The [PSI+] prion causes widespread readthrough translation and is rare in natural populations of Saccharomyces, despite the fact that sex is expected to cause it to spread. Using the recently estimated rate of Saccharomyces outcrossing, we calculate the strength of selection necessary to maintain [PSI+] at levels low enough to be compatible with data. Using the best available parameter estimates, we find selection against [PSI+] to be significant. Inference regarding selection on modifiers of [PSI+] appearance depends on obtaining more precise and accurate estimates of the product of yeast effective population size Ne and the spontaneous rate of [PSI+] appearance m. The ability to form [PSI+] has persisted in yeast over a long period of evolutionary time, despite a diversity of modifiers that could abolish it. If mNe < 1, this may be explained by insufficiently strong selection. If mNe > 1, then selection should favor the spread of [PSI+] resistance modifiers. In this case, rare conditions where [PSI+] is adaptive may permit its persistence in the face of negative selection.
[PSI+] is the prion form of the protein Sup35 (Wickner et al. 1995). Sup35 is involved in stop codon recognition during gene translation (Stansfield et al. 1995; Zhouravleva et al. 1995). In prion form, Sup35 is sequestered in aggregates, depleting the availability of functional Sup35 (Wickner et al. 1995). This leads to an elevated rate of readthrough error at every stop codon in the Saccharomyces genome (Firoozan et al. 1991).
Given the likely cost of these translation readthrough errors, one might expect [PSI+] to have substantial deleterious effects. Nevertheless, in standard lab conditions [PSI+] strains containing prions seem to grow just as well as [psi−] strains that lack them (True and Lindquist 2000). While it is difficult to detect small differences in fitness in the lab, wild yeast species have large effective population sizes of ∼107 (Tsai et al. 2008), making natural selection extremely sensitive to tiny differences in fitness.
In Figure 1 we show the logic of all possible scenarios of selection on [PSI+], including the necessary conditions for them to hold, as derived in this article, and our assessment of the plausibility of those conditions. [PSI+] must be adaptive, neutral, or deleterious under the majority of normal conditions found in the wild. A predominantly adaptive role for [PSI+] is obviously not compatible with its rarity (Chernoff et al. 2000; Nakayashiki et al. 2005).
A predominantly deleterious role for [PSI+] would raise the question as to why the ability to form [PSI+] has not been eliminated by natural selection, but instead been conserved over long periods of yeast evolution (Chernoff et al. 2000; Kushnirov et al. 2000a; Santoso et al. 2000; Nakayashiki et al. 2001). Consider a modifier locus called prf [prion-forming (Masel and Bergman 2003)] with allele prf+ permitting [PSI+] formation and allele prf0 preventing it. When [PSI+] is deleterious, then prf+ lineages are also at a disadvantage, as they repeatedly give rise to [PSI+] progeny: this is known as indirect selection. If indirect selection is strong enough, this should lead to the fixation of the [PSI+]-resistant prf0 allele in the population. Similarly, rare positive selection on [PSI+] would lead to indirect positive selection on the prf+ allele that generated the favored [PSI+] lineage.
A variety of modifiers exist whose mutation could impart resistance to [PSI+], including the [PIN+] prion (Derkatch et al. 1997) and chaperone molecules (Chernoff et al. 1999; Kushnirov et al. 2000b; Sharma and Masison 2008). One particular modifier is an oligopeptide repeat region within Sup35 that is required for [PSI+] formation and propagation (Parham et al. 2001). Although this region (Harrison et al. 2007), together with the ability of the Sup35 protein to form [PSI+] (Chernoff et al. 2000; Kushnirov et al. 2000a; Santoso et al. 2000; Nakayashiki et al. 2001), is conserved in yeast evolution, some natural populations of Saccharomyces cerevisiae carry a deletion within this oligopeptide repeat region of Sup35 that eliminates [PSI+]-forming ability (Resende et al. 2003). If this region has some inseparable pleiotropic function apart from promoting [PSI+] formation, then this function cannot be essential over short evolutionary timescales.
