Razib Khan One-stop-shopping for all of my content

January 13, 2011

More bad mutations = greater fitness

ResearchBlogging.orgDoes the chart above strike you as strange? What it shows is that the mean fitness of a population drops as you increase the rate of deleterious mutation (many more mutations are deleterious than favorable)…but at some point the fitness of the population bounces back, despite (or perhaps because of?) the deleterious mutations! This would seem, to me, an illustration of bizzaro-world evolution. Worse is better! More is less! Deleterious is favorable? By definition deleterious isn’t favorable, so one would have to back up and check one’s premises.

And yet this seems just what a new paper in PLoS ONE is reporting. Purging Deleterious Mutations under Self Fertilization: Paradoxical Recovery in Fitness with Increasing Mutation Rate in Caenorhabditis elegans:

Compensatory mutations can be more frequent under high mutation rates and may alleviate a portion of the fitness lost due to the accumulation of deleterious mutations through epistatic interactions with deleterious mutations. The prolonged maintenance of tightly linked compensatory and deleterious mutations facilitated by self-fertilization may be responsible for the fitness increase as linkage disequilibrium between the compensatory and deleterious mutations preserves their epistatic interaction.

Got that? OK, you probably need some background first….

The authors used C. elgans as a model organism. This “worm” is ubiquitous in biology. There’s an enormous community of developmental biologists, geneticists, and neuroscientists, who work with elegans as a model organism. For the purposes of evolutionary genetics you need to know a few things about elegans though. The vast majority of reproduction of elegans occurs through “selfing.” That is, most elegans are hermaphrodites who fertilize themselves. They’re obviously not asexual, but their habits are straight out of South Park. A small minority of reproductive events among elegans are sexual in a conventional manner, because a few of the worms in any given generation are males. For the purposes of this experiment you need to ignore this aspect; they’re focusing on the selfing. To do this they removed males out of the equation, either by introducing a male killing mutation, xol-1, or, manually removing them.

So now we have just the selfers. If you pick up a standard pop gen text, e.g. Principles of Population Genetics, you’ll find out that selfers tend to have some peculiar and interesting properties when it comes to the long term arc of evolutionary genetics. In particular, they “purge” “genetic load” like crazy. What this means is that deleterious alleles get removed from selfing populations very fast through negative selection. Why? How?

Let’s go back to genetics 101. Imagine a locus where an individual is a heterozygote, and carries an allele which is “wild type” and another which is deleterious, and recessively expressed. Cystic fibrosis is a recessive disease that is common among Europeans. 1 out of 25 Europeans is a heterozygote, and there is a 1 out of 25 chance that these individuals will mate with someone who is also a carrier. Out of these pairings, 50% of the offspring will also be carriers, 25% will be wild type homozygotes, and 25% will express the cystic fibrosis disease because they’re homozygotes for the deleterious allele. With the numbers given that means 1 out of 2,500 births will result in a child with cystic fibrosis.

Cystic fibrosis is a lethal disease which sharply reduces fitness (many individuals are just infertile). This is negative selection against the deleterious allele. But, the selection is relatively weak. Why? Take a look at the ratio between those who carry the allele, but have normal fitness, and those who carry two copies and have reduced fitness. It’s 100 to 1. Most copies of the deleterious allele are “masked” from any negative fitness consequences because they’re paired up with a normal wild type which complements and compensates the function of the mutant variant. This is one reason why we carry so many deleterious alleles; they’re often paired up with a “good” copy which prevents the fitness of the individual from cratering.

