Thursday, July 05, 2007

Mutation Rates

Each of us was born with at least 350 new mutations that make our DNA different from that of our parents.

Douglas Futuyma (2005) p. 162
Let’s think about the number of mutations that could accumulate in a population over time. A few pages ago we looked at the origin of antibiotic resistance in bacteria in order to prove that mutations occur randomly. Now we’ll consider just how frequency those mutations could arise in bacteria. Then we’ll ask how frequently mutations occur in humans.

Our model bacterium is Esherichia coli the common, and mostly benign, intestinal bacterium. The entire genome was sequenced in 1997 (Blattner et al., 1997) and its size is 4,200,000 base pairs (4.2 × 106 bp). Every time a bacterium divides this amount of DNA has to be replicated; that’s 8,400,000 nucleotides (8.4 × 106).

The most common source of mutation is due to mistakes made during DNA replication when an incorrect nucleotide is incorporated into newly synthesized DNA. The mutation rate due to errors made by the DNA polymerase III replisome is one error for every one hundred million bases (nucleotides) that are incorporated into DNA. This is an error rate of 1/100,000,000, commonly written as 10-8 in exponential notation. Technically, these aren't mutations; they count as DNA damage until the problem with mismatched bases in the double-stranded DNA has been resolved. The DNA repair mechanism fixes 99% of this damage but 1% escapes repair and becomes a mutation. The error rate of repair is 10-2 so the overall error rate during DNA replication is 10-10 nucleotides per replication (10-8 × 10-2) (Tago et al., 2005).

Since the overall mutation rate is lower than the size of the E. coli genome, on average there won’t be any mistakes made when the cell divides into two daughter cells. That is, the DNA will usually be replicated error free.

However, one error will occur for every 10 billion nucleotides (10-10) that are incorporated into DNA. This means one mutation, on average, every 1200 replications (8.4 × 106 × 1200 is about ten billion). This may not seem like much even if the average generation time of E. coli is 24 hours. It would seem to take four months for each mutation. But bacteria divide exponentially so the actual rate of mutation in a growing culture is much faster. Each cell produces two daughter cells so that after two generations there are four cells and after three generations there are eight cells. It takes only eleven generations to get 2048 cells (211 = 2048). At that point you have 2048 cells dividing and the amount of DNA that is replication in the entire population is enough to ensure at least one error every generation.

In the laboratory experiment the bacteria divided every half hour so after only a few hours the culture was accumulating mutations every time the bacteria divided. This is an unrealistic rate of growth in the real world but even if bacteria only divide every 24 hours there are still so many of them that mutations are abundant. For example, in your intestine there are billions and billions of bacteria. This means that every day these bacteria accumulate millions of mutations. That’s why there’s a great danger of developing drug resistance in a very short time.

Calculating the rate of evolution in terms of nucleotide substitutions seems to give a value so high that many of the mutations must be neutral ones.

Motoo Kimura (1968)
I based my estimate of mutation rate on what we know about the properties of the replisome and repair enzymes. Independent measures of mutation rates in bacteria are consistent with this estimate. For example, the measured value for E. coli is 5.4 × 10-10 per nucleotide per replication (Drake et al., 1998). Many of these mutations are expected to be neutral. The rate of fixation of neutral mutations is equal to the mutation rate so by measuring the accumulation of neutral mutations in various lineages of bacteria you can estimate the mutation rate provided you know the time of divergence and the generation time. (Ochman et al., 1999) have estimated that the mutation rate in bacteria is close to 10-10 assuming that bacteria divide infrequently.

The mutation rate in eukaryotes should be about the same since the properties of the DNA replication machinery are similar to those in eukaryotes. Measured values of mutation rates in yeast, Caenorhabditis elegans, Drosophila melanogaster, mouse and humans are all close to 10-10 (Drake et al., 1998).

The haploid human genome is about 3 × 109 base pairs in size. Every time this genome is replicated about 0.3 mutations, on average, will be passed on to one of the daughter cells. We are interested in knowing how many mutations are passed on to the fertilized egg (zygote) from its parents. In order to calculate this number we need to know how many DNA replications there are between the time that one parental zygote was formed and the time that the egg or sperm cell that unite to form the progeny zygote are produced.