Although a variety of candidate modifier loci exist, in our analysis we consider an abstract modifier locus in the tradition of theoretical population genetics, rather than a specific, empirically identified modifier. We assume two alleles at this locus, a prf0 allele that completely suppresses de novo [PSI+] formation and a prf+ allele that allows for it.
Any specific modifier of [PSI+], including but not limited to changes in the sequence of Sup35, could of course be subject to pleiotropic constraint, but given the diversity of available modifiers and the long period of evolutionary time, we would expect resistance to [PSI+] to have fixed were it advantageous. Instead, the relevant pleiotropic constraint may be a single adaptive function of [PSI+] itself, rather than a series of different pleiotropic functions constraining each and every one of the possible modifier loci. It is possible that [PSI+]-formation ability has not been lost because [PSI+] occasionally has advantageous effects by exposing cryptic genetic variation in novel environments (C. K. Griswold and J. Masel, unpublished results; True and Lindquist 2000; Masel and Bergman 2003; Masel 2005; Giacomelli et al. 2007; King and Masel 2007; Joseph and Kirkpatrick 2008). This relatively rare role in promoting adaptation would explain its persistence over long evolutionary timescales, despite not being essential on short timescales.
An alternative hypothesis states that [PSI+] is better regarded as a sexually transmitted disease of yeast (Nakayashiki et al. 2005). A Mendelian genetic element is inherited by only half the meiotic products and remains at a constant frequency in the absence of other forces such as selection or drift. In contrast, [PSI+] is inherited cytoplasmically during both asexual and sexual reproduction. Since [PSI+] is inherited by all four meiotic products, it will therefore increase in frequency when outcrossing occurs, giving rise to the analogy of a sexually transmitted disease (Nakayashiki et al. 2005). [PSI+] is not found at high frequency in natural populations, so either negative selection against [PSI+] or high epigenetic reversion rates must be invoked to counter the fact that outcrossing will increase [PSI+] frequency. The extent of selection (and/or reversion) needed depends on the amount of outcrossing that spreads [PSI+]. The rate of outcrossed sex in S. paradoxus was recently estimated as only 10−5 per reproductive event (Tsai et al. 2008). Here we quantify (through Equation 3) the parameter range necessary to keep [PSI+] at its observed low frequency, given realistic parameters describing wild yeast sex.
If [PSI+] is deleterious, then given the variety of modifiers and the long evolutionary period during which the ability to form [PSI+] has persisted, one might expect yeast to have evolved resistance to the [PSI+] “disease” through the evolution of modifiers of [PSI+] formation. For most transmissible diseases, pathogen coevolution makes this difficult, but the evolution of [PSI+] resistance needs only to adapt to a stationary target and so should be straightforward. However, indirect selection may be too weak to overcome genetic drift. With direct selection, selective costs are incurred in every generation. With indirect selection, the same cost is incurred only infrequently and is therefore less effective as an evolutionary force, since not all prf+ individuals incur the cost of a [PSI+] phenotype. So it is possible that although direct selection against the deleterious effects of [PSI+] is strong enough to overcome genetic drift and keep [PSI+] at low frequency, indirect selection may not be strong enough to fix modifier or resistance alleles against [PSI+]. In a finite population, arguments concerning the strength of selection amount to an assessment of whether or not sNe > 1, where s is the selection coefficient and Ne is the effective population size.
