Genetica per Scienze Naturali a.a. 04-05 prof S. Presciuttini Mutation Rates Ultimately, the source of genetic variation observed among individuals in.

Genetica per Scienze Naturalia.a. 04-05 prof S. Presciuttini

Mutation Rates Ultimately, the source of Ultimately, the source of genetic genetic variation variation observed among individuals in observed among individuals in

populations ispopulations is gene gene mutationmutation.. Mutation generates new alleles, and these are the Mutation generates new alleles, and these are the substance of all evolutionary change.substance of all evolutionary change.

The The mutation ratemutation rate is defined as the probability that a copy of an allele changes to is defined as the probability that a copy of an allele changes to some other allelic form in one generation.some other allelic form in one generation.

Mutation rates at the gene level depends on mutation rates at other levels:Mutation rates at the gene level depends on mutation rates at other levels: Mutation rates for different kinds of mutations can be expressed as Mutation rates for different kinds of mutations can be expressed as mutations per mutations per

locus, per gene, per nucleotide, locus, per gene, per nucleotide, andand per gamete per gamete. All of these indicate a specific type . All of these indicate a specific type of mutation occurring of mutation occurring per generationper generation (higher eucaryotes)(higher eucaryotes) oror per DNA replication per DNA replication (microorganisms)(microorganisms), , reflecting mutations arising anew reflecting mutations arising anew in the unit timein the unit time..

In addition, mutations rates may be expressed is relation to In addition, mutations rates may be expressed is relation to visible phenotypesvisible phenotypes or or in relation to of in relation to of DNA sequence changesDNA sequence changes

Therefore, it is useful distinguishing between mutation rates: Therefore, it is useful distinguishing between mutation rates: per base pair per generation (or replication)per base pair per generation (or replication) per gene per generation (or replication)per gene per generation (or replication) per genome or gamete per generation (or replication)per genome or gamete per generation (or replication)


Estimating the mutation rate in the fluctuation test Luria and Delbrück's fluctuation test provides Luria and Delbrück's fluctuation test provides

a way of measuring the mutation ratea way of measuring the mutation rate towards towards acquisition of resistance to phage T1acquisition of resistance to phage T1. .

Examine in more detail the results of their Examine in more detail the results of their experiment relative to the 20 small cultures. experiment relative to the 20 small cultures. TheThe total number of mutant cells was 227, out total number of mutant cells was 227, out of a total population of 4 x 10of a total population of 4 x 1088 cells. cells.

This leads to a frequency of mutant cells in This leads to a frequency of mutant cells in the total population of 5.7 x 10the total population of 5.7 x 10-7-7..

Note that this is the proportion of mutants Note that this is the proportion of mutants among all the living cells at the end of the among all the living cells at the end of the experiment; this is not the mutation rate. experiment; this is not the mutation rate.

Culturenumber

Number T1R

mutantsTotal number

of cells

1 1 0.2 x 108

2 0 0.2 x 108

3 3 0.2 x 108

4 0 0.2 x 108

5 0 0.2 x 108

6 5 0.2 x 108

7 0 0.2 x 108

8 5 0.2 x 108

9 0 0.2 x 108

10 6 0.2 x 108

11 107 0.2 x 108

12 0 0.2 x 108

13 0 0.2 x 108

14 0 0.2 x 108

15 1 0.2 x 108

16 0 0.2 x 108

17 0 0.2 x 108

18 64 0.2 x 108

19 0 0.2 x 108

20 35 0.2 x 108

Total 227 4 x 108

Mutation frequency =231 / 4x108 =

5.7 x 10-7


Mutation frequency and mutation rate To estimate the mutation rate, we need to estimate how many cell duplications To estimate the mutation rate, we need to estimate how many cell duplications

occurred to produce the extant population in each culture, and to estimate how occurred to produce the extant population in each culture, and to estimate how many times a mutation toward resistance occurred among all these cell duplicationsmany times a mutation toward resistance occurred among all these cell duplications

Difference between mutation frequency and mutation rate.

