in this system if transition rates between states are low. In addition to examining the effects of selection with respect to differing magnitudes of transition parameters, we compared cases where the difference between transition rates between proteination states were not dependent on methylation status (6b, 8d = 0) and when methylation status affected the rate of transition between proteination states (5b> 0, 6d < 0). Modifying these rates favoured proteinated CpGs relative to when protein attachment was assumed to be independent of methylation status (see Figure 4). The values selected for the 6,terms were motivated by the observation that M B D proteins have an affinity for binding to methylated CpGs (Fraga et ai, 2003). This is related to two features of the model: 1) the fact that 8b is positive and that 8d is negative, and 2) the fact that maintenance methylation is much greater value than de novo methylation. The positive value for 8d and the negative value for 8b indicate that CpGs are more likely to be in the state of unmethylated, unproteinated (X4) than unmethylated, proteinated (X3). From the unmethylated, unproteinated state, CpGs are likely to move to the state of methylated, no protein attached (X2, see Figure 1 for reference) because maintenance methylation is set to a high value (0.96). From this state, protein attachment is more likely (8d < 0), reflecting the affinity of proteins for methylated CpGs. The increased 46 level of CpGs with proteins attached observed when 6b > 0 and 5d < 0 disappears when maintenance methylation is decreased to a level on par with de novo methylation, or if the sign and magnitude of the transition parameters between states of proteination are reversed, reflecting the biological impositions placed on the model. This model is limited for a number of reasons. We consider CpGs individually, so that the methylation status between CpG sites in a certain promoter region can be different. Evidence suggests that some M B D proteins require a certain density of methylated CpGs to bind to the promoter region (Boyes and Bird, 1992; Fraga et al., 2003). However, the well-studied MBD protein MeCP2 is known to bind to a single methylated CpG dyad (Bird and Wolffe, 1999). This model is more realistic, therefore, when MeCP2 is considered. While DNA methylation and M B D protein structure are the subject of much research, little is known about the success rates of protein attachment and how frequently methylated CpGs are unproteinated. This limits the biological accuracy of the parameter values we have estimated for our numerical simulations. As more information regarding the rate parameters is found, it can be applied to improve our understanding of DNA methylation and transcriptional silencing. We have examined DNA methylation and protein attachment in vertebrate genomes in order to gain a better understanding of aberrant gene silencing and activation. We can draw two conclusions: 1) CpGs will respond to selection based on their proteination status, but 2) the efficacy of selection is mitigated by a high rate of transition between states. Our results have implications for cases, like cancer, where selection at the level of the cell conflicts with selection on the organism as a whole. When transition rates between states of proteination are dependent on methylation status (db > 0, Sd < 0), there 47 is a shift towards proteinated CpGs relative to when movement between proteination states is independent of methylation status (6, = 0), regardless of what state of proteination selection favours (Figure 4). This implies that the proportion of cancerous cells will be greater when cancerous cells with M B D proteins attached replicate at faster rate than when cancerous cells with MBD no proteins attached replicate at faster rate. However, for selection at the level of the cell to be effective, the processes of methylation and protein attachment must be conserved (Figure 4). Although we do not explore the case of methylation status being dependent on proteination state, we leave the model general such that it can be examined in the future (da, 8C terms). In addition, future research should continue to provide information about the role of M B D proteins in gene repression, and the effects of DNA methylation on gene repression and activation. 48 Figure 3.1. The four possible states of a CpG, and their relative frequencies denoted by X;. The symbols a through d and 8a through 8d denote transition rates between the states. M = methylated; U = unmethylated; P = proteins attached; N = no proteins attached. 