R ATES OF P OINT M UTATION

The rate of mutation = the number of new sequence variants arising in a predefined target region per unit time. Target region = a specific sequence of predefined length and location, a gene, a gamete, a chromosome, or a genome. Time units may be (1) taxon specific, such as replication time or generation time, or (2) absolute, such as chronological time (days, years).

The chief difficulties in estimating the rate of mutation is (1) the fact that mutations occur at a very low rate and (2) that many mutations are highly deleterious or lethal and, therefore, unobservable.

There are essentially three main approaches to estimating mutation rates.

First approach (Danforth 1923; Halda 1927, 1935). Based on the assumption that deleterious alleles in a population exist because of a balance between (1) the process of mutation creating these alleles and (2) purifying selection eliminating them. For autosomal dominant mutations, the equilibrium allele frequency, q, can be calculated as where μ is the mutation rate and |s| is the selection coefficient associated with the deleterious mutant. The mutation rate is, therefore

For X-linked recessive mutations, such as hemophilia, the mutation rate is (the denominator contains 3 since one-third of the X chromosomes in the population are carried by males) If most hemophiliacs do not reproduce (i.e., if s ≈ -1), then the mutation rate is roughly one third the frequency of male carriers. By using empirically determined values of s and q, Haldane (1935) inferred that mutations causing hemophilia arise at a mean rate of roughly 2  10 –5 per generation.

The second method of estimating mutation rate is based on the very important theoretical result (Kimura 1968) that the neutral mutation rate (μ) is equal to the rate of substitution for neutral alleles (K). Thus, homologous stretches of nonfunctional DNA, on which selection does not operate and which evolve by random genetic drift, can be compared between two species to calculate the amount of sequence divergence. If the generation time and the time since the two species have diverged from each other are known, then the mutation rate per generation can be easily estimated. Example: This approach has been used for synonymous sites and for pseudogenes in comparisons between human and chimpanzee, and these studies suggested mutation rates of about 2 × 10 –8 per nucleotide site per generation.

Given that the total length of the human diploid genome is approximately 7  10 9 base pairs, we can multiply the mutation rate per site per generation (2 × 10 –8 ) by the genome size, and deduce that each newborn in the human population carries around 140 new point mutations not found in their parents.

The third method of inferring mutation rate is the most direct. In this method, large nonrecombining stretches of DNA, such as human Y chromosomes, are sequenced in individuals related to one another by descent. One the pedigree below, about 10 Mb of Y-chromosome DNA was sequenced from two males (and their living relatives) separated by 13 generations. The common ancestor of the two individuals was born in 1805, i.e., about 200 years before the analysis. Four mutations have been discovered. Thus, the rate of mutation in the human nuclear genome was estimated to be 4/(10 7  200  2) = 1  10 –9 mutations per site per year. Do you know your great-great-great- great-great-father?

With the dramatic drop in the cost of sequencing from about 3 billion dollars per haploid human genome in the 1990s to about 50,000 dollars per diploid genome in 2010, it has become practical to sequence whole genomes of parents and children and identifying all mutations. One such study (Roach et al. 2010) yielded an unbiased point mutation rate estimate of 1.1  10 –8 mutations per site per generation, which translates into a mutation rate of about 0.4  10 –9 mutations per site per year under the assumption that the current generation time in humans is 30 years. Thus, every newborn carries on average 70 new mutations in their diploid genome. Other findings: The transition-to-transversion ratio was approximately 2.3, and the rate of mutation in males was higher than that in females.

Caveat: Mutations having large deleterious effects on fitness cannot be observed.

In some experimental organisms, one can overcame the problem of our inability to detect deleterious mutations, by using the fact a mutation will behave as a neutral mutation as long as its selective disadvantage, s, is smaller than 1/(2Ne), where Ne is the effective population size.

By keeping Ne at the absolute minimum, one can ensure that all but the most deleterious mutations will be observed. For instance, one can use a population of the hermaphrodite nematode, Caenorhabditis elegans, in which a single individual in each generation is used to produce the succeeding generation. Such an experiment can last hundreds of generations.

One such experiment yielded a mean estimate of about 10 –6 point mutations per site per year, i.e., the mean mutation rate in C. elegans was inferred to about three orders of magnitude larger that that in the nuclear genome of mammals.

The rate of mutation in mammalian mitochondrial DNA has been estimated to be at least 10 times higher than the average nuclear rate. The mean rate of mutation in the mitochondrial genome of Drosophila has been estimated to be approximately 6 × 10 −8 per site per generation, which translates into a rate of about 10 −6 per site per year (Haag-Liautard et al. 2008).

Mutation rates in viruses span a range of approximately six orders of magnitude, from the single-stranded RNA swine vesicular stomatitis virus at about 10 –3 mutations per site per year, to the double-stranded DNA herpesvirus at about 10 –9 mutations per site per year. herpesvirusswine vesicular stomatitis virus