our understanding of alleles and genetic linkage, described later. Mendel’s observations remain one of the most important contributions of critical descriptive science in the history of genetics.
Hardy–Weinberg Equilibrium
Another historical landmark in genetics occurred in the early 1900s as evolutionary biologists attempted to explain why the frequency of a dominant trait or disease in the population did not increase until everyone in the population was affected. The answer to this question was provided independently by Hardy (1908) and Weinberg (1908), who predicted the behavior of genetic traits in a population using the binomial theorem. Their proof, now called the Hardy–Weinberg theorem, shows that in a large, randomly mating population, the frequency of an autosomal genetic trait (a trait that is not dependent on sex) will achieve and remain in a state of equilibrium after one generation. Several evolutionary forces can alter the equilibrium frequencies, including selection for or against a phenotype, migration into or out of a population, new mutations, or genetic drift, a phenomenon in which allele frequencies fluctuate in a small population due to chance.
Figure 2.1 Principles of Mendel’s first law of segregation of heritable characters for a dominant trait.
In a two‐allele autosomal system with alleles “A” and “a” (having frequencies p and q, respectively), p + q = 1 and p2 + 2pq + q2 = 1. The Hardy–Weinberg theorem predicts that the frequencies of genotypes “AA”, “Aa,” and “aa” are p2, 2pq, and q2, respectively. Various manipulations of these algebraic formulas allow many useful calculations, such as carrier frequencies of diseases, disease prevalence, and gross estimates of penetrance, the proportion of individuals with a specific genotype that exhibit a particular phenotype. Examples of applications of the Hardy–Weinberg theorem are shown in Table 2.1.
Figure 2.2 Principles of Mendel’s second law of independent assortment with a dominant trait.
Table 2.1 Useful applications of Hardy–Weinberg theory.
| Recall that p + q = 1 and p2 + 2pq + q2 = 1 Example 1. Cystic fibrosis (CF), an autosomal recessive disease, has an incidence of 1 in 3200. What is the frequency of CF carriers in the general population?The population frequency of the disease (1 in 3200) is represented by q2In order to calculate the frequency of the carrier state (2pq), one must first determine q q = √(1/3200) = 1/57 Since p + q = 1, p = 56/57 The frequency of CF carriers is calculated as 2pq = 2(1/57)(56/57) = 1/29, or 0.0344. Example 2. The frequency of the allele (q) for an autosomal dominant disorder in 1/100. What is the frequency of the disease itself in the population?Since the frequency of the disease allele in 1/100, the frequency of the normal allele (p) = 1 − 1/100 = 99/100.Since the disease is dominant, both heterozygous carriers and homozygous individuals are affected with the disease: 2pq + q2 = 2(99/100)(1/100) + (1/100)2 = 0.0199 Example 3. An autosomal dominant disorder with incomplete penetrance (f) has a population prevalence of 16/1000. If the allele frequency for the normal allele (p) is 0.99, what is the estimated penetrance of the disease allele?Since p = 0.99, then q = 0.01As in Example 2, both heterozygous and homozygous gene carriers are affected (assuming no difference in penetrance) between homozygotes and heterozygotes. Therefore, f(q2) + f(2pq) = 0.016 f(q2 + 2pq) = 0.016 f((0.01)2 + 2(0.99)(0.01)) = 0.016 f(0.0199) = 0.016 f = 0.804 |
DNA, Genes, and Chromosomes
Structure of DNA
When Mendel described the unit of inheritance, he did not know the underlying biological factor. It was 90 years later when the actual genetic molecule was identified. The fundamental unit of inheritance that Mendel’s work uncovered was later termed “the gene.” A gene contains the information for synthesizing proteins necessary for human development, cellular and organ structure, and biological function. DNA is the molecule that comprises the gene and encodes information for synthesizing both proteins and ribonucleic acid (RNA). DNA is present in the nucleus of virtually every cell in the body. It is made up of three components: a sugar, a phosphate, and a base. In DNA, the sugar is deoxyribose, whereas in RNA, the sugar is ribose. The four bases in DNA are the pyrimidines adenine (A) and guanine (G) and the purines cytosine (C) and thymine (T). A DNA sequence is often described as an ordered list of bases, each represented by the first letter of its name (e.g. ACTGAAACTTGATT). A nucleoside is a molecule made of a base and a sugar; a nucleotide is made by adding a phosphate to a nucleoside.
A single strand of DNA is a polynucleotide, consisting of nucleotides bonded together. A single strand of DNA is, however, unstable. The double‐helical nature of DNA, which confers stability to the molecule, was hypothesized in 1953 by J. D. Watson and F. H.C. Crick. Their cohesive theory of the structure of DNA accounted for some of the previously identified properties of DNA (Watson and Crick 1953).
Figure 2.3 The DNA double helix is packaged and condensed in several different forms.
(Source: Reprinted by permission from Thompson et al. (1991).)
Specifically, Watson and Crick postulated that DNA is a double‐stranded structure and that the two strands of DNA are arranged in an antiparallel orientation (Watson 1968). In the central portion of the molecule, hydrogen bonds link a base with its complement, such that a purine always bonds with a pyrimidine (e.g. adenine always bonds with thymine and guanine always bonds with cytosine). The conformation of the resultant molecule is the double helix, which undergoes several levels of compacting to fit within the cell (Figure 2.3).
The sequence of DNA bases represents a code for synthesizing proteins. The fundamental unit of this genetic code is termed a codon, which consists of three nucleotides. Since there are four different nucleotides (one made with each of the four bases) and a codon is made of three nucleotides, there are 43, or 64, different codons. However, these 64 codons specify only 20 different amino acids, which are the building blocks of proteins. Thus, the genetic code is degenerated, meaning that different codons may code for the same amino acid (Figure 2.4). In addition, some codons act as punctuation. For instance, one specific codon signals the start for the reading of the DNA and several other codons signal the reading process to cease. These reading signals are called start and stop codons, respectively (see Figure 2.4).
While some of the DNA in a cell codes for a protein product, the vast majority of the DNA sequence does not carry information for the formation of a protein. Within a gene, exons are the portions utilized to make proteins. Introns are the sequences between exons that do not code for the final protein product. The size and number of introns and exons vary dramatically between genes.
The central dogma of genetics is that the utilization of DNA is unidirectional such that DNA → RNA → protein (Figure 2.5). Specifically,
