Human Genetics II: Population Genetics — Hardy–Weinberg Equilibrium and Its Applications, Random, Assortative and Consanguineous Mating, the Inbreeding Coefficient, Genetic Load, Isolates, Drift, Genetic Distance and Balanced and Transient Polymorphism; and Molecular Genetics — DNA, RNA, the Genetic Code, Protein Synthesis, RFLPs, VNTRs, STRs, SNPs, Mitochondrial DNA and Genic and Genomic Mutations

G.H. Hardy, a Cambridge mathematician, and Wilhelm Weinberg, a Stuttgart physician, showed independently in 1908 that in a large, randomly mating population with no mutation, selection or migration, allele frequencies do not change from generation to generation, and genotype frequencies settle after one generation into the proportions p² : 2pq : q² for a locus with two alleles of frequencies p and q (p + q = 1, so p² + 2pq + q² = 1). The law is the null model of population genetics: departures from it reveal one of the forces at work. Its applications are three. First, the carrier frequency of a recessive condition can be found from the frequency of affected individuals, who are not otherwise distinguishable from carriers. Worked: albinism occurs in 1 in 10,000 births. q² = 1/10,000, so q = 1/100 = 0.01 and p = 0.99; carriers 2pq = 2 × 0.99 × 0.01 = 0.0198, about 1 in 50 — so for every affected person there are roughly 200 carriers, which is why recessive disease persists. Second, allele frequencies can be read directly where genotypes are distinguishable. Worked: in a village of 500 people the MN blood groups are M 180 (36%), MN 240 (48%) and N 80 (16%). Frequency of M = (2 × 180 + 240) ÷ 1,000 = 600 ÷ 1,000 = 0.6, and of N = 0.4; the expected Hardy–Weinberg genotype counts are 0.36 × 500 = 180, 0.48 × 500 = 240 and 0.16 × 500 = 80, so the village is in equilibrium. Third, for an X-linked recessive such as red–green colour blindness with frequency q in males (about 0.08), the frequency of affected females is q² (0.0064), which is why the condition is common in men and rare in women. The ABO system, with three alleles, extends the law to (p + q + r)² = 1, and Bernstein's 1924 analysis used it to prove that ABO is one locus with three alleles.

Random mating (panmixia) is the Hardy–Weinberg assumption: any individual is equally likely to mate with any other of the opposite sex, whatever their genotype. Assortative mating is mate choice by phenotype — positive when like marries like (stature, skin colour, deafness, education) and negative when unlike marries unlike; positive assortment raises the frequency of homozygotes at the loci concerned without changing allele frequencies. Consanguineous mating is marriage between blood relatives — first cousins, uncle and niece (both common in South India, where cross-cousin and maternal-uncle marriages are preferred), second cousins — and it raises homozygosity at every locus. Its measure is Sewall Wright's inbreeding coefficient F (1922): the probability that the two alleles an individual carries at a locus are identical by descent, that is, copies of one allele in a common ancestor. For a path through n individuals connecting the parents via a common ancestor, F = Σ (1/2)^n over all paths (× (1 + F of the ancestor) if the ancestor is inbred). Worked: first cousins share two grandparents. The path from the child's father up to one shared grandparent and down to the child's mother runs father → father's parent → grandparent → mother's parent → mother, n = 5 individuals, contributing (1/2)⁵ = 1/32; the other shared grandparent gives a second path of the same length, so F = 2 × 1/32 = 1/16 = 0.0625. So the offspring of first cousins has F = 1/16; of double first cousins, uncle–niece or half-siblings 1/8; of second cousins 1/64; of full siblings or parent–child 1/4. The risk of a recessive disease in a first-cousin marriage is q² + Fpq rather than q²: for q = 0.01, 0.0001 + 0.0625 × 0.99 × 0.01 = 0.0001 + 0.00062 ≈ 0.00072, about seven times the random-mating risk. Genetic load (Muller, 1950; Crow) is the reduction in mean fitness of a population relative to its fittest genotype, caused by the deleterious recessive alleles every person carries (an estimated 3–5 lethal equivalents); mutational load, segregational load (the cost of maintaining a balanced polymorphism, as with sickle cell) and substitutional load are its components, and consanguinity exposes it as raised infant mortality. A genetic isolate is a population closed to gene flow by geography, religion, caste or language — the Andamanese, the Parsis, Ashkenazi Jews, many Indian castes — in which drift and inbreeding raise the frequency of otherwise rare alleles; Dahlberg's isolate size (1948) estimates the effective breeding population from the frequency of cousin marriage, and Wahlund's effect (1928) is the deficit of heterozygotes seen when subdivided isolates are pooled and treated as one population.

