Some Additional Discussion of Bo

Some Additional Discussion of Box 7.4:

Estimating the Age of the CCR5-Δ32 Mutation

Those of you who have taken Genetics may remember that crossover events are stochastic events, that is, they occur at random but with predictable frequencies over long periods of time. Therefore, knowledge of specific crossover frequencies can be used in certain circumstances to establish a sort of "molecular clock," in a fashion similar to the use of specific mutation rates.

In the case of the three loci, CCR5, GAAT, and AFMB, we have two independent crossover rates to consider, the crossover rate between CCR5 and GAAT and the crossover rate between CCR5 and AFMB. Those rates are 0.0021 and 0.0072 respectively.

Since GAAT and AFMB are multi-allelic systems, we have to consider just the rate of crossovers for the specific haplotype changes that are involved in the data related to the haplotype:

/ CCR5 - Δ32 / /GAAT - 197/ /AFMB - 215/

where the CCR5-Δ32 mutation first arose.

See Figure 7.12: Three Loci on the Short Arm of Chromosome 3,

and Selected Haplotype Frequencies in a European Population

To start with, we need to know the frequency of the ancestral haplotype to the new mutation. That haplotype is: / CCR5 - + / /GAAT - 197/ /AFMB - 215/ .

Within the European population, / CCR5 - + / /GAAT - 197/ /AFMB - 215/ occurs in 36% of all Europeans.

Therefore, the other CCR5 - + "wildtype" chromosome haplotypes comprise the remaining 64% of the chromosomes.

Therefore, a single crossover in the region between CCR5 and GAAT will produce a crossover chromosome haplotype with any other GAAT allele other than 197 and any other AFMB allele other than 215.

Such chromosomes can be represented as: / CCR5 - + / /GAAT - other 2 of 3 / /AFMB - other 3 of 4 / .

The text represents that set of chromosomes as "+ - other" in Figure 7.12. It would have been better, probably, to have represented them as "+ other - other."

This gives us our first molecular clock estimator for the age of the CCR5 - Δ32 mutant.

Here’s the logic. The rate of crossover between the CCR5 locus and the GAAT locus is 0.0021, but we are only interested in the rate for crossover for one particular chromosome haplotype:

/ CCR5 - + / /GAAT - 197/ /AFMB - 215/ .

Since only 36% of the population’s chromosome haplotypes are " + 197 215," the crossover rate for just that haplotype is the frequency of all the other remaining chromosome haplotypes, "+ other other" (64%), in the population times the general crossover rate for those two loci which is 0.0021.

The product of (0.64 x 0.0021) = 0.001344. (You can see that 0.001344 is about two-thirds of the total crossover frequency between CCR5 and GAAT, which is 0.0021.)

We will use the same logic to establish a "molecular clock" for a double crossover in the region between CCR5 and AFMB.

A double crossover occurs when there has been a single crossover between CCR5 and GAAT as well as a single crossover between GAAT and AFMB.

Such a double crossover, occurring on our ancestral chromosome haplotype, "+ - 197 - 215," will produce a double crossover chromosome haplotype with any of the three GAAT alleles (x = 191, 193, or 197) but only the AFMB allele 215, which is restored by the second crossover event, which brings back the ancestral DNA after the second break and repair.

Such chromosomes can be represented as: / CCR5 - + / /GAAT - x = any of 3 / /AFMB - only 215 / .

The text represents that set of chromosomes as "+ - x -other" in Figure 7.12. This gives us our second "molecular clock" estimator for the age of the CCR5 - Δ32 mutant. It’s the same logic.

The rate of crossover between the CCR5 locus and the AFMB locus is 0.0072, but we are only interested in the rate for double crossover for one particular chromosome haplotype:

/ CCR5 - + / /GAAT - 197/ /AFMB - 215/ .

Since only 52% of the population’s chromosome haplotypes are " + - 197 - 215," the double crossover rate for just that haplotype is the frequency of all the other remaining chromosome haplotypes, "+ - x - other" (48%), in the population times the general crossover rate for those two loci which is 0.0072.

The product of (0.48 x 0.0072) = 0.003456. (You can see that 0.003456 is about half of the total crossover frequency between CCR5 and AFMB, which is 0.0072.)

Therefore, as shown in Box 7.4, the combined frequency rate which includes crossovers at between both pairs of loci, CCR5 and GAAT and CCR5 and AFMB, is:

c = (0.64 x 0.0021) + (0.48 x 0.0072) = 0.001344 + 0.003456 = 0.0048 = 0.005 .

The value of c in addition to an independent estimate of a mutation rate of μ = 0.001.

The chance that our ancestral chromosome haplotype, "+ - 197 - 215," will remain unchanged is:

1 - c - μ .

We need a formula to estimate the change over several generations, so we establish the variable g = number of generations. If so, then the frequency of the ancestral chromosome haplotype, "+ - 197 - 215," remaining unchanged through g generations is:

P_g = (1 - c - μ)^g

We already have actual data for the frequency that remain unchanged since the origin of the new mutation at CCR5 - Δ32.

It is the 84.8% of chromosome haplotypes which remain as "Δ32 - 197 - 215."

So we can now enter all necessary terms into the formula for estimating P_g solve for g, the number of generations since the mutation producing CCR5 - Δ32 occurred.

The researchers solved for g and obtained a g of 27.5 generations, which is where their best estimate of 688 years since the mutation occurred was calculated.

Whew, what a lot of math!