Text Assignment: Chapter 15, 445 - 457.
Major concepts
Nomenclature used: In the text, alleles at linked loci are shown with a solid line under (or above) them to show the linkage. For purposes of posting these notes in html, the alleles from two linked loci are written without a space between them. Thus, ab+ describes a recessive allele at locus a that is linked to a wild type allele at locus b. Alternatively, the dominant allele may be indicated by a capital letter (aB).
Coupling and repulsion: For two loci on the same autosome, (or sex chromosome in the homogametic sex) there are two possible alternative configurations. If both dominant (or wild-type) loci are carried on the same locus (cis), the arrangement is sometimes described as being in coupling conformation. If the two dominant (or wild-type) loci are on different chromosomes (trans), they can be described as in repulsion conformation. The repulsion (trans) conformation is commonly used to demonstrate crossover. This practice is probably ultimately based on starting with two separate true-breeding stocks, each carrying one of the recessive (or mutant) markers being studied. As an example, a parental cross of ab+/ab+ x a+b/a+b will yield an F1 hybrid of the composition ab+/a+b, which will be a wild-type double heterozygote in a repulsion or trans-configuration.
Crossing over: Because of crossing over during meiosis, which leads to genetic recombination, the linkage between non-allelic mutations on the same chromosome is nearly always less than 100%. However, crossing over does not ever occur on any of the chromosomes in male Drosophila. In addition, in many other species where some degree of crossing over does occur in both sexes, the relative frequencies of crossing over in males and females are often quite different (usually smaller in males and larger in females -- see, for example, figure 15.9).
Linkage on the X chromosome: Because it became possible to identify genes carried on the X chromosome well before other chromosomal assignments could be made, much of the pioneering work on linkage was done with X-linked genes, as described in the text. Studies in the laboratory of Thomas Hunt Morgan rather quickly showed that these genes did not remain totally linked. Although each X-linked allele was transmitted from a heterozygous female to half of her male progeny, studies involving females that were heterozygous at two different X-linked loci revealed that alleles that had originally been on different X chromosomes could be transmitted to the same male offspring, although with a reduced frequency compared to either of the alleles alone. This led Morgan to propose that a genetic exchange between paired chromosomes was occurring at the chiasmata that could be seen during meiotic prophase. He also proposed that crossover would be relatively rare for genes that were close together and more frequent for genes further apart.
Undergraduate research: The next step was taken by Alfred H. Sturtevant, who at the time was an undergraduate student working in Morgan's laboratory. Sturtevant realized that crossover frequencies, which had been proposed by Morgan to be larger for genes that were further apart, might be used to construct a map of the relative postions of the genes on the chromosome. He found that distances were roughly additive for the first 3 genes he studied, and went on to construct a map with the relative positions of five different loci (figure 15.2). This preliminary mapping, described in 1911, was the beginning of detailed chromosomal maps, such the one (from 1935) shown for Drosophila in figure 15.3. A variety of modern maps and other types of genetic information for Drosophila can be obtained from Flybase, an online information service comparable to OMIM and the Mouse Genome Informatics web sites described in earlier lectures.
Mapping with test crosses: Experiments designed to detect linkage are usually done as test crosses. In these experiments, an organism that is heterozygous for the genetic loci whose linkage is being analyzed is crossed with an individual that is homozygous recessive for those genes. In most cases, the heterozygous individual is female because of higher crossover rates. (It is important to use the same sex consistently if results from various experiments are to be compared and used to construct maps). If there is no crossing over, all of the progeny of the test cross will have the same phenotypes as the true-breeding parents of the heterozygote. The amount of crossing over can be evaluated in terms of the fraction of progeny that exhibit recombinant phenotypes (which in a test cross accurately reflects the fraction of gametes with recombinant genotypes).