49 o in protein time , t . a t tachment a n d DNA methylat ion t j m e _ selection unat tachment a n d replication Figure 3.2. T h e c e l l c y c l e w i t h r e s p e c t t o s e l e c t i o n , p r o t e i n a t t a c h m e n t / u n a t t a c h m e n t , m e t h y l a t i o n a n d r e p l i c a t i o n . 0 . 8 0 . 6 0 . 4 0 . 2 - t * r j - j - ! r i z ; = i _ _ : 0 . 0 2 5 0 . 0 5 0 . 0 7 5 0 . 1 0 . 1 2 5 0 . 1 5 0 . 1 7 5 0 . 2 — I — i — i — i — i — | — 0.8 0.6 0.4 0.2 • - » - * - * - * = * = ^ * - = _ - = _ = l r : 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2 selection coefficient 0.8 0.6 0.4 0.2 ._.-»-_-•- m--m--i C 0.025 0.05 0.075 0.1 0.125 0 .15 0.175 0.2 1 0.8 0.6 0.4 0.2 —.A---— 0.025 0.05 0. 075 0. 1 0. 125 0.15 0 . 175 0.2 selection coefficient Figure 3.3. Exact numerical solutions of the equilibrium frequencies when protein attachment is favoured (a, c) and when no protein attachment is favoured (b, d). The values for a and |3 are held constant at 0.96 and 0.17 (a, b), or 0.95 and 0.05 (c, d), respectively. The remaining parameters are set for all graphs as follows: b = 0.05, d = 0.1, c\ = 0.05, 6rf=-0.05. 0 . 8 proportion proteinated 0 w 6 CpGs 0 .4 0 .2 0 .4 0 . 6 . 0 . 8 magnitude of transition rates 0 . 8 proportion proteinated 0 6 CpGs 0 .4 0 .2 0 .2 0 .4 0 . 6 0 . 8 magnitude of transition rates Figure 3.4. The effect of the size of transition rate parameters a, b, c and d on selection on proteinated CpGs {X, + X3) when selection is strong (a; s = 0.1) and when selection is weak (b; s = 0.01). Solid lines indicate <5, = 0; dashed lines indicate 8b = 0.05 and dd= -0.05. Bold lines indicate that protein attachment is favoured, unbolded lines indicate no protein attachment is favoured. Base parameter values are set at a = 0.02, b = 0.05, c = 0.085 and d = 0.1. 52 Table 3.1. S o l u t i o n s t o t h e f i r s t a n d s e c o n d o r d e r o f t h e e q u i l i b r i u m v a l u e s (Xt) e q u a t i o n s meth * prot + srel * meth * prottl - prot) meth * noprot - srel * meth * prottl - prot) unmeth * prot + srel * (1 - meth) * prot(l - prot) * 4 . unmeth * noprot - srel * (1 - meth) * prot(\ - prot) w h e r e : meth = c/(a+c), t h e p r o p o r t i o n o f m e t h y l a t e d s i t e s unmeth = a/(a+c), t h e p r o p o r t i o n o f u n m e t h y l a t e d s i t e s prot = d/(b+d), t h e p r o p o r t i o n o f p r o t e i n a t e d s i t e s noprot = b/(b+d), t h e p r o p o r t i o n o f u n p r o t e i n a t e d s i t e s srel = s(l-b-d)/(b+d), s e l e c t i o n r e l a t i v e t o t h e r a t e o f m o v e m e n t b e t w e e n p r o t e i n a t e d a n d u n p r o t e i n a t e d s t a t e s Literature Cited Ballestar, E. , Paz, M . F., Valle, L. , Wei, S., Fraga, M . F., Espada, J., Cigudosa, J. C , Huang, T. H. M . , and M . Esteller, 2003 Methyl-CpG binding proteins identify novel sites of epigenetic inactivation in human cancer. E M B O J. 22: 6335-6345. Ballestar, E. and A. P. Wolffe, 2001 Methyl-CpG-binding proteins: targeting specific gene repression. Eur J Biochem 268: 1-6. Bestor, T. H., 1992 Activation of mammalian DNA methyltransferase by cleavage of a Zn-binding regulatory domain. EMBO J. 11: 2611-2617. Bird, A., 2002 DNA methylation patterns and epigenetic memory. Genes Dev. 16: 6-21. Bird, A. and A. P. Wolffe, 1999 Methylation-induced repression - belts, braces and chromatin. Cell 99: 451-454. Boyes, J. and A. Bird, 1992 Repression of genes by DNA methylation depends on CpG density and promoter strength: evidence for involvement of a methyl-CpG binding protein. EMBO J. 11: 327-333. Colot, V. , and J. L. Rossignol, 1999 Eukaryotic DNA methylation as an evolutionary device. BioEssays 21: 402-411. Cui, H , Cruz-Correa, M . , Giardiello, F. M . , Hutcheon, D. F., Kafonek, D. R., Brandenburg, S., Wu, Y., He, X., Powe, N. R., and A. P. Feinburg, 2003 Loss of IGF2 imprinting: a potential marker of colorectal cancer risk. Science 299: 1753-1755. Fraga, M . F., Ballestar, E. , Montoya, G., Taysavang, P., Wade, P. A. and M . Esteller, 2003 The affinity of differenct M B D proteins for a specific methylated locus depends on their intrinsic binding properties. Nucl Acids Res 31: 1763-1774. Genereux, D. P., Miner, B. E. , Bergstrom, C. T., and C. D. Laird, 2005 A population-epigenetic model to infer site-specific methylation rates from double-stranded DNA methylation patterns. PNAS 102: 5802-5807. Hendrich, B. and A. Bird, 1998 Identifcation and