• The number of mutant cells in the final population (M) of this example is 10, and the total number of cells (N) is 16 x 4 = 64 (mutation frequency = M/N =1.6 x 10-1).

• The mutation rate is the number of mutation events ( = 2) among the total number of cell duplications D (= 15 x 4 = 60); thus = D = 3.3 x 10-2.


Estimating mutation rates in bacteria In the real case, we cannot count the number of independent mutation events the In the real case, we cannot count the number of independent mutation events the

occurred in each culture; we can only distinguish among the cultures in which no occurred in each culture; we can only distinguish among the cultures in which no mutation had occurred (zero mutants) from all the others.mutation had occurred (zero mutants) from all the others.

Thus, theThus, the 20 cultures that were tested for phage T1 resistance 20 cultures that were tested for phage T1 resistance can be divided among can be divided among those in which no mutation had occurred those in which no mutation had occurred (11 of the 20(11 of the 20 = 0.55 = 0.55)) and those in which a and those in which a mutation had occurred once or moremutation had occurred once or more. . This This situation is well described by the Poisson situation is well described by the Poisson distributiondistribution, in which the probability of zero occurrences of an event (, in which the probability of zero occurrences of an event (PP00) is given ) is given

by by PP00 = e = e--, where , where is the probability that an event will occur. is the probability that an event will occur.

We can estimate We can estimate from the data by letting 0.55 = from the data by letting 0.55 = ee-- and solving for and solving for ( ( = -ln = -ln 0.550.55); this gives ); this gives = 0.6= 0.6 mutation events per tube. mutation events per tube.

We can now estimate the number of cell duplications (We can now estimate the number of cell duplications (DD) that occurred in each tube. ) that occurred in each tube. If If NN is very large, and if the original number of cells was very small, then a is very large, and if the original number of cells was very small, then a sufficiently accurate estimate of sufficiently accurate estimate of DD is given by is given by NN itself. itself.

Thus, sinceThus, since DD = 0.2 × 10 = 0.2 × 1088, we , we arrive at an estimate of the mutation rate arrive at an estimate of the mutation rate = 0.6/ = 0.6/ 0.2×100.2×1088 = = 3 3 × 10× 10--88..

Note that Note that is expressed as number of mutations per gene per DNA replication. is expressed as number of mutations per gene per DNA replication.


Forward mutation rates Mutation rates Mutation rates

estimated by counting estimated by counting mutant individuals mutant individuals based on a Mendelian based on a Mendelian phenotype include all phenotype include all mutations that cause mutations that cause the appearance of that the appearance of that phenotypephenotype

In practice, this In practice, this approach estimate the approach estimate the forward mutation rate, forward mutation rate, or any DNA change or any DNA change that abolishes or that abolishes or severely impede the severely impede the production of a production of a functional product at a functional product at a locus.locus.

Forward mutations are Forward mutations are changes away from the changes away from the wild-type allelewild-type allele


Forward and Backward mutation rates If we consider a locus with If we consider a locus with

two possible alleles (A and two possible alleles (A and a)) then we can consider a a)) then we can consider a forward (u) and backward forward (u) and backward mutation (v).mutation (v).

Forward mutation is the Forward mutation is the mutation from wildtype mutation from wildtype allele to the detrimental allele to the detrimental allele. Backward mutations allele. Backward mutations undo the forward mutation.undo the forward mutation.

Because there are many Because there are many ways to destroy the function ways to destroy the function but fewer ways to undo that but fewer ways to undo that harm, backward mutations harm, backward mutations are normally more rare than are normally more rare than forward mutations. forward mutations.