In the case of females, this number is about 30, which means that each female egg is the product of 30 cell divisions from the time the zygote was formed (Vogel and Rathenberg, 1975). Human females have about 500 eggs. In males, the number of cell divisions leading to mature sperm in a 30 year old male is about 400 (Vogel and Motulsky, 1997). This means that about 9 mutations (0.3 × 30) accumulate in the egg and about 120 mutations (0.3 × 400) accumulate in a sperm cell. Thus, each newly formed human zygote has approximately 129 new spontaneous mutations. This value is somewhat less than the number in most textbooks where it's common to see 300-350 mutations per genome. The updated value reflects a better estimate of the overall rate of mutation during DNA replication and a better estimate of the number of cell divisions during gametogenesis.

With a population of 6 billion individuals on the planet, there will be 120 × 6 × 109 = 7.2 × 1011 new mutations in the population every generation. This means that every single nucleotide in our genome will be mutated in the human population every 20 years or so.



Blattner,F.R., Plunkett,G., Bloch,C.A., Perna,N.T., Burland,V., Riley,M., ColladoVides,J., Glasner,J.D., Rode,C.K., Mayhew,G.F., Gregor,J., Davis,N.W., Kirkpatrick,H.A., Goeden,M.A., Rose,D.J., Mau,B., and Shao,Y. (1997) The complete genome sequence of Escherichia coli K-12. Science 277:1453-1474.

Drake,J.W., Charlesworth,B., Charlesworth,D., and Crow,J.F. (1998) Rates of spontaneous mutation. Genetics 148:1667-1686.

Ochman,H., Elwyn,S., and Moran,N.A. (1999) Calibrating bacterial evolution. Proc. Natl. Acad. Sci. (USA) 96:12638-12643.

Tago,Y., Imai,M., Ihara,M., Atofuji,H., Nagata,Y., and Yamamoto,K. (2005) Escherichia coli mutator Delta polA is defective in base mismatch correction: The nature of in vivo DNA replication errors. J. Mol. Biol. 351:299-308.

Vogel,F. and Motulsky,A. (1997) Human Genetics: Problems and Approaches. (Berlin, New York: Springer-Verlag).

Vogel,F. and Rathenberg,R. (1975) Spontaneous Mutation in Man. Adv. Hum. Genet. 5:223-318.
©Laurence A. Moran (2007)

11 comments :

  1. These calculations seem reasonable for the mutation rate in zygotes, but isn't there another step between estimating the rate in the general population? I'm sure plenty of those mutations can end in premature death of the embryo, thus effectively eliminating some mutations from the population. Furthermore, mutations may not be Poisson distributed but could instead clump, giving rise to a small set of highly mutated and a large set of sparsely mutated gametes.

    Have such factors been studied?

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  2. And there are other sources of mutations in the eukaryotic germline besides recombination. For example, transcription and recombination can be mutagenic.

    The differences in cell divisions between the male and female germlines also lead to different rates of evolution on the X, Y, and autosomes.

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  3. Well done, but you might want to revise up the base mutation rate by about an order of magnitude, based on the results of this direct sequencing study, especially since you're explicitly considering neutral rates:

    Denver, DR, K Morris, M Lynch & WK Thomas. 2004. Nature 430:697-700. High mutation rate and predominance of insertions in the Caenorhabditis elegans nuclear genome.

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  4. DGS, there are many studies that confirm a base mutation rate of 10^-10 nucleotides per replication. You don't throw those out every time a new paper is published with a value that contradicts the established values.

    One of the most difficult things to understand about science is how to discriminate among papers that conflict. Most people seem to think that every single paper is given exactly the same weight in making a decision about the correct view of biology. That's why the popular version of science imagines that scientists are in a constant state of flux, changing their views from one day to the next as this week's issue of Nature arrives in the mail.

    That's not how science works. I've looked at the paper you mentioned but for now I'll file it under "interesting but probably wrong." If that pile gets too big I'll think about revising my estimate of mutation rate but for now there are far more papers filed under "interesting and probably correct."

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  5. Very nice post that I intend to use with my students in the Fall.
    Would it be possible to extend these calculations to determine how much sequence divergence should be observed between human and chimpanzee based on their estimated last common ancestor? This estimation should come close to the observed value of 99% similarity right?

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  6. I've done this calculation before. There is a paper by Crow in the first issue of Nature Reviews Genetics that lists the cell divisions.

    The tricky part is the age of the father. Depending on the father's age a zygote can have anywhere from 90-500 point mutations.

