7.03 Lecture 26 11/14/01

Transcription

1 Now we are going to consider how allele frequencies change under the influence of mutation and. First, we will consider mutation. Mutation A µ a µ = q mut = Phenylketonuria (PKU) allele frequency q number of generations Typically, µ = per generation, so q will increase a little each generation. Consider phenylketonuria (PKU), an autosomal recessive disease caused by a defect in the enzyme phenylalanine hydroxylase. The absence of the enzyme prevents phenylalanine from being metabolized, causing unusually high levels of phenylalanine to accumulate in the body, leading to severe mental retardation. Assume we begin with a mutant allele frequency, q, of zero. The frequency of PKU will then slowly increase each generation. But when the allele frequency gets high enough, against PKU homozygotes will counterbalance the increase due to new mutations and q will eventually reach a constant, steady-state value. 1

2 To calculate what this steady-state value for q will be we need a quantitative parameter for. S = 1-S = If S = 0.75 then This means that individuals with this genotype will have as an average individual. Fitness can thus be thought of as the relative probability that an individual will survive to maturity and reproduce (as compared to an average individual). 2

3 recessive disease Genotype Frequency with no Frequency with frequency A/A A/a a/a At steady state: (for recessive disease) For PKU, so, at steady state, Low-phenylalanine diet Even for a recessive lethal allele with µ = 10-8, q will be In the US population, this represents about 50,000 heterozygous individuals. What happens when fitness changes as a result of a changing environment? Modern medicine has developed an effective treatment for PKU by feeding individuals with this disorder a low-phenylalanine diet. Because of this treatment, S < 1 for PKU. If S fell to zero, the frequency of PKU should start to rise at a rate q mut = 10-4 per generation. But the fractional change in q will only amount to an increase of about 1% per generation and it will take a long time for this change in environment to have a significant impact on disease frequency. 3

4 Now consider a dominant disease with allele frequency q = f(a) Note that for a rare dominant trait almost all affected individuals are heterozygotes. dominant disease Genotype Frequency with no Frequency with frequency A/A A/a a/a q sel = At steady state: q sel + q mut = 0 (dominant disease) Thus after, 2Sq heterozygotes are lost each generation but only half of their alleles are A. For the extreme case where S = 1 and q= µ, only new muta tions will be obse rve d. Be caus e the tra it is dominant, the number of affected individuals will be 2µ. When S<1 the allele frequency can get quite high. A good example is Huntington's disease which has a late onset of degeneration of neuromuscular system at > 35 years. This disease is disastrous for affected individuals but has little effect on their reproductive fitness. 4

5 An important type of allele is one that is deleterious in the homozygous state but is beneficial in the heterozygous state. In this case, a balance between for the heterozygote and against the homozygote will set the steady state value of q. We will need a new parameter h. Balanced Polymorphism: h = (amount by which reproductive fitness of heterozygote exceeds that of an average individual) Genotype Frequency with no Frequency with frequency A/A A/a a/a q sel = At steady state: (choosing to neglect mutation in this analysis) In the simple case where S = 1, then q= h. 5

6 The possibility of a subtle for (or against) the heterozygote for an allele that appears to be recessive means that in practice the estimates of µ from a lle le fre quencie s a re not ve ry re lia ble. Example: Recessive disease with Consider 2 possibilites: 1. Balance between and mutation: If and then 2. Balanced polymorphism with mutation: If and then Unfortunately, since a 1% increase in heterozygote advantage cannot be detected with any reliability, we sometimes cannot distinguish between these two possibilities. 6

7 The best understood case of balanced polymorphism in human populations is sickle-cell disease and resistance to malaria. Infection with malaria, a parasite, causes millions of deaths each year in human populations living near the equator. The malarial parasite infects red blood cells. When it does, intracellular O 2 falls to very low levels, andβ S β S or ββ S cells will sickle. The sickled cells tend to either lyse or be filtered out in fine capillaries the net effect being the selective removal of infected cells. β genotype Hemoglobin tetramer [O 2 ] normal [O 2 ] low [O 2 ] very low (malaria) Sickle disease Resistant to malaria β S : In parts of Africa, the β S allele frequency This implies that the The allele frequency forβ S is substantial in many equatorial populations where malaria is common, such as sub-saharan Africa, the Mediterranean, and Southeast Asia. 7