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Genetics, Vol. 178, 1571-1578, March 2008, Copyright © 2008
doi:10.1534/genetics.107.080853
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Department of Biology, University of Utah, Salt Lake City, Utah 84112
1 Address for correspondence: Department of Biology, University of Utah, 257 South 1400 East, Salt Lake City, UT 84112.
E-mail: joebiohorn{at}msn.com
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ABSTRACT |
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 TOP ABSTRACT MATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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4800 generations in 48 lines of yeast protected from effective selection by frequent passage through single-cell bottlenecks. Changes in fitness were evaluated by direct competition with matched parental stocks differing only at a selectively neutral marker locus. Average fitness declined by 5% over the course of the experiment. The rate of change increased sharply in later generations, strongly suggesting synergistic epistasis. Divergence among lines increased rapidly relative to the change in average fitness and also at an accelerating pace. Both results are well matched by a model assuming that fitness cost increases exponentially (approximately second order) with the number of accumulated mutations. This result is consistent with fitness loss due primarily to interactions between specific pairs of gene products. I also estimate that 25% of the mutations with detectable fitness effects were beneficial. This result can be explained by the fact that the effects of most mutations are small relative to the distance from a local fitness optimum.
Assessment of fitness effects in lines that have accumulated multiple spontaneous mutations is time and labor intensive but is the most direct approach (MUKAI 1969). Alternative hypotheses lead to straightforward testable predictions (KOUYOS et al. 2007). Independent action, the most useful null hypothesis, should produce multiplicative effects in combination. For multiple mutations with small effects that have not been measured individually, a plot of log fitness against the number of mutations (or the time of accumulation) should yield a straight line. Deviations from linearity indicate epistatic interaction and provide information about the nature of those interactions; negative curvature indicates synergistic epistasis while positive curvature reveals antagonistic or "diminishing returns" interactions. I report here the results of a mutation accumulation experiment with yeast using sensitive competition experiments (THATCHER et al. 1998) to directly measure realized fitness relative to a marked standard in a defined environment.
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MATERIALS AND METHODS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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1, ura3-52, MAT
). Random insertions into FY10 of LacZ in a construct that also carried LEU2 as a selectable marker were recovered and tested for fitness effects in previous experiments (THATCHER et al. 1998). Preliminary experiments showed that leu2 was not selectively neutral even in rich medium, so leu2 in FY10 was repaired by homologous recombination to produce FY10(LEU+). For these experiments I chose one of the LacZ insertions (TD50) that, within the sensitivity of our methods, is selectively neutral in comparison to FY10(LEU+). Lines A, C, and E were derived from FY10(LEU+) while B, D, and F are from TD50 (carrying the LacZ marker used to score competition experiments). A and B were converted to MATa (HERSKOWITZ and JENSEN 1991), C and D are MAT, and E and F are diploids homozygous at all loci other than MAT, produced by mating A to C and B to D, respectively. The manipulations at the MAT locus were intended to facilitate future genetic analyses of the MA lines and are not directly relevant to this experiment. In competition experiments to measure fitness, the parental A line serves as a competitor for all B accumulation lines while the B parent serves reciprocally for the A lines. Similarly, C pairs with D and E with F. Reference stocks of the parental lines were stored frozen and periodic control experiments confirmed that the matched parents continue to be selectively neutral with respect to each other. Thus, each fitness determination is, in essence, a direct comparison to zero time fitness.
Mutation accumulation:
The 48 MA lines were passed through single-cell bottlenecks on a 3- to 4-day cycle for 200 cycles. Each cycle was initiated by picking a random colony of each line and streaking on rich medium (YPD). Random selection was assured by overlaying each plate on a template with a marked target and selecting the colony closest to that target. Each cycle represents 24 generations (growing to a colony of 2 x 107 cells). Because the single-cell bottlenecks predominate, the effective population size is 10 (HARTL and CLARK 1997). Thus, deleterious mutations with a fitness effect < 10% should be "invisible" to selection and accumulate at a rate that simply reflects mutation rates. Conversely, beneficial mutations of similar magnitude will not be favored by selection.