Estimated mutation rates Bacteria, Archae, and Eukaryotic microbes produce about one mutation per 300 Bacteria, Archae, and Eukaryotic microbes produce about one mutation per 300

chromosome replications. For E. coli this works out to be between 10chromosome replications. For E. coli this works out to be between 10 -6-6 and 10 and 10-7-7 mutations per gene per generation, however it is important to note that there are mutations per gene per generation, however it is important to note that there are certain "hot spots" or "cold spots" for spontaneous mutations.certain "hot spots" or "cold spots" for spontaneous mutations.

Higher eukaryotes have the same rate of spontaneous mutation, so that rates per Higher eukaryotes have the same rate of spontaneous mutation, so that rates per sexual generation are about one mutation per gamete (close to the maximum sexual generation are about one mutation per gamete (close to the maximum compatible with life). RNA viruses have much higher mutation rates - about one compatible with life). RNA viruses have much higher mutation rates - about one mutation per genome per chromosome replication - and even small increases in mutation per genome per chromosome replication - and even small increases in their mutation rates are lethal.their mutation rates are lethal.

Because a complex individual has a trillion or so nucleotides, each individual is Because a complex individual has a trillion or so nucleotides, each individual is likely to sustain one or more mutations.likely to sustain one or more mutations.

Rates of expressed gene mutations average about 1 per 100,000 to 1 per million:Rates of expressed gene mutations average about 1 per 100,000 to 1 per million: rates of expression of phenotypic effects are often higher because they are controlled by rates of expression of phenotypic effects are often higher because they are controlled by

many genesmany genes


Nucleotide mutation rate Rates of spontaneous mutation seem to be determined by evolutionary balances Rates of spontaneous mutation seem to be determined by evolutionary balances

between the deleterious consequences of between the deleterious consequences of too too many mutations and the additional many mutations and the additional energy and time required to further reduce mutation rates.energy and time required to further reduce mutation rates.

In microorganisms, tIn microorganisms, the rate of mutation for any nucleotide he rate of mutation for any nucleotide (point mutations) (point mutations) is is generally included between generally included between 1010-9-9 and and 1010-10-10 per DNA replication per DNA replication..

Although this rate of mutation may seem exceedingly small, the total amount of new Although this rate of mutation may seem exceedingly small, the total amount of new genetic variation introduced by spontaneous mutation at each DNA replication is genetic variation introduced by spontaneous mutation at each DNA replication is significant. Consider the genome ofsignificant. Consider the genome of E. coli E. coli, of the size of about 5 x 10, of the size of about 5 x 106 6 bp. With a bp. With a mutation rate intermediate between those listed above (say 5 x 10mutation rate intermediate between those listed above (say 5 x 10 -10-10), 25 x 10), 25 x 10-4-4, or one , or one every 400 cells carries a new point mutation.every 400 cells carries a new point mutation.

This means that in a single large bacterial culture (1 litre), in which concentrations of 2 x This means that in a single large bacterial culture (1 litre), in which concentrations of 2 x 10109 9 cells/ml are easily obtained (=2 x 10cells/ml are easily obtained (=2 x 101212 total cells), some 5 x 10 total cells), some 5 x 1099 new mutations are new mutations are present, corresponding to 1,000 mutations for each base pair.present, corresponding to 1,000 mutations for each base pair.

In practice, all possible nucleotide substitutions and all possible single In practice, all possible nucleotide substitutions and all possible single insertion/deletions, as well as many large rearrangements are represented in a moderately insertion/deletions, as well as many large rearrangements are represented in a moderately large bacterial populationlarge bacterial population


Measuring mutation rates in human The The mutation ratemutation rate is a measure of the frequency of a given mutation is a measure of the frequency of a given mutation

per generation (or per gamete, which is equivalent). Ordinarily, rates per generation (or per gamete, which is equivalent). Ordinarily, rates are given for specific loci. Thus the mutation rate for achondroplasia are given for specific loci. Thus the mutation rate for achondroplasia is 6-13 mutants per million gametes. This means that each gamete has is 6-13 mutants per million gametes. This means that each gamete has about 1 chance in 100,000 of carrying a new mutation for about 1 chance in 100,000 of carrying a new mutation for achondroplasia. achondroplasia.

