Mapping the human genome 1

Linkage

What is it?

Mendel's second law (of independent assortment) breaks down in one important way - when two genes lie close together on the same chromosome. In this case, alleles which were inherited from one parent tend to stick together when transmitted to the next generation because they are part of the same DNA molecule. However, the further apart two genes are along the molecule, the more likely it is that a meiotic crossover can occur between them and thus create a new combination of alleles. By measuring the frequency of recombinant chromosomes in the progeny, we can estimate the distance that separates the two genes and can make a genetic map.

Such maps are not made just to satisfy scientific curiosity, they have direct application both in science and in medicine.

• First, by mapping the gene responsible for a genetic disease, we can identify it even when we have little or no idea what it does. For examples, see the cystic fibrosis cloning story or the cloning of TSC1 (M. van Slegtenhorst et al. Identification of the tuberous sclerosis gene TSC1 on chromosome 9q34. Science 277:805-808, 1997.).
• Also, even before a gene is identified, if it can be mapped with respect to other genes or to anonymous segments of DNA (known as markers or marker loci), then information gained from studying the linked loci can be used to deduce, for instance, whether or not a person is a carrier of a mutant gene or to give antenatal diagnosis as to whether an embryo is affected with the disease.

The mathematics of linkage analysis can be frightening. However, the fundamentals of the subject are easy to grasp particularly if we start by studying experimental organisms in which we can set up those crosses which we need. Later on we must consider how to make the same type of measurements in humans whose "crosses" cannot be experimentally manipulated but where we must make deductions from families in which genetic diseases (or interesting variants) are present.

Measurement in experimental organisms such as Drosophila

A female Drosophila melanogaster laying an egg. Note her (wild type) red eye colour. From Microsoft Encarta Encyclopedia

The first observation of data from a dihybrid cross which did not fit the predicted Mendelian 9:3:3:1 ratio were made by Bateson and Punnett investigating genes affecting flower pigmentation and seed shape in sweet peas. However, the first thorough investigation was conducted by Thomas Hunt Morgan using the fruitfly Drosophila melanogaster. To minimize the variables he considered a cross between fruitflies in which the females were heterozygous at two loci, the genes purple and vestigial (one affecting eye colour and the other wing shape) while the males were homozygous for each mutant gene. The mutant alleles are written pr and vg respectively and the "wild type" alleles are written pr⁺ and vg⁺.

Morgan's First Cross:

"precross"          pr+pr+ vg+vg+    x    prpr vgvg
                                    /
                                   /
                                  /
                                 /
 backcross                pr+pr vg+vg    x    prpr vgvg
                           (females)           (males)
                                         |
                                         |
                                         |
                                         V
 progeny        pr+pr vg+vg,   pr+pr vgvg,    prpr vg+vg,     prpr vgvg
 phenotype      wild type    red, vestigial  purple, normal   purple, vestigial
 expected ratio     1      :        1      :       1       :      1

The table shows the actual progeny observed:

Backcross to measure linkage between pr and vg

Phenotype	female gamete	Observed	Expected
wild type	pr+, vg+	1339	709.75
red, vestigial	pr+, vg	151	709.75
purple, normal	pr, vg+	154	709.75
purple, vestigial	pr, vg	1195	709.75

Even without doing any statistics on this result it is obvious that it is very far from the Mendelian expectation.

The reason is that the two genes under consideration are on the same chromosome as shown below in the diagram and the parental combinations of alleles remain together unless separated by a recombination event.

The closer together two genes are, the more likely they are to be inherited in the parental combination.

We can quantify this statement. We define the Recombination Fraction, theta.
q = (number of recombinant progeny) / (total number of progeny)
Theta must lie in the range from 0 to 0.5. A value of 0 means that the two genes are so close to each other that they never recombine, a value of 0.5 implies that the genes are unlinked. (The maximum value of 0.5 and not 1 comes from the fact that crossing over takes place after DNA replication and involves only one chromatid per chromosome of the pair, see diagram.) In this case, the recombination fraction between the purple and vestigial genes is (151+154) / (1339+151+154+1195) = 0.107

The linkage map

Because genes are organized along a linear structure, a DNA molecule, we could expect to create a linear map if we measure the frequencies of recombination between them. We make the recombination frequency the measure of the genetic distance between loci. The map unit corresponds to 1% recombination and is named a centiMorgan in honour of Thomas Hunt Morgan. So the purple and vestigial genes above are 10.7cM apart.

SAQ

1. Here is a table of recombination frequencies for pairs of X linked genes in Drosophila. Use the information to construct a map of the chromosome.

Answer

Three point crosses

The data in the question above come from seven separate crosses each involving only two genes. If a cross is set up involving more than one pair of genes it can confirm the approximately linear nature of the map and, by consideration of the relative frequencies of different classes of offspring it will also show directly the order of the genes.

Here is an example of a cross set up by Sturtevant between Drosphila females heterozygous for yellow, white and miniature and males hemizygous for the same three mutations. Notice that in this case the genetic notation has changed to an alternative form. When it is quite clear which gene we are referring to, it is acceptable simply to refer to the wild type allele as + instead of for instance, y⁺ or w⁺ etc.

The male gamete received by any progeny in the above cross is either an X chromosome bearing y w m or a Y chromosome, in either case the genotype of the female gamete is obvious. The order of the genes is as written but it could have been deduced by considering which is the rarest class of female gametes. That must have been due to double recombination and its frequency will be, at most, the product of the frequencies of the two single crossovers. In fact, because the presence of one crossover reduces the likelihood of any other in its neighbourhood, the observed frequency of double crossovers is less than this.

The map distances deduced from the above data are:

y to w, 100 * (28 + 32 + 6 + 3) / 10,495 = 0.66 cM
w to m, 100 * (1,754 + 1,700 + 6 + 3) / 10,495 = 33cM
y to m, 100 * (1,754 + 1,700 + 28 + 32) / 10,495 = 33.48 cM

Recommended reading

The topics include

• estimation of recombination frequency
• genetic maps
• the centiMorgan

Read the relevant chapter in any basic (not specifically aimed at human) genetics textbook. One good possibility is Weaver and Hedrick, Genetics, 3rd edition, pub. W.C. Brown, ch. 5 pp104 - 113. See the end of the next lecture for the relevant material from the recommended course text books.

More SAQs

Unfortunately the virtual fly lab to which the question below refers went commercial so we can no longer do this activity. So imagine it!! and then look at the answer. I'll improve this question when I have time!

2. Try setting up a cross using the "Virtual Fly Lab" to measure the genetic distance between white (eyes) and miniature (wings). (Or try here if the other URL is slow to reply.) This activity is best performed in the morning before America wakes up.