Map distances: The discussion that follows is based on looking for crossing over between two loci on the same chromosome. If the loci are not on the same chromosome, independent assortment will occur and the test cross will yield a 1:1:1:1 ratio of all four possible phenotypes. For linked loci, the probability of crossing over increases with physical distance between the two loci (although not always strictly linearly). If recombination occurs, some of the progeny of the test cross will no longer exhibit the parental phenotypes. The percentage of recombinants detected in the progeny of the test cross increases with the distance between the genes, and is referred to as map distance. As an example, consider a test cross of a female of genotype AB/ab that yields the following phenotypes: 495 AB, 495 ab, 5 Ab, and 5 aB. In a total of 1000 progeny, there are 5 Ab and 5aB phenotypes, which when added together represent 10 recombination events in 1000 gametes. This corresponds to a recombination frequency of 0.01, more commonly expressed as 1% crossing over.
Map units (centimorgans): A recombination frequency of 1% has historically been called one map unit since the time of the pioneering experiments of Sturtevant and Morgan. Although the term "map unit" is still widely used, one map unit is now often referred to as one centimorgan, honoring Thomas Hunt Morgan. One morgan corresponds to 100 map units, but this unit is too large for practical use, as discussed below. Note that a capital M is used in the abbreviation, cM, so it will not confuse with centimeter, but when centimorgan is written out, a capital M is not used.
Cytological evidence for crossing over: The textbook uses two linked markers in maize for a series of demonstrations. Dominant C1 yields a colored kernel, whereas recessive c1 yields a colorless kernel when homozygous. Dominant Wx yields a starchy kernel, and recessive wx yields a waxy kernel when homozygous. Boxed examples 15.1 and 15.2 show that similar map distances that average 26.7 centimorgans are obtained with these markers in coupling or in repulsion. Example 15.3 looks at recombination of these two markers in a situation where there are visible markers at both ends of one of the parental chromosomes. This historic experiment becomes a bit confusing to interpret because it was not done as a test cross. However, as shown in figure 15.6, it clearly demonstrates that crossing over between the two genetic markers is accompanied by crossing over between the visible end markers of the chromosomes that are involved.
Double crossovers: As the distance between two genetic loci increases, the probability that two crossovers may occur between them begins to increase. If two crossovers occur, the resulting gamete once again has the parental genotype, and the test is scored as if there had been no crossover. Thus, double crossovers that restore the parental genotypes cause map distaces measured in two-point crosses to become smaller than expected for genetic loci that are relatively distant from each other.
Interference: Another phenomenon, called interference, tends to prevent double crossovers from occuring close to each other. Because of this, direct measurements of two point crosses work reasonably well up to about 20 centimorgans, after which the observed rate, based on frequency of recombinant gametes, begins to be substantially less than the actual map distance (figure 15.11). In addition, because unlinked genes exhibit 50% recombination due to independent assortment, it becomes impossible to do a direct measurement of map distances for genes that are at large distances from one another.
Additive distances: One way to determine map distance for genes that are located far from each other is to add the map distances between each of a series of pairs of loci positioned at reasonably short distances along the chromosome. If three genes are oriented ABC on a chromosome, measured distance AB plus measured distance BC will normally be larger than directly measured distance AC. The most accurate chromosomal maps are thus constructed by adding a series of relatively short map distances between more closely spaced alleles.
Crossing over in duplicated chromosomes: In the previous discussion, we have only considered the genotype of individual gametes that are produced as a result of a meiosis in which crossing over occurs. As emphasized in figure 15.8, crossing over occurs in a meiotic tetrad at pachynema (see figure 11.12), and can involve any two of the four strands. In addition, as shown in figure 15.10, double crossovers can involve 2, 3, or all four strands of the tetrad, with each patern generating a different fraction of recombinant gametes. This averages out to 50% recombinant gametes for all of the possibilities.
Map distance correction: As described above, the observed crossover frequency for loci relatively far apart is always less than the map distance obtained by adding distances for a series of relatively closely spaced loci in intermediate positions (figure 15.11). This is due to multiple crossovers (mostly double), with the effect somewhat reduced at short distances by interference. Several mathematical formulations have been developed to attenmp to account for these effects. Our textbook presents two widely used formulations without attempting to go into the mathematical reasoning behind them.