Preliminary experiments showed that petite mutations, almost all defective in the mitochondrial genome, are fixed in 5% of the lines in each cycle. These have relatively large fitness effects that would mask the mutations of small effect that I wanted to study, so I eliminated petites as follows: In addition to streaking on YPD, each selected colony was patched to medium with glycerol as the major carbon source (YPG), on which petites do not grow. When the next cycle was initiated, the YPG patch plate was inspected to identify petites, and the corresponding streaks were discarded. To maintain those lines, I returned to the plates from the previous cycle (stored refrigerated for that purpose) and selected a new random colony. The appearance of petites was a minor annoyance, but provides direct confirmation that the bottlenecking procedure was working as expected to allow fixation even of mutations with rather significant deleterious effects. All stocks also were checked regularly for LacZ and MAT phenotypes, and the rare deviations (mostly loss of LacZ in B and D lines and switching of diploids to MATa or MAT) were corrected by returning to the most recent available refrigerated or frozen sample with the correct phenotype. The combination of eliminating petites and, to a lesser extent, other phenotypic deviations means that actual elapsed generations is, on average, 6% less than the nominal value.
Fitness measurements:
My method for determining relative fitness is slightly modified from that previously described (THATCHER et al. 1998). Briefly, an overnight culture of each MA line was mixed 1:1 with a similar culture of the matched parent differing at the LacZ marker and then immediately diluted 1:256 into fresh medium. Overnight cultures go to saturation, so the relative frequencies of the two genotypes in the initial mixture is close to 1:1. The mixed cultures were maintained at 30° in 1 ml of rich medium (YPD) in 16- x 100-mm tubes angled at 25° from the horizontal and rotated at 40 rpm. They were back diluted 1:256 daily. Under these conditions, cultures return to saturation each day, completing eight generations per dilution cycle. Appropriately diluted samples were plated periodically and scored for frequency of LacZ colonies. A selection coefficient is estimated from the slope of a natural log plot of the ratio of the two colony types as a function of generations of competition (LENSKI 1991). This procedure detects fitness differences as small as 0.5% (see RESULTS).
LacZ detection:
Yeast colonies positive for LacZ do not stain readily on X-gal plates so the following procedure was adopted. Test plates contained 100 mg/liter of X-gal in YPD with 2% agar. Samples from the competition cultures were plated at a dilution calculated to give a few hundred colonies per plate and incubated at 30° for 3 days to give easily visible colonies. Plates were then exposed to chloroform vapor for 30 min and incubated at 37° to develop the blue color. The chloroform kills enough of the cells to release easily detected amounts of β-galactosidase. Blue and white colonies were hand counted.
Adaptation lines:
To estimate the fitness of the parental lines relative to a local fitness optimum, a series of 24 lines (4 each from parents A–F) was allowed to adapt for 160 cycles (1280 generations) to the conditions used for the competition experiments. Effective population sizes were very large, allowing effective selection. Improvements in fitness were then estimated from standard competition experiments in comparison to the matched frozen parental line. The average improvement across all lines was 8% and the maximum was 12%.
An exponential model of synergistic interactions:
Results of the accumulation experiments are evaluated in comparison to a simple model that assumes a linear increase in the average number of mutations, a Poisson distribution of mutation frequency, and a fitness cost that is an exponential function of the number of mutations. The following five-step algorithm was executed in a standard spreadsheet program.
Once templates for all steps were generated, a series of trials with different values of input variables explored the response across a plausible parameter space. Thus, two variables are considered (genomewide mutation rate and the exponent assigned to fitness costs) and it is the shapes of the curves that are of interest.