Now let’s bring this back to selfing. In a human population we pair up with others. So you have to multiply independent probabilities, 1/25 × 1/25, to produce a Punnett square where two heterozygotes are crossed. In a scenario of selfing the probabilities are different. There’s perfect assorting of genotype to genotype for selfers, because the genotypes are simply being crossed with themselves. If you’re a fertile hermaphrodite who carries the mutant cystic fibrosis allele there’s a 25% chance that you’re offspring will be homozygotes for cystic fibrosis, because you know that the cross will be with another heterozygote (yourself). Now imagine that the whole population consists of selfers. Instead of 1 out of 100 copies being exposed to selection, 1 out of 2 copies are exposed to selection! This is how selfers purge genetic load so well. When selection only operates on homozygotes, their tendency to produce homozygotes means that deleterious alleles are far more exposed to selection. Why do selfing populations in the aggregate produce so many homozygotes? Heterozygotes mating with heterozygotes produce both heterozygotes and homozygotes. Homozygotes mating with homozygotes produce only homozygotes. The “toy” chart I’ve put together shows what happens when you take a uniform population of heterozygote selfers in generation 1, and allow them to reproduce down the generations. Each generation the proportion of heterozygotes, those individuals where deleterious alleles are masked and so protected from the purging power of natural selection, decreases. Selection becomes more and more efficacious in purging genetic load from the population.

There are still two other concepts important to understanding the implications of this paper. Epistasis and genetic linkage. But let’s move on to some results first, and then digest them with a further helping of conceptual condiments. Here’s figures 3 & 4, which I’ve reedited a bit. On the left you see fitness (fecundity) as a function of the concentration of mutagen. In other words, as you move up the mutagen concentration on the x-axis the mutation rates are increasing. On the right you see a plot which shows the mean fitness after x # of generations, which each set of data points represent differing concentrations of the mutation. I’ve highlighted the lines with no mutagen, and maximal mutagen.

The bizarro aspect is the jump between 80 mM and 100 mM. As mutation rates increase there is a bounce back of fitness. Imagine that you were rolling a boulder up an incline which got progressively steeper in its grade. Common sense and basic physics would tell you that you’d have to use more and more force to move the boulder the same distance. Now imagine that beyond a certain grade of steepness you actually had to use less force! That would make no sense. In some ways that’s what’s going on here. But then, evolutionary processes may not be so linear and predictable as Newtonian mechanics.

Of course there could be some straightforward reasons for this strange behavior. For example, the xol-1 mutant which produced maleless populations may have had pleiotropic effects. To test for this they manually removed males from a population without the mutation, and obtained similar results. Additionally, they also took a divergent elegans line with the xol-1 mutant and performed the same experiments, and again the same pattern recapitulated itself. Finally, there’s always the possibility that resistance to the mutagen had developed above a certain concentration. If resistance to the mutagen had developed presumably taking the population which had exhibited the increased fitness ~100 mM, and placing it back into lower concentration environments, would produce a different response curve than we saw before. That is not what occurred, as you can see in figure 6.

Now that we have the core results under our belt, let’s move on to trying to make sense of how water can flow uphill like this. So back to the concepts, genetic linkage, and epistasis. The first is easy. Genes are arrayed along physical DNA strands. The closer the physical position of the genes, the more likely they are inherited together in a straightforward fashion. The kink in the expectation is recombination. In diploid organisms you have two copies of each gene on the two strands. Recombination can shuffle specific gene copies from one strand to the other (or, more accurately, break and recombine strands in a fashion so that both differ from the state before the event). The further the distance between any two gene copies on a physical strand, the greater the likelihood for recombination to separate the two. When two copies are very close there’s only a small physical distance across which recombination might operate to separate them. Therefore, the closer the copies the more “linked” the genes are.

Before explaining why this matters, let’s talk about epistasis. Epistasis can be thought of generally as gene-gene interaction. In the mechanistic molecular sense you’re referring to biophysical processes whereby one gene has some interaction with another gene. But there’s another way to think about: fitness or trait value. In this sense epistasis as gene-gene interaction introduces non-linearities into the mapping of genotype to phenotype, as well as genotype to fitness. This is what matters for the purposes of this paper. In particular, epistasis manifesting as compensatory deleterious mutations.