Genetic drift is random change in allele frequencies from generation to generation through sampling error in small populations — Sewall Wright's contribution to the synthesis. Its two dramatic forms are the founder effect (a colony started by few individuals carries only their alleles: the Amish and Ellis-van Creveld syndrome, the Afrikaners and variegate porphyria) and the bottleneck (a population reduced to few survivors loses variation, as the Andamanese and, at species level, humans did). Drift, isolation and inbreeding together explain why isolates differ from their neighbours at random, while selection explains directional, environmental patterns. Genetic distance is a number summarising how much two populations differ in allele frequencies across many loci: Nei's standard distance D (1972) measures the accumulated codon differences per locus, D = −ln I where I is the normalised identity of genes, and Cavalli-Sforza and Edwards's chord distance (1967) treats frequencies as points on a sphere; either can be turned into a tree (UPGMA, neighbour-joining) of populations, and Cavalli-Sforza's History and Geography of Human Genes (1994) mapped the world that way. Wright's fixation index F_ST measures the proportion of total variation that lies between populations. A genetic polymorphism (Ford, 1940) is the occurrence in one population of two or more alleles at a locus, the rarest at a frequency too high (conventionally above 1%) to be maintained by mutation alone. A balanced polymorphism is maintained by selection — usually heterozygote advantage: the sickle-cell allele HbS, whose heterozygotes (HbA/HbS) resist falciparum malaria while homozygotes die of anaemia, reaches 10–20% where malaria is holoendemic (Allison, 1954), and G6PD deficiency, the thalassaemias and Duffy negativity are its companions; the ABO and HLA systems are also probably balanced. A transient polymorphism is a passing state in which one allele is replacing another under directional selection — the peppered moth's melanic form during industrialisation and its decline afterward, or lactase persistence spreading in pastoralists; the frequencies are moving, not held.

DNA, the double helix of Watson and Crick (1953, on Franklin's and Wilkins's X-ray data), is two antiparallel chains of nucleotides — a deoxyribose sugar, a phosphate and one of four bases, adenine, guanine (purines), thymine and cytosine (pyrimidines) — held together by hydrogen bonds between complementary pairs, A with T (two bonds) and G with C (three). Its replication is semiconservative (Meselson and Stahl, 1958), each strand templating a new partner. RNA has ribose, uracil in place of thymine and is usually single-stranded: messenger RNA carries the gene's sequence from nucleus to ribosome, transfer RNA brings each amino acid to the ribosome by matching its anticodon to a codon, and ribosomal RNA forms the ribosome itself. The central dogma (Crick, 1958) runs DNA → RNA → protein: transcription by RNA polymerase, then in eukaryotes splicing out of introns and capping and tailing, then translation. The genetic code, cracked by Nirenberg, Matthaei, Khorana and Holley (1961–66), reads triplets: 64 codons, of which 61 specify the 20 amino acids and three (UAA, UAG, UGA) are stop signals, with AUG (methionine) the start; it is degenerate (most amino acids have several codons), non-overlapping, commaless and nearly universal, mitochondria having a few variants. Protein structure is primary (the amino-acid sequence), secondary (α-helix and β-sheet), tertiary (the folded chain) and quaternary (several chains: haemoglobin's two α and two β); sickle-cell haemoglobin is a single base change, GAG → GTG, replacing glutamic acid by valine at position 6 of the β-chain — the first "molecular disease" (Pauling, 1949; Ingram, 1956). The human nuclear genome is about 3.1 billion base pairs carrying some 20,000 protein-coding genes, under 2% of the sequence, the rest being introns, regulatory sequences and repeats.

Mutation is the ultimate source of all variation, and it is classified by scale. Gene (genic, point) mutations change one or a few bases: substitutions are transitions (purine for purine, A↔G, or pyrimidine for pyrimidine, C↔T) or transversions (purine for pyrimidine); by effect they are silent or synonymous (a different codon, the same amino acid — the degeneracy of the code), missense (a different amino acid — sickle cell), or nonsense (a stop codon — a truncated protein, as in many β-thalassaemias); insertions and deletions of a number of bases not divisible by three cause frameshifts that scramble everything downstream (cystic fibrosis's ΔF508 deletes three bases and so is in-frame); and trinucleotide-repeat expansions (CAG in Huntington's disease, CGG in fragile X) grow across generations, producing anticipation. Chromosomal (structural) mutations rearrange segments — deletion, duplication, inversion, translocation — and genomic (numerical) mutations change chromosome number: aneuploidy (trisomy, monosomy) through non-disjunction, and polyploidy (triploidy is lethal in humans, though common in plants). Mutation rates for human genes are about 10⁻⁵ to 10⁻⁶ per locus per generation, and each child carries some 60–70 new base changes; most mutations are neutral or harmful, a few — lactase persistence, the EPAS1 altitude allele, the Duffy-null malaria resistance — are the raw material of adaptation. Somatic mutations affect only the body and its clones (cancer); germ-line mutations are inherited.