Mapping function: The mapping function developed by Haldane is based on the frequency with which any number of crossovers greater than zero occurs between the two loci, further adjusted for the probability of obtaining recombinant gametes from each class of crossover event. Therefore, the primary determinant of recombinational frequency is 1.0 minus the probability of no crossovers (as opposed to 1, 2, 3, etc.) If one does not take interference into consideration, the Poisson distribution can be used to calculate the probability of 0, 1, 2, 3, ...n events (in this case crossovers) occurring under conditions where the mean number is known and reasonably small. The mathematics go beyond what this class can be expected to do, but the end result is equation 15.1 in the textbook.
Use of F2 frequencies to calculate map distance: Crossing over causes F2 phenotypic frequencies to be intermediate between the 9:3:3:1 ratio expected for independent assortment and the 3:1 ratio of parental phenotypes expected for complete linkage. The actual calculation of map distance is made more complex by the fact that several different genotypes that can be affected differently by recombination must be added together to obtain each phenotype. This makes the calculations sufficiently complex so that one usually works backward from a table of possibilities as shown in boxed example 15.5 and Tables 15.1a and 15.1b. In addition, even when tables are used, a further correction may be needed for differences in crossover rates between males and females (although it is sometimes possible to apply an averaged rate to both sexes without getting into too much trouble).
Doing the calculation: To understand the complexity that is involved, pick a recombination frequency and construct a Punnett square with the four possible gametes in the frequencies predicted from the recombination frequency. Multiply these frequencies together to obtain the frequencies of each of the 16 possible genotypic combinations on the Punnett square. Then add together all of the values for each of the four possible phenotypes. As an example of the unexpected, in table 15.1b, the double recessive frequency (aabb) for a recombination rate of 0.01 is shown as 0.0000. At first this seems unreasonable. However, with the alleles in repulsion and with 0.01 recombination, the ab gametes will have have a frequency of 0.005 (one half of the 0.01 recombination rate, which also includes AB gametes). Multiplying 0.005 by 0.005 yields 0.000025, which when rounded to four decimal places is 0.0000.
Linkage groups: The term linkage group refers to all of the genes that are located on the same chromosome. Those that are close enough together will exhibit linkage in genetic crosses. However, the probability of crossover increases with the physical distance between genes on a chromosome, and genes that are located quite far from each other within a linkage group may not exhibit any detectable linkage in direct genetic tests. The term "linkage group" is also used to refer to genes that exhibit linked behavior in genetic systems where chromosomal assignments have not yet been made.
Linkage to intermediate loci: In Drosophila, linkage can always be demonstrated in males, no matter how far apart the loci are, because of the total absence of crossing over. However, in species where crossing over occurs in both sexes, linkage of genetic loci that are quite far from each other on the same chromosome can only be demonstated by showing that both loci exhibit linkage to other loci located at intermediate positions along the chromosome. Total map distances on some large chromosomes can be well over 100 map units. For example, figure 15.7 indicates that the total map length of the human X chromosome is 224.1 centimorgans. Similarly, chromosome 2 in Drosophila is about 108 centimorgans (figure 15.3).
Three point crosses: In many cases, even after a gene has been shown to be linked to a particular chromosome, its exact placement on the chromosome will not be known. In the next lecture, we will examine the three point cross, which has proven to be a particularly useful tool, both for determining the order of placement of genes on a chromosome, and for calculating corrected map distances. The special value of the three point cross lies in the use of relatively less common double crossover events to identify the middle locus in any group of three genetic loci, and to refine map distances obained by single crossover measurements. Unfortunately, the three point cross is also one of the most difficult concepts in genetics for a beginner to understand fully.
You are strongly
advised to read the lecture 31 notes before coming to that lecture. I will
try to get them prepared as far ahead as possible -- the principles will not
be changed from last year, but the details will be modifed somewhat to match
our current textbook.