Revised November 11, 1999. This lecture is based on 1998 Lecture 13.

Lecture 31, MCDB 2150, Fall 1999

LINKAGE: GENE ORDER, CHROMOSOME MAPS

Textbook assignment: Chapter 15, Pages 458 - 464.

Important concepts:

Introduction: The overview of three point crosses that follows has been carried forward almost unchanged from last year. In general, it parallels our current textbook and I have inserted references