The focus of this article is to determine the conditions for the different scenarios described above and in Figure 1 by (1) calculating the strength of direct selection sPSI+Ne against [PSI+] and (2) calculating the strength of indirect selection sprf+Ne against a modifier allele prf+ that permits [PSI+] formation. Our inferences are based on the Tsai et al. (2008) data on sexual frequencies in S. paradoxus and a spontaneous rate of epigenetic conversion from [psi−] to [PSI+] of ∼10−7–10−5 in lab strains of S. cerevisiae (N. Koloteva-Levine, G. H. Merrit and M. F. Tuite, personal communication; Lund and Cox 1981; Chernoff et al. 1999). The reversion rate from [PSI+] to [psi−] is known to be <2 × 10−4 (Tank et al. 2007) and is widely believed to be similar to the rate of [PSI+] appearance, although it is less studied: we explore a substantial range for this parameter. The effective population size Ne in S. paradoxus can be estimated as θ(1 + F)/(4μ), where θ is the pairwise sequence divergence estimated as 0.0032–0.0038 (Tsai et al. 2008), the inbreeding coefficient F = 0.98 (Tsai et al. 2008), and the genomewide per-base-pair point mutation rate μ is ∼3.3 × 10−10 (Lynch et al. 2008) to 5 × 10−10 (Lang and Murray 2008). This yields Ne ≈ 3 × 106–6 × 106. We use Ne = 5 × 106 in Figures 2–4⇓⇓. We also use an upper bound of 1% on the frequency of [PSI+] within wild prf+ populations of a variety of Saccharomyces species (Nakayashiki et al. 2005; see below).
MODEL AND RESULTS
[PSI+] frequency in the wild:
[PSI+] is rarely found at high frequency within natural populations (Chernoff et al. 2000; Nakayashiki et al. 2005). Nevertheless, in the presence of a second prion [PIN+] (Derkatch et al. 1997), [PSI+] forms de novo at a rate of ∼m = 10−7–10−5 per generation (N. Koloteva-Levine, G. H. Merrit and M. F. Tuite, personal communication; Lund and Cox 1981; Chernoff et al. 1999). Although it may be subject to both negative selection and reversion to [psi−], [PSI+] reappears every generation and is expected to spread by sex. Its frequency within a [PIN+] population may therefore be low, but will not be zero.
Prion presence was assessed by the visible presence of GFP-fusion protein aggregates, and 11 of 70 natural populations of various Saccharomyces species were positive for [PIN+] and competent to form [PSI+] following Sup35 overexpression (Nakayashiki et al. 2005). Although none were composed primarily of [PSI+] cells, 4 of these 11 [PIN+] populations had a low but detectable frequency (<5%) of cells positive for Sup35 aggregates almost immediately after transformation with a Sup35-GFP fusion product (Nakayashiki et al. 2005). This may (Zhou et al. 2001) or may not (Salnikova et al. 2005) be a reliable indicator of the preexisting presence of [PSI+]. What is clear is that this sets an upper bound on the [PSI+] frequency within these populations. Taking into account likely limits of detection in the other 7 [PIN+] populations, we estimate a maximum frequency of 1% of [PSI+] in [PIN+] populations and use this value of ε = 0.01 to illustrate our calculations. To determine the sensitivity of our calculations to [PSI+] false positives, we also consider the implications of a frequency of 0.01%.
Selection against [PSI+]:
Consider a [PIN+] population that can form [PSI+]. We assume the population is fixed for [PIN+] together with any other modifiers necessary for [PSI+] formation. Fixation is consistent with the finding of Nakayashiki et al. (2005) that [PIN+] was either completely absent or strongly present for any given population.
We model discrete generations of reproduction followed by selection. We approximate the haploid life stage as instantaneous, so that a sexual generation takes no longer than an asexual one. We assume that [PSI+] loss occurs with probability during cell division when a daughter cell fails to inherit any prion aggregates. We assume de novo [PSI+] appearance occurs with probability m during cell growth in diploids. These assumptions mean that [PSI+] loss can be followed by [PSI+] gain within a single generation, but not vice versa.
Let z be the frequency of [PSI+] individuals. In each generation, yeast undergo meiosis with probability psex; otherwise they reproduce clonally. Following meiosis, yeast reproduction may involve within-tetrad fertilization with probability pauto, random mating with probability pamphi, or haplo-selfing (haploid mother–daughter mating enabled by mating-type switching) with probability phaplo. Note that . Taking into account reproductive strategy and spontaneous [PSI+] appearance and disappearance as described above, the frequency of [PSI+] after reproduction is(1)Equation 1 captures the increase in [PSI+] frequency during sex, as well as its appearance and disappearance by epimutation. Note that the rate of outcrossing psexpamphi is the most important sexual parameter in Equation 1, with the other forms of sex having more subtle quantitative effects on the effective epimutation rates.