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RESULTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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0.1). At cycles 130 and 200, the corresponding values are 0.981 ± 0.00045 and 0.948 ± 0.00093, both highly significant (P < 0.01 and P < 0.0005, respectively). Even by cycle 45 there was a 100-fold increase in the variance relative to zero time controls (a change in the standard deviation 3.7 times the change in the mean), suggesting that there have been real changes but offsetting gains and losses. This is relevant to the evidence for frequent beneficial mutations discussed below. I also evaluated separately the haploid and diploid lines. Surprisingly, the quantitative differences are modest and not significant. For example, at cycle 200, the haploid and diploid means are 0.941 ± 0.0011 and 0.962 ± 0.0017 and the difference is not significant (P 0.5). It is of interest in this context that many of the initially haploid lines apparently accumulate duplications to approach a diploid chromosome number (M. LYNCH, personal communication). This change probably is not driven by immediate selective advantage since standard competition experiments with parental haploids against matched diploids (A or C against F and B or D against E) reveal no significant differences. In any case, the qualitative trends (negative curvature of a log mean fitness plot and accelerating increase in the variance) that are the focus of the following analysis are the same for nominally haploid and diploid lines, so all are treated together.
Comparisons to an exponential model:
Changes in log mean fitness and in the fitness variance are summarized in Figure 2 in comparison to results of the exponential model of fitness costs described above. The parameter space evaluated in the model covers U over a 30-fold range from 0.00037 through 0.011 and cost exponents from 1 through 4. The range of mutation rates was based on several reasonably careful of estimates of U in yeast (DRAKE 1991; WLOCH et al. 2001b; ZEYL and DEVISSER 2001), ranging from 0.00024 to 0.0031. Perhaps the most direct determination is by WLOCH et al. (2001b) who scored phenotypes segregating in a large number of tetrads. Their estimate is 0.0011. That is almost certainly low for my purposes, perhaps substantially so, since only mutations with detectable phenotypes were counted. Cryptic mutations that could have significant synergistic effects may be much more common than mutations with detectable effects (DAVIES et al. 1999). Thus, I took the above estimates as defining the low end of the range that should be evaluated and went as high as 10-fold above the value given by WLOCH et al. (2001b).
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Beneficial mutations:
It is generally believed that the vast majority of new mutations are deleterious, so I examined the frequency and significance of the apparent improvements seen in Figure 1 in more detail. I assume that the tight clustering of the zero time controls (parent vs. parent competitions) is an indication of the precision and reproducibility of the fitness assays. It seems reasonable that variation among such replicates approximates a normal distribution (even if the effects of mutations do not) and it is experimental error that is at issue in identifying "real" changes, so I use the standard deviation of the control experiments (±0.0024) as the point of reference for estimating the probability that a given change is significant. In the context of estimating the fraction of changes that are improvements, it is not entirely clear whether one should worry more about rejecting real changes (e.g., with stringent criteria that incorporate correction for multiple comparisons) or accepting spurious ones. Fortunately, the results in this case are not very sensitive to the chosen criterion. At P < 0.05 (with no correction for multiple comparisons), we "accept" 65 changes throughout the experiment, 16 of which (24.6%) are improvements. Similarly at P < 0.01, 14 of 57 changes (24.6%) are improvements, as are 11 of 48 (22.9%) at P < 0.001 and 10 of 45 (22.2%) at P < 0.00035. The last threshold corresponds to the Bonferroni correction for P < 0.05 for 144 comparisons (48 lines over three intervals). The largest positive changes are 2% by cycle 45 and 4% for later comparisons, well below the level at which selection should be effective (10%), so I conclude that almost a quarter of the significant fitness changes fixed by drift were improvements.