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  7. I have a question. An obvious "improvement" in improving the fidelity of stem cells would be to segregate the two daughter cells and preserve the one that had the "original" half strand. Has anyone looked to see if that happens or not?

    There was a study on DNA in the brains of individuals exposed to higher C14 from atmospheric nuclear tests, and it showed the DNA of neurons had the C14 content characteristic of childhood exposure.

    It might be very hard to see in vivo if the segregation is even slighyly imperfect.

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  8. Larry said... DGS, there are many studies that confirm a base mutation rate of 10^-10 nucleotides per replication. You don't throw those out every time a new paper is published with a value that contradicts the established values.

    One of the most difficult things to understand about science is how to discriminate among papers that conflict. Most people seem to think that every single paper is given exactly the same weight in making a decision about the correct view of biology. That's why the popular version of science imagines that scientists are in a constant state of flux, changing their views from one day to the next as this week's issue of Nature arrives in the mail.


    I'm not an idiot, Larry, and I don't think you are, either. This is not a flavor-of-the-week sort of issue. There is a fundamental difference in direct vs. indirect mutation rate estimates. There are plenty of good reasons to think that the direct mutation rate, the actual rate of appearance of mutations from one generation to the next, is going to be higher than the rate of fixed mutations, which is the rate that shows up in phylogenetically-oriented studies, or other studies that are not explicitly designed to enhance the fixation of mutations generally and do not directly observe these mutations. And while the Denver et al. paper is certainly not the last word on the subject (Brian Charlesworth's lab provided a Drosophila-oriented estimate using HPLC that is not so high) it does provide pretty good support for higher rates of direct mutation.

    I like what you did. It's just that, in my view, you're talking about an apple, and I'm talking about a bigger apple, which is much harder to measure, so most people ignore it. But I think it's at least reasonable to think of the bigger apple as the true "opportunity" created by mutation, hence the relevance of my comment within the context of your post.

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  9. DGS says,

    I'm not an idiot, Larry, and I don't think you are, either. This is not a flavor-of-the-week sort of issue. There is a fundamental difference in direct vs. indirect mutation rate estimates. There are plenty of good reasons to think that the direct mutation rate, the actual rate of appearance of mutations from one generation to the next, is going to be higher than the rate of fixed mutations, which is the rate that shows up in phylogenetically-oriented studies, or other studies that are not explicitly designed to enhance the fixation of mutations generally and do not directly observe these mutations. And while the Denver et al. paper is certainly not the last word on the subject (Brian Charlesworth's lab provided a Drosophila-oriented estimate using HPLC that is not so high) it does provide pretty good support for higher rates of direct mutation.

    A mutation rate of 10^-10 is consistent with the known in vitro error rates in DNA replication and repair. If you want to increase that error rate by a factor of ten then you should try and explain how the extra mutations are created.

    Are you suggesting that most (9/10) mutations are generated by something other than errors in DNA replication or are you suggesting that DNA replication/repair is more error prone in vivo than it is in vitro?

    Recall that I base my estimate on the biochemistry of the process and not measured mutation rates in populations. The fact that the population rates are (mostly) consistent is satisfying but because they are indirect they are less convincing to me than the direct measurements. (And, yes, I am aware of the difference between mutation rates and fixation rates.)

    We know that there are regions of the genome that are error prone. The error rates in these regions can easily be ten or a hundred times higher.

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  10. hmmmm if I look it this as a applicable research in my investigation about the changes in the genetic human structure, maybe I could find the answer that I need to complete my theory.

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  11. In regards to the comments on the debated rate, at least in bacteria nobody has estimated the spontaneous mutation rate in a statistically satisfying way (at least to my knowledge, though would love to know otherwise!).

    Basically, all of the good data comes from fluctuation assays, which only estimate a rate at which a phenotype appears (and these estimates are often downward biased because a lot use rif resistance as the phenotype, and don't account for how much slower resistant mutants grow in the analysis). Also, converting a phenotypic rate to a genomic mutation rate is very difficult. The spectrum of mutations that are available to confer resistance are not the same as those available to the entire genome, and so a lot of sequencing has to be done to determine what mutants were available, and then a comparison must be made to the entire genome. I know of no study that has done this so far, or estimated the uncertainty that carries through, I don't think we as a community have the rate down to right within an order of magnitude for prokaryotes, though much better work has been done in eukaryotes.

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