So how does this matters for selfers? Recall that above we were talking about how selfers purge deleterious genetic load by cranking up the proportion of homozygotes exposed to negative selection. Implicitly our model was single locus. We were looking at one gene, and one mutant. But how about if you had a large number of mutants? Can selfers produce all those homozygotes simultaneously, and so purge the load efficiently? Purging load through natural selection entails reduced fitness for many members of a population; purge too much and the population crashes and you’re liable to just go extinct through mutational meltdown. This where linkage and recombination come back to the fore. Recombination is often thought of as a way to create new genetic combinations. But in homozygous selfing lineages recombination doesn’t live up to that promise: there’s not enough heterozygosity within the genomes of these organisms so that the shuffling of the strands across each other produces anything new! Selfing lineages exhibit very strong linkage between sequences of genetic variants across loci because of the inability of recombination to break apart associations. So, if you have two genes, A and B, which are linked, and A is very fit and B is moderately unfit, if they are co-inherited B may sweep up to fixation with A. As you crank up mutation rates then the theory predicts that deleterious alleles will simply swamp out the ability of selfing lineages to purge the load fast enough to prevent ultimate extinction. Even if the genetic background wasn’t homozygous, too many mutations within the genome would be swapping out deleterious copies for other deleterious copies during recombination.

That theory was born out more or less at concentrations of the mutagen below 100 mM. But then expectation was confounded. Why? This is where epistasis steps into the picture. In the previous model we implicitly assumed an additive model. Imagine the fitness of allele 1 at gene A ~ 3 and the fitness of allele 2 and gene B ~ -2. Summing them together ~1. And so on. Epistasis confuses this simple picture because it implies non-linear computations. The fitness value of A and B may be conditional on the state of a third gene, C. In any case, a compensatory mutation is one where more deleterious is in fact less deleterious. Precisely, having two deleterious mutations may actually have less of a fitness hit than having one deleterious mutation! In some ways this becomes a matter of semantics and analytic philosophy. -10 + – 10 > – 10 is just incoherent.

Since this is not a philosophy blog, how does this relate to selfing lineages? It goes back to linkage. Recall that tight linkage may produce situations where recombination can not break apart unhealthy associations where favorable variants are linked with unfavorable ones, and the latter may hitchhike with the former in selective sweeps (in populations with more heterozygosity recombination would increase the range of combinations across which selection operated; see Muller’s ratchet). This is the bad. But in the case of compensatory mutations the inability of recombination to break apart associations may be a positive. These epistatic interactions are contingent on robust combinations persisting. Recombination would break apart those combinations, preventing the fitness gains from persisting across generations. But in these selfing linages the homogenized genetic backgrounds are relatively fixed palettes against which these mysterious genetic interactions which turn expectations upside down can perform their magic.

This paper had some moderately weird results. The response to mutagen concentration increases seemed robust within their set of experiments, but who knows how general this phenomenon is? A reliance on compensatory mutation also strikes me as only less weird because the results were so weird. In the last paragraph the authors seem to acknowledge the general strangeness at work:

Regardless of the mechanism driving the fitness increase exhibited by populations exposed to 100 mM EMS, the result is a testament to the resiliency of the genome. Consistent exposure to high mutation rates should wreak havoc on the genome, and repeated exposure to 80 mM EMS (Figure 5) appears to do just that. However, the genome is able to recover a large proportion of the fitness lost at 80 mM EMS when exposed to 100 mM EMS (Figure 3). This result is quite surprising and challenges the long-held beliefs concerning the relationship between mutation rates and fitness.

The long-held belief presumably being that high mutation rates are correlated with decreased mean fitness, and ultimately likely extinction. A great deal of post-apocalyptic fiction from the Cold War period was predicated on just this assumption. And clearly in most cases this seems to be a warranted axiom. On the other hand, sometimes in biology the minor exceptions are more important in explaining the patterns of diversity we see around us. If there was a veil of ignorance over us and we had to predict the nature of replicating organisms on this planet would we predict the incredible diversity we see all around us? Would we predict intelligent life? I suspect that there would be the preference for a simple and elegant model where life on earth was optimized toward extremely simple and highly robust rapid replicators. Prokaryotes. And to a first approximation that logical inference based on Darwinian assumptions would be correct. Prokaryotes are omnipresent. In fact, some estimate that there are 10 times as many bacterial cells within a human body as human cells. But obviously there are creatures on the Earth besides prokaryotes. And we care a great deal about this “residual” from the expected trend line….

Citation: Morran LT, Ohdera AH, & Phillips PC (2010). Purging Deleterious Mutations under Self Fertilization: Paradoxical Recovery in Fitness with Increasing Mutation Rate in Caenorhabditis elegans. PloS one, 5 (12) PMID: 21217820

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