Independence of late fitness changes:
One other feature of the line histories is less evident by inspection; early fitness loss does not predispose to increased fitness loss in later accumulation cycles. Kendall's rank correlation coefficient was used to test for correlation between fitness at each intermediate cycle and the change in fitness over each subsequent interval. None of three comparisons (w45:w45
130, w45:w45200 and w130:w130200) was significant (P > 0.2 in all cases), and the tendency in the second comparison was even of reversed sign. A standard correlation analysis of the quantitative data gives substantially similar results. One comparison (w45::w45130) has a correlation coefficient of 0.6, which is significant, given the large number of data points. However, that result depends entirely on one data point (stock D1, which had the largest loss by cycle 45). With that line dropped from the analysis, the magnitude of the correlation is no longer significant and the sign is reversed. Thus, in general, present fitness is a poor predictor of vulnerability to subsequent fitness loss. One explanation, examined below, is that cumulative fitness is affected by specific interactions that have little to do with the independent fitness effects of individual mutations.
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DISCUSSION |
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What interactions between pairs of gene products are relevant? Mutations in a single pathway might interact (RICE 1998), but according to metabolic control theory (KACSER and BURNS 1981; SZATHMARY 1993) these effects should be antagonistic. Synergistic interactions seem more likely for molecules that make contact with and recognize specific partners. At least 50% of yeast proteins seem to be members of direct-interaction networks (HO et al. 2002; GAVIN et al. 2006). Examples include components of the same molecular complex, cis- and trans-acting factors involved in regulation of the same gene, and partners in a signal transduction event. Proteins in large complexes may interact with multiple partners (KIM et al. 2006) but typically do so through different surfaces or in a mutually exclusive way (hence, still pairwise). In all of these cases, alterations in one component alone may have little effect but may be incompatible with specific alterations in a partner. Second-site noncomplementation, used in genetic screens to identify interaction partners, depends on just such specific incompatibilities. (STEARNS and BOTSTEIN 1988; HAWLEY and WALKER 2003; KOMILI and ROTH 2007).
Mechanisms that enhance robustness in gene networks, whether evolved under stabilizing selection (WAGNER 2000) or emerging as intrinsic properties of complex networks (SIEGAL and BERGMAN 2002), also involve pairwise interactions. Of two principal mechanisms identified by WAGNER (2000), interactions between genes of unrelated function seem more prevalent than duplicate or overlapping functions, but either seems compatible with mutations in specific pairs of sites being more deleterious than single hits. Also, the lack of correlation between early and late fitness changes is entirely consistent with specific pairwise interactions since the effect of a given mutation is contingent on others present in the same background.
Results of a few other MA experiments also suggest synergistic interactions (MUKAI 1969; FRY 2004; AVILA et al. 2006). In the most recent of those, new Drosophila MA lines were established from end-products of an earlier experiment; declines in viability were substantially accelerated relative to that previous experiment. The authors interpret that result in terms of an elevated mutation rate in the later accumulation cycles. That is certainly a formal possibility (also for my data), but synergistic interaction seems a more parsimonious explanation; the mutation rate hypothesis requires that many lines independently acquire mutators.
Other studies have failed to detect synergistic epistatsis or have reported variable results (KOUYOS et al. 2007). However, the designs of many experiments are not well suited to detection of specific pairwise interactions. For example, combining a limited number of known mutations (DE VISSER et al. 1997; ELENA and LENSKI 1997; WHITLOCK and BOURGUET 2000; SZAFRANIEC et al. 2003; SANJUAN and ELENA 2006) should reveal epistasis only sporadically (when appropriate pairs happen to be included). In addition, knockout mutations may not be suitable since there is no opportunity for interaction with a partner (YOOK et al. 2001). In fact, knockouts of two essential components in the same complex might show antagonistic epistasis since either alone could inactivate the complex. Some studies have used insertional mutations that are likely to block the formation of any functional gene product (ELENA and LENSKI 1997, 2001). Others have used a mutator to accelerate the process in MA experients (WLOCH et al. 2001A), but those mutators are known to produce a large proportion of frameshifts that, again, most often will be knockouts (KORONA 1999).