characterization of a family of mammalian methyl-CpG binding proteins. Mol Cell Bio 18: 6538-6547. Jones, P. A. and S. B. Baylin, 2002 The fundamental role of epigenetic events in cancer. Nat Rev Genetics 3: 415-428. Laird, C. D. Pleasant, N. D., Clark, A. D., Sneeden, J. L. , Anwarul Hassan, K. M , Manley, N. C , Vary, Jr., J. C , Morgan, T., Hansen, R. S. and R. Stoger, 2004 Hairpin-bisulfite PCR: assessing epigenetic methylation patterns on complementary strands of individual DNA molecules. PNAS 101: 204-209. Nan, X., Ng, H , Johnson, C. A., Laherty, C. D., Turner, B. M . , Eisenman, R. N. and A. Bird, 1998 Transcriptional repression by the methyl-CpG-binding protein MeCP2 involves a histone deactylase complex. Nature 393: 386-389. Otto, S. P. and V. Walbot, 1990 DNA methylation in eukaryhotes: kinetics of demethylation and de novo methylation during the life cycle. Genetics 124: 429-437. \ Pfeifer, G. P., Steigerwald, S. D., Hansen, R. S., Gartler, S. M . and A. D. Riggs, 1990 Polymerase chain reaction-aided genomic sequencing of an X chromosome-linked CpG island: methylation patterns suggest clonal inheritance, CpG site autonomy, and an explanation of activity state stability. PNAS 87: 8252-8256. 54 Robertson, K. D., 2005 DNA methylation and human disease. Nat Rev Genetics 6: 597-610. Robertson, K. D., 2001 DNA methylation, methyltransferases, and cancer. Oncogene 20: 3139-3155. \ 55 Chapter Four General Conclusions This thesis consists of two chapters that address two distinct topics. In Chapter Two, my research falls under the broad heading of the maintenance of sexual reproduction. Sexual reproduction is associated with many ecological and genetic costs (Otto and Lenormand, 2002), yet most organisms engage in sexual reproduction at some point during their life cycle, if not exclusively (Barton and Charlesworth, 1998). This naturally leads to the question, why is sex so pervasive? In Chapter Two I aimed to answer questions that would provide information needed to address this question. Chapter Three of this thesis examines the dynamics of DNA methylation and its associated proteins (methyl-CpG-domain binding proteins; M B D proteins). Like with sexual reproduction, DNA methylation occurs in a widespread group of organisms (Colot and Rossignol, 1998). In vertebrate genomes, methylation is associated with transcriptional repression (Bird, 2002) and thus with everything from X-inactivation to cancer (Robertson, 2005). Methylation dynamics have been addressed previously (Otto and Walbot, 1990; Pfeifer et al., 1990; Genereux et al, 2005), but no model had yet been developed to examine the interaction between methylation and M B D proteins. This is worthy of consideration because evidence suggests that it is these M B D proteins that are responsible for repression of transcription, and that methylation acts as a marker for the binding of these proteins (Bird and Wolffe, 1999). In Chapter Three, I examine these dynamics in the context of selection at the level of the cell. 5 6 Summary of Objectives and Conclusions Chapter Two The research questions of Chapter Two were addressed in the facultatively sexual, single-celled eukaryote Saccharomyces cerevisiae, commonly known as budding yeast. Sexual reproduction in budding yeast (sporulation) is easily discernible, making S. cerevisiae an ideal study organism. The objectives of Chapter Two were to determine the rate of loss of sporulation, as a proxy for sexual function, in Saccharomyces cerevisiae; to determine if the net effect of pleiotropy between asexual growth (budding) and sporulation is positive or negative, and; to determine the mutation rate per diploid genome per generation (Usex) and the average heterozygous effect size per mutation (ssex) with respect to sporulation. It was found that sporulation rate is lost slowly in budding yeast, at a rate of 1 %/100 generations, and that a net effect of positive pleiotropy is occurring between asexual and sexual function. This result is in contrast with the net effect of negative pleiotropy between sexual and asexual function found in a distantly related fungus Cryptococcus neoformans (Xu, 2002). In addition, the maximum likelihood values for Usex and ssex were estimated as 2.3 x 10"4 and 0.23, respectively, approximately an order of magnitude greater than estimates of U and 5 with respect to asexual growth previously estimated for S. cerevisiae (Zeyl and DeVisser, 2001; Joseph and Hall, 2004). From these results, it can be concluded that while sporulation in