KAPLAN_USMLE_STEP_1_LECTURE_NOTES_2018_BIOCHEMISTRY_and_GENETICS

Part II ●●●Medical Genetics

Note

Genotype frequencies measure the proportion of each genotype in a population. Allele frequencies measure the proportion of chromosomes that contain a specific allele (of a gene).

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The genotype frequency is then obtained by dividing the count for each genotype by the total number of individuals. Thus, the frequency of genotype 1-1 is 49/100 = 0.49, and the frequencies of genotypes 1-2 and 2-2 are 0.42 and 0.09, respectively.

Allele Frequencies

The allele frequency measures the proportion of chromosomes that contain a specific allele. To continue the earlier RFLP example, we wish to estimate the frequencies of alleles 1 and 2 in our population. Each individual with the 1-1 genotype has 2 copies of allele 1, and each heterozygote (1-2 genotype) has one copy of allele 1. Because each diploid somatic cell contains 2 copies of each autosome, our denominator is 200. Thus, the frequency of allele 1 in the population is:

(2×49)+ 42 = 0.7 200

(The same approach can be used to estimate the frequency of allele 2, which is 0.3. A convenient shortcut is to remember that the allele frequencies for all of the alleles of a given locus must add up to 1. Therefore, we can obtain the frequency of allele 2 simply by subtracting the frequency of allele 1 (0.7) from 1.

HARDY-WEINBERG EQUILIBRIUM

If a population is large and if individuals mate at random with respect to their genotypes at a locus, the population should be in Hardy-Weinberg equilibrium. This means that there is a constant and predictable relationship between genotype frequencies and allele frequencies. This relationship, expressed in the Har- dy-Weinberg equation, allows one to estimate genotype frequencies if one knows allele frequencies, and vice versa.

The Hardy-Weinberg Equation

p2 + 2 pq + q2 = 1

In this equation:

p = frequency of allele 1 (conventionally the most common, normal allele) q = frequency of allele 2 (conventionally a minor, disease-producing allele) p2 = frequency of genotype 1-1 (conventionally homozygous normal)

2pq = frequency of genotype 1-2 (conventionally heterozygous)

q2 = frequency of genotype 2-2 (conventionally homozygous affected)

In most cases where this equation is used, a simplification is possible. Generally p, the normal allele frequency in the population, is very close to 1 (e.g., most of the alleles of this gene are normal). In this case, we may assume that p ~ 1, and the equation simplifies to:

1 + 2q + q2 ~ 1

The frequency of the disease-producing allele in question, q, is a very small fraction. This simplification would not necessarily be used in actual medical genetics practice, but for answering test questions, it works quite well. However, if the disease prevalence >1/100, e.g., q >1/10, the complete Hardy-Weinberg equation should be used to obtain an accurate answer. In this case, p = 1 - q.

Although the Hardy-Weinberg equation applies equally well to autosomal dominant and recessive alleles, genotypes, and diseases, the equation is most frequently used with autosomal recessive conditions. In these instances, a large percentage of the disease-producing allele is “hidden” in heterozygous carriers who cannot be distinguished phenotypically (clinically) from homozygous normal individuals.

A simple example is illustrated by the following case.

A 20-year-old college student is taking a course in human genetics. She is aware that she has an autosomal recessive genetic disease that has required her lifelong adherence to a diet low in natural protein with supplements of tyrosine and restricted amounts of phenylalanine. She also must avoid foods artificially sweetened with aspartame (Nutrasweet™). She asks her genetics professor about the chances that she would marry a man with the diseaseproducing allele.