Beneficial mutations and "Fisher's microscope":
It is widely believed that the vast majority of new mutations are harmful (CHARLESWORTH and CHARLESWORTH 1998; KEIGHTLEY and LYNCH 2003). However, the available data compel only the conclusion that the average effect is deleterious (SHAW et al. 2003), and beneficial mutations have been reported to be a significant fraction of total detected mutations in a few MA studies broadly similar to this one. For example, the beneficial fraction is 0.05 in another study with yeast (JOSEPH and HALL 2004) and almost half in Arabidopsis (SHAW et al. 2000). Other studies have detected small spontaneous improvements or an increase in variance without significant decrease in the mean without explicitly analyzing those features (KEIGHTLEY and CABALLERO 1997; ZEYL and DEVISSER 2001). Interestingly, selection experiments with Escherichia coli detect beneficial mutations of small effect at an elevated frequency when effective population sizes are small (PERFEITO et al. 2007). At Ne = 2 x 104, 10% of mutations with detectable fitness effects were beneficial (1000-fold higher than obtained with Ne = 107), and the mean selection coefficient was only 0.013.
R. A. Fisher famously used a microscope analogy to argue that adaptation depends primarily on mutations of small effect (FISHER 1930). Central to his argument was the expectation that the probability of improvement increases as the magnitude of the effect decreases, approaching 50% as a limit. It follows that if most mutations have very small effects (THATCHER et al. 1998), almost half of all mutations will be improvements. How small must the effects be to see frequent improvement? The key is magnitude relative to distance (in phenotypic space) from a nearby optimum (ORR 2001). For variation in one dimension, Fisher's geometrical model gives the frequency of beneficial mutations as 
where r is the magnitude of the change and d is the distance from an optimum. Mutations affect phenotypes in a multidimensional space, but measuring distance from a local fitness optimum in a defined environment essentially collapses all of those effects to one dimension. When allowed to adapt at large effective population sizes to the exact conditions of the fitness assays (the defined environment), the lines used in this experiment improved in fitness by an avareage of 0.08 and by a maximum of 0.12. The latter value presumably represents a better estimate of the distance from a local optimum. The average selection coefficient for 65 significant changes (P < 0.05) observed in my accumulation lines is 0.055. If we use d = 0.012 and r = 0.0055 in Fisher's expression, the expected frequency of improvements is 0.27—in remarkable agreement with the 0.22–0.25 actually observed.
There have, of course, been refinements and alternatives to Fisher's model in the intervening years (WAXMAN and WELCH 2005; MARTIN and LENORMAND 2006; ORR 2006), but these do not fundamentally challenge the expectation that very small changes have a reasonable chance of being improvements. The present results provide empirical support for that insight. Direct physical interactions between specific partners, as suggested for synergistic fitness loss, also may be relevant to stochastic improvements; second-site suppression of a mutant phenotype is another well-known phenomenon used in genetic screens to identify interaction partners (HAWLEY and WALKER 2003). It is to be expected that the frequency of spontaneous improvement will vary from experiment to experiment since that frequency should depend on how far the starting stocks were from an optimum for the conditions used to measure fitness. Indeed, this leads to a testable prediction; stochastic improvements should largely disappear if strains are adapted to the test environment for many generations at large effective population sizes prior to use in MA experiments.
So the idea that most mutations are harmful might more correctly be applied to the relatively small class of mutations with fitness effects large enough to be detected by conventional methods. And there is no fundamental conflict between the finding that beneficial mutations are relatively common in specific MA experiments and molecular evidence, suggesting that most nonsynonomous mutations are eliminated by purifying selection. The former result relates to specific stocks that may, by chance, sit some distance from the optimum for the chosen experimental conditions; the latter presumably integrates results over the fluctuating environments experienced by natural populations. The present results nevertheless are relevant to natural populations; they suggest that a population displaced from an adaptive optimum or shifting to a new one will not have long to wait for mutations that are beneficial in the new environment. This fits nicely with recent evidence for frequent adaptive substitutions in both coding and noncoding DNA sequences (SMITH and EYRE-WALKER 2002; ANDOLFATTO 2005).
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ACKNOWLEDGEMENTS |
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TOPABSTRACTMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSLITERATURE CITED |
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LITERATURE CITED |
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