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MAPPING HEREDITY: USING PROBABILISTIC MODELS AND ALGORITHMS TO MAP GENES AND GENOMES 27 GENETIC MAPPING The Concept of Genetic Maps Genetic mapping is based on the perhaps counterintuitive notion that it is possible to find where a gene is without knowing what it is. Specifically, it is possible to identify the location of an unknown disease-causing gene by correlating the inheritance pattern of the disease in families with the inheritance pattern of known genetic markers. To understand the foundation of genetic mapping, it is useful to return to the work of Gregor Mendel. Based on his experiments with peas (see Chapter 1), Mendel concluded that individuals possess two copies, called alleles, of each gene. Mendel's Laws of Inheritance are as follows: ⢠First Law. For any gene, each parent transmits one allele chosen at random to its offspring. ⢠Second Law. For any two genes, the alleles transmitted by a parent are independent (that is, there is no correlation in the alleles transmitted). Although Mendel's First Law has held up well over the past 130 years, the Second Law turned out to be false in general. Two genes on different chromosomes show no correlation in their inheritance pattern, but genes on the same chromosome typically show correlation. Consider the backcross in Figure 2.1, showing the inheritance of two genes A and B on the same chromosome. The F1 individual carries one chromosome with alleles a1 and b1 at the two genes and another chromosome with alleles a2 and b2. Often, one or the other chromosome is transmitted completely intact to the offspring. If this always happened, the inheritance pattern at the two genes would be completely dependent: a1 would always be co-inherited with b1. But the situation is more interesting. Crossing over can occur at random points along the chromosomes, involving an even swap of DNA material. If a crossover occurs between genes A and B, it results in recombination between the genes, producing a chromosome carrying a new combination of alleles: a1b2 or a2b1. In fact, multiple crossovers can occur along a chromosome;
MAPPING HEREDITY: USING PROBABILISTIC MODELS AND ALGORITHMS TO MAP GENES AND GENOMES 28 recombination between two loci will result whenever an odd number of crossovers occur. Figure 2.1 Schematic drawing of genetic recombination in an F1 heterozygote with distinct alleles at two loci (marked as A and B) on a chromosome. When no recombination occurs between A and B in meiosis, chromosomes carrying the original pair of alleles result. When recombination occurs, the resulting chromosomes carry a new combination of alleles. Genetic mapping is based on the recognition that the recombination frequency q between two genes (or loci) provides a measure of the distance between them. If two genes are close together, θ will be small. If they lie farther apart, q will be larger. If the recombination frequency is significantly less than 0.50, the genes are said to be linked. The first genetic linkage map (Figure 2.2), showing the location of six genes in the fruit fly Drosophila melanogaster, was constructed in 1911 by Alfred Sturtevant, when he was still a sophomore at Columbia University en route to a career as a great geneticist. Genetic maps were a triumph of abstract mathematical reasoning: Sturtevant was able to chart the location of mutations affecting fly developmentâeven though he understood neither the biochemical basis of the defects nor even that genes were made of DNA! The genetic distance dA,B between two genes A and B (measured in units called morgans, after the fly geneticist Thomas Hunt Morgan) is defined as the expected number of crossovers between the genes. If one assumes that crossovers are distributed independently with respect to one
MAPPING HEREDITY: USING PROBABILISTIC MODELS AND ALGORITHMS TO MAP GENES AND GENOMES 29 another, genetic distance can easily be converted into recombination frequency. (This assumption of independence is not quite right but is adequate for many purposes.) For the number of crossovers between genes A and B will then be Poisson distributed with mean d = dA,B, and so the probability of an odd number of crossovers can be shown (by summing alternate terms of the Poisson distribution) to be Figure 2.2 The first genetic map, showing six loci on the Drosophila X chromosome, was constructed by Alfred Sturtevant in 1911. This equation, relating recombination frequency to genetic distance, is known as Haldane's mapping function. For small distances, the formula reduces to θ â d, which reflects the fact that the possibility of more than one crossover can be neglected. For large distances d, the recombination frequency θ approaches 0.50âthat is, independent assortment. Mammalian chromosomes are typically 1 to 3 morgans in length. Geneticists typically report distances between genes in centimorgans. Incidentally, genetic distance between two genes is not necessarily proportional to the physical distance measured in nucleotides. Since crossing over is a biological process carried out by enzymes acting on the chromosome, the distribution of crossovers need not be (and typically is not) uniform with respect to the DNA sequence. Accordingly, molecular geneticists work with two different kinds of maps: genetic maps based on crossover frequency and physical maps based on nucleotide distances. There can be considerable inhomogeneity between the maps, although human geneticists often employ the rough rule of thumb of 1 centimorgan â1 megabase. (The relationship between genetic and physical length varies among organisms: 1 centimorgan is about 2 megabases in the mouse, about 200 kilobases in the nematode worm Caenorhabditis elegans, and about 3 kilobases in yeast.)