The geneticist tells her that the known prevalence of PKU in the population is 1/10,000 live births, but the frequency of carriers is much higher, approximately 1/50. Her greatest risk comes from marrying a carrier for two reasons. First, the frequency of carriers for this condition is much higher than the frequency of affected homozygotes, and second, an affected person would be identifiable clinically. The geneticist used the Hardy-Weinberg equation to estimate the carrier frequency from the known prevalence of the disease in the following way:

Disease prevalence = q2 = 1/10,000 live births Carrier frequency = 2q (to be calculated)

q = square root of 1/10,000, which is 1/100 2q = 2/100, or 1/50, the carrier frequency

The woman now asks a second question: “Knowing that I have a 1/50 chance of marrying a carrier of this allele, what is the probability that I will have a child with PKU?”

The geneticist answers, “The chance of you having a child with PKU is 1/100.” This answer is based on the joint occurrence of two nonindependent events:

•The probability that she will marry a heterozygous carrier (1/50), and

•If he is a carrier, the probability that he will pass his PKU allele versus the normal allele to the child (1/2).

These probabilities would be multiplied to give:

• 1/50 × 1/2 = 1/100, the probability that she will have a child with PKU.

Chapter 2 ● Population Genetics

Note

Hardy-Weinberg Equilibrium in

Phenylketonuria (PKU)

•Prevalence of PKU is 1/10,000 live births

•Allele frequency =

(1/10,000) = 1/100 = 0.01

•Carrier frequency = 2(1/100) = 1/50

Bridge to Statistics

If events are nonindependent, multiply the probability of one event by the probability of the second event, assuming that the first has occurred.

For example, what is the probability that the student’s husband will pass the disease-producing allele to the child? It is the probability that he will be a carrier (1/50, event 1) multiplied by the probability that he will pass the disease-causing gene along (1/2, event 2), assuming he is a carrier.

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Part II ●●●Medical Genetics

Note

Assuming random mating, the HardyWeinberg principle specifies a predictable relationship between allele frequencies and genotype frequencies in populations. This principle can be applied to estimate the frequency of heterozygous carriers of an autosomal recessive mutation.

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In summary, there are 3 major terms one usually works with in the HardyWeinberg equation applied to autosomal recessive conditions:

•q2, the disease prevalence

•2q, the carrier frequency

•q, the frequency of the disease-causing allele

When answering questions involving Hardy-Weinberg calculations, it is important to identify which of these terms has been given in the stem of the question and which term you are asked to calculate.

This exercise demonstrates two important points:

•The Hardy-Weinberg principle can be applied to estimate the prevalence of heterozygous carriers in populations when we know only the prevalence of the recessive disease.

•For autosomal recessive diseases, such as PKU, the prevalence of heterozygous carriers is much higher than the prevalence of affected homozygotes. In effect, the vast majority of recessive genes are hidden in the heterozygotes.

Hardy-Weinberg Equilibrium for Dominant Diseases

The calculations for dominant diseases must acknowledge that most of the affected individuals will be heterozygous. In this case, the prevalence is 2q. (One can again use the assumption that p ~ 1.) The term q2 represents the prevalence of homozygous affected individuals who, although much less commonly seen, may have more severe symptoms. For example,

•1/500 people in the United States have a form of LDL-receptor deficiency and are at increased risk for cardiovascular disease and myocardial infarction.

•Taking 2q = 1/500, one can calculate that q2 = 1/106, or one in a million live births are homozygous for the condition. These individuals have greatly elevated LDL-cholesterol levels, a much-higher risk for cardiovascular disease than heterozygotes, and are more likely to present with characteristic xanthomas, xanthelasmas, and corneal arcus.

In contrast, in Huntington disease (autosomal dominant), the number of triplet repeats correlates much more strongly with disease severity than does heterozygous or homozygous status.

Sex Chromosomes and Allele Frequencies

When considering X-linked recessive conditions, one must acknowledge that most cases occur in hemizygous males (xY). Therefore, q = disease-producing allele frequency but, paradoxically, it also equals the prevalence of affected males. Thus, the statement “1/10,000 males has hemophilia A” also gives the allele frequency for the disease-producing allele: 1/10,000.