If the relative fitness of [PSI+] individuals is (1 − sPSI+), then after selection the frequency of [PSI+] is(2)The equilibrium frequency of [PSI+] satisfies . Given an observed equilibrium frequency of [PSI+] , we estimate sPSI+ as(3)
Substituting in the estimates m = 10−7–10−5 (N. Koloteva-Levine, G. H. Merrit and M. F. Tuite, personal communication; Lund and Cox 1981; Chernoff et al. 1999), psex = 0.001, pauto = 0.94, pamphi = 0.01, and phaplo = 0.05 (Tsai et al. 2008), we find that the strength of selection against [PSI+] is significant (i.e., sPSI+Ne > 1) as long as (Figure 2). If the spontaneous rate of [PSI+] loss is larger, back epimutation alone is sufficient to keep [PSI+] at low levels, and we do not need to invoke selection against [PSI+] to explain why sex does not cause [PSI+] to rise to high frequency.
Selection against prion-forming modifiers:
We determine the effective strength of indirect selection against prf+ (sprf+) by comparing the long-term growth rates of populations fixed for one or the other allele. Assume that [psi−] individuals have R offspring on average while [PSI+] individuals have R(1 − sPSI+). In the population fixed for prf+, let Y1(t) and be the numbers of [PSI+] and [psi−] individuals, respectively, so [PSI+] is present at equilibrium frequency . In the prf0 population, [PSI+] is absent. The population dynamics of a prf+ population, given mutation, selection, and the reproductive modes described in the previous section, now follow(4)The long-term prf+ population growth rate is determined by the leading eigenvalue of (4), while the long-term growth rate of prf0 populations is R. The strength of selection against prf+ is(5a)(5b)The strength of selection against prf+ is negligible (i.e., sprf+Ne ≪ 1) for and equal to the rate of [PSI+] appearance m for (Figure 3 ), using the same parameters as before. The latter selection strength indicates that [PSI+] lineages are effectively “doomed” from the moment of their appearance.
For selection of any kind to be effective, we need sNe > 1. The disease hypothesis requires selection on [PSI+] to be effective while selection on prf+ is not. When mNe > 1, the small shaded region in Figure 4 indicates values of m and where the conditions for the disease hypothesis are met. Outside this narrow shaded region, either both [PSI+] and prf+ are deleterious or both are nearly neutral. Pending more precise experimental estimates of ε, m, and , the condition seems unlikely to be satisfied. This implies that if mNe > 1, then both [PSI+] and prf+ are likely deleterious.
Our analysis does, however, support the disease hypothesis if mNe < 1. Ne is currently estimated as ≈3 × 106–6 × 106 in the wild (see calculation in the Introduction) and m as 10−7–10−5 in the lab (N. Koloteva-Levine, G. H. Merrit and M. F. Tuite, personal communication; Lund and Cox 1981; Chernoff et al. 1999; H. L. True, personal communication). This yields mNe ≈ 0.3–60, a range that is not sufficiently precise either to accept or to reject the disease hypothesis. Note, however, that conversion assays may return only a subset of particularly strong and stable [PSI+] colonies (H. L. True, personal communication), suggesting that the true value of m may be higher: if this result is borne out, the disease hypothesis could be rejected in favor of relatively weak but still appreciable selection against prf+. On the other hand, previous conversion assays have not accounted for the possibility that multiple colonies may arise from the same conversion event: such a correction can be made by using a fluctuation test based on fitting a Luria–Delbrück distribution and may lead to a lower estimate of m. Accurate measurement of m at the lower end of the current parameter range would support the disease hypothesis, in which indirect selection is too weak to eliminate the ability to form the generally deleterious [PSI+] prion.