Mutation rates are based almost exclusively on rare autosomal Mutation rates are based almost exclusively on rare autosomal dominant or X-linked recessive traits. It is virtually impossible to dominant or X-linked recessive traits. It is virtually impossible to measure autosomal recessive traits accurately. The range of known measure autosomal recessive traits accurately. The range of known mutation rates varies from 1 in 10,000 for Duchenne muscular mutation rates varies from 1 in 10,000 for Duchenne muscular dystrophy and neurofibromatosis type-1 (the largest genes known) to dystrophy and neurofibromatosis type-1 (the largest genes known) to several genes in the range of 1 in 10,000,000. several genes in the range of 1 in 10,000,000.

Mutation rate studies Mutation rate studies nevernever measure all the possible mutations at a measure all the possible mutations at a locus. Many of the mutations cause no obvious phenotypic effect and locus. Many of the mutations cause no obvious phenotypic effect and could only be recognized by direct analysis of DNA sequences. could only be recognized by direct analysis of DNA sequences.


A recent work about mutation rate in human The approach by Nachman and Crowell to measuring the human mutation The approach by Nachman and Crowell to measuring the human mutation

rate takes advantage of the well-known result that for neutral mutations, the rate takes advantage of the well-known result that for neutral mutations, the mutation rate is equal to the rate of mutation substitutionmutation rate is equal to the rate of mutation substitution

Knowing Knowing divergence time and generation lengthdivergence time and generation length of two species allowed of two species allowed themthem to to estimate of the rate and pattern ofestimate of the rate and pattern of mutation mutation in in stretches of DNA stretches of DNA without functionwithout function

They They sequenced 18 pseudogenes in humans and chimpanzees, including 12 sequenced 18 pseudogenes in humans and chimpanzees, including 12 on autosomes and 6 on the X chromosomeon autosomes and 6 on the X chromosome. In this way, they. In this way, they1.1. estimated the average mutation rate per nucleotide siteestimated the average mutation rate per nucleotide site2.2. compared mutation rates for different sites and for different classes of mutation compared mutation rates for different sites and for different classes of mutation

to evaluate heterogeneity of mutation rateto evaluate heterogeneity of mutation rate3.3. compared rates of divergence on the X chromosome and on autosomes to compared rates of divergence on the X chromosome and on autosomes to

evaluate the hypothesis that the X chromosome has a lower mutation rate than evaluate the hypothesis that the X chromosome has a lower mutation rate than the autosomesthe autosomes

4.4. provided an approximation of the genomic deleterious mutation rate by provided an approximation of the genomic deleterious mutation rate by considering the total mutation rate and the fraction of the genome that is subject considering the total mutation rate and the fraction of the genome that is subject to constraintto constraint



Nachman and Crowell main results


Nachman and Crowell results (1)








Summary of mutation rates in human

Mutation rates per generationMutation rates per generation

• Per base pair ~10Per base pair ~10-8 -8

• Per gene ~10Per gene ~10-6 -6 - 10- 10-5-5

• Per genomePer genome All point mutations: All point mutations: ~~100 per gamete100 per gamete Deleterious mutations: 1 Deleterious mutations: 1 ~~ 2 per gamete 2 per gamete

The rate of nucleotide substitutions is on the order of 1 per The rate of nucleotide substitutions is on the order of 1 per 100,000,000 nucleotides. Since there are 3 billion nucleotides per 100,000,000 nucleotides. Since there are 3 billion nucleotides per genome, that means that every gamete has about 30 new mutations genome, that means that every gamete has about 30 new mutations involving nucleotide substitutions.involving nucleotide substitutions.

Genetica per Scienze Naturali a.a. 04-05 prof S. Presciuttini Mutation Rates Ultimately, the source of genetic variation observed among individuals in.

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