•q2 = prevalence of disease in females (1/108, or 1/100,000,000)

•2q = prevalence of female carriers (1/5,000)

FACTORS RESPONSIBLE FOR GENETIC VARIATION IN/AMONG POPULATIONS

Although human populations are typically in Hardy-Weinberg equilibrium for most loci, deviations from equilibrium can be produced by new mutations, the introduction of a new mutation into a population from outside (founder effect), nonrandom mating (for example, consanguinity), the action of natural selection, genetic drift, and gene flow. Although these factors are discussed independently, often more than one effect contributes to allele frequencies in a population.

Mutation

Mutation, discussed previously, is ultimately the source of all new genetic variation in populations. In general, mutation rates do not differ very much from population to population.

In some cases, a new mutation can be introduced into a population when someone carrying the mutation is one of the early founders of the community. This is referred to as a founder effect. As the community rapidly expands through generations, the frequency of the mutation can be affected by natural selection, by genetic drift (see below), and by consanguinity.

Branched Chain Ketoacid Dehydrogenase Deficiency

Branched chain ketoacid dehydrogenase deficiency (maple syrup urine disease) occurs in 1/176 live births in the Mennonite community of Lancastershire, Pennsylvania. In the U.S. population at large, the disease occurs in only 1/180,000 live births. The predominance of a single mutation (allele) in the branched chain dehydrogenase gene in this group suggests a common origin of the mutation. This may be due to a founder effect.

Natural Selection

Natural selection acts upon genetic variation, increasing the frequencies of alleles that promote survival or fertility (referred to as fitness) and decreasing the frequencies of alleles that reduce fitness. The reduced fitness of most disease-producing alleles helps explain why most genetic diseases are relatively rare. Dominant diseases, in which the disease-causing allele is more readily exposed to the effects of natural selection, tend to have lower allele frequencies than do recessive diseases, where the allele is typically hidden in heterozygotes.

Note

The 4 evolutionary factors responsible for genetic variation in populations are:

•Mutation

•Natural selection

•Genetic drift

•Gene flow

Part II ●●●Medical Genetics

Note

Consanguineous matings are more likely to produce offspring affected with recessive diseases because individuals who share common ancestors are more liable to share disease-causing mutations.

Gene Flow

Gene flow refers to the exchange of genes among populations. Because of gene flow, populations located close to one another often tend to have similar gene frequencies. Gene flow can also cause gene frequencies to change through time: The frequency of sickle cell disease is lower in African Americans in part because of gene flow from other sectors of the U.S. population that do not carry the disease-causing mutation; in addition, the heterozygote advantage for the sickle cell mutation (see text box) has disappeared because malaria has become rare in North America.

Consanguinity and Its Health Consequences

Consanguinity refers to the mating of individuals who are related to one another (typically, a union is considered to be consanguineous if it occurs between individuals related at the second-cousin level or closer). Figure II-2-2 illustrates a pedigree for a consanguineous union. Because of their mutual descent from common ancestors, relatives are more likely to share the same disease-causing genes. Statistically,

•Siblings (II-2 and II-3 or II-4) share 1/2 of their genes.

•First cousins (III-3 and III-4) share 1/8 of their genes (1/2 × 1/2 × 1/2).

•Second cousins (IV-1 and IV-2) share 1/32 of their genes (1/8 × 1/2 × 1/2).

These numbers are referred to as the coefficients of relationship. Thus, if individual III-1 carries a disease-causing allele, there is a 1/2 chance that individual III-3 (his brother) has it and a 1/8 chance that individual III-4 (his first cousin) has it.

I

II

III

IV

Figure II-2-2. A Pedigree Illustrating Consanguinity

Consequently, there is an increased risk of genetic disease in the offspring of consanguineous matings. Dozens of empirical studies have examined the health consequences of consanguinity, particularly first-cousin matings. These studies show that the offspring of first-cousin matings are approximately twice as likely to present with a genetic disease as are the offspring of unrelated matings. The frequency of genetic disease increases further in the offspring of closer unions (e.g., uncle/niece or brother/sister matings).