Our calculations imply that [PSI+] is usually deleterious if , and we infer that effective selection also extends to modifiers of [PSI+] if both and mNe > 1. Spontaneous conversion from [psi−] to [PSI+] has been estimated in lab strains to have a rate of ∼10−7–10−5 (N. Koloteva-Levine, G. H. Merrit and M. F. Tuite, personal communication; Lund and Cox 1981; Chernoff et al. 1999) and a reverse rate < 2 × 10−4 (Tank et al. 2007). Pending more precise measurements, it seems likely that the condition < m/(10ε) is easily met. This argument is even stronger if not all the Sup35 aggregates observed by Nakayashiki et al. (2005) correspond to [PSI+] and ε is therefore even <0.01. If mNe > 1, we can therefore infer that selection against both [PSI+] and its modifiers is effective. If instead mNe < 1, then this would support the disease hypothesis in which indirect selection is too weak to eliminate a propensity to form the generally deleterious element [PSI+].
Improved measurement of the parameters, particularly the product mNe, is critical to understanding selective forces on [PSI+]. Inference ultimately depends on the range of parameters in effect over long periods of yeast evolution, so extrapolation of population genetic measurements of Ne and of sexual frequencies in S. paradoxus to cover the history of a clade of closely related species is not unreasonable. However, it is hard to rule out the important possibility that lab strains have substantially different epimutation rates m and m′ than wild species, especially when those lab strains have been extensively used to study [PSI+]. Our population genetic model is very general in its treatment of well-characterized yeast and [PSI+] biology. Correct inference from the model ultimately depends on accurate parameter estimates.
Note that the rate of [PSI+] appearance increases in response to stress (Tyedmers et al. 2008). Negative selection against [PSI+]-forming ability, as calculated here, depends largely on the value of mNe under normal conditions, while only the adaptive potential of [PSI+]-forming ability increases with m under stress.
If it turns out that mNe > 1, and both [PSI+] and prf+ are therefore inferred to be significantly deleterious under most conditions, then something else must be acting to maintain prion-forming ability over long periods of yeast evolution. Insurmountable pleiotropic constraint for each of the many possible modifiers, each enduring over long periods of evolutionary time, seems an unlikely explanation. Indeed, the data directly show that prion-forming ability can be dispensable in wild populations on short evolutionary timescales (Resende et al. 2003). Instead of multiple insurmountable constraints at each possible modifier, [PSI+] itself could have a single, mechanistic inseparable adaptive pleiotropic function that counters its other deleterious effects. With this view, long periods of relatively weak selection against [PSI+] and its modifiers would be balanced by short, intense periods of positive selection for them (Masel and Bergman 2003; King and Masel 2007; Masel et al. 2007). During the long periods of selection against [PSI+], the rarity of outbreeding, combined with weak negative selection, explains why meiosis does not drive [PSI+] to high frequency. [PSI+] is predicted to occur at high frequency during occasional episodes of [PSI+]-mediated adaptation. These episodes are likely to be both rare and brief, however, and so theoretical considerations suggest that it is not surprising that none were seen in a sample of 70 natural populations (Masel et al. 2007).
Note that while improved measurements showing that mNe > 1 would support a rare adaptive role for [PSI+], a finding that mNe < 1 would not rule adaptation out. Indeed, it should be easier for an adaptive modifier allele prf+ to evolve when only negligible selection acts against it at other times. The appearances of [PSI+] as a disease at some times and as an adaptation at others are not mutually exclusive.
We thank Heather True and the anonymous reviewers for helpful comments on the manuscript. This work was supported by the BIO5 Institute at the University of Arizona and by National Institutes of Health grant R01 GM076041. J.M. is a Pew Scholar in the Biomedical Sciences and an Alfred P. Sloan Research Fellow.
↵2 Present address: Department of Integrative Biology, University of Guelph, Guelph, ON N1G 2W1, Canada.
Communicating editor: M. W. Feldman
- Received December 30, 2008.
- Accepted January 10, 2009.
- Copyright © 2009 by the Genetics Society of America