S. cerevisiae is not lost easily, it is being maintained because the costs of sex are mitigated by selection on asexual growth. The estimates of the rate of loss of sex and of mutational parameters are likely underestimates because we examined only one component of sexual fitness. In the future, studies should examine a wider variety of mating traits (including SI sporulation ability, spore viability and mating propensity) in S. cerevisiae to generate a more informed estimate of the rate of loss of sex in yeast. In addition, future studies should determine mutational parameters with respect to sex for a variety of species, so that the generality of these parameters can be assessed. Chapter Three To address the research questions of Chapter Three, a mathematical model was created that examined a population of cells at a specific CpG substrate site. The model focused on three factors: the methylation status at the CpG, the protein-attachment status at the CpG and the effect of selection at the level of the cell. The main objective of this chapter was to determine the effect of selection on the dynamics of protein attachment and methylation in the context of disease like cancer. We were able to conclude that selection is able to affect the proportion of proteinated CpGs (when selection occurs with respect to protein status only, but that the effects of selection are diminished by transitions between the states of methylation and proteination. These transitions states of are effectively a randomizing factor that counteracts selection. It can be concluded that selection will be effective when state fidelity is high. As much research is currently being done on methylation and M B C proteins, future work should focus on determining realistic parameter values for epigenetic models, such as how efficient M B D proteins are at attaching to methylated CpGs. Summary The chapters of this thesis, while unrelated to one another, share the fact that they address widespread biological phenomena, sexual reproduction and DNA methylation. In Chapter Two, it was determined that sporulation, as a proxy for sexual function in yeast, 58 is lost at a very slow rate and the costs of its maintenance are mitigated by pleiotropy with asexual function. In Chapter Three, selection was found to be an important influence on methylation and proteination status of CpGs, but its effectiveness was relative to the rate of protein attachment/unattachment. Future research should work to broaden our knowledge with respect to both chapters by examining the loss of sex in other facultative systems, and elucidating the importance of M B D proteins and methylation to transcriptional repression. 59 Literature Cited Barton, N. H., and B. Charlesworth, 1998 Why sex and recombination? Science 281: 1986-1990. Bird, A., 2002 DNA methylation patterns and epigenetic memory. Genes Dev. 16: 6-21. Bird, A. and A. P. Wolffe, 1999 Methylation-induced repression - belts, braces and chromatin. Cell 99: 451-454. Colot, V. , and J. L. Rossignol, 1999 Eukaryotic DNA methylation as an evolutionary device. BioEssays 21: 402-411. Genereux, D. P., Miner, B. E. , Bergstrom, C. T., and C. D. Laird, 2005 A population-epigenetic model to infer site-specific methylation rates from double-stranded DNA methylation patterns. PNAS 102: 5802-5807. Joseph, S. B., and D. W. Hall, 2004 Spontaneous mutations in diploid Saccharomyces cerevisiae: more beneficial than expected. Genetics 168: 1817-1825. Otto, S. P., and T. Lenormand, 2002 Resolving the paradox of sex and recombination. Nat Rev Genet 3: 252-261. Otto, S. P. and V. Walbot, 1990 DNA methylation in eukaryhotes: kinetics of demethylation and de novo methylation during the life cycle. Genetics 124: 429-437. Pfeifer, G. P., Steigerwald, S. D., Hansen, R. S., Gartler, S. M . and A. D. Riggs, 1990 Polymerase chain reaction-aided genomic sequencing of an X chromosome-linked CpG island: methylation patterns suggest clonal inheritance, CpG site autonomy, and an explanation of activity state stability. PNAS 87: 8252-8256. Robertson, K. D., 2005 DNA methylation and human disease. Nat Rev Genetics 6: 597-610. Xu, J., 2002 Estimating the spontaneous mutation rate of loss of sex in the human pathogenic fungus Cryptococcus neoformans. Genetics 162: 1157-1167. Zeyl, C , and J. A. G. M . DeVisser, 2001 Estimates of the rate and distribution of fitness effects of spontaneous mutation in Saccharomyces cerevisiae. Genetics 157: 53-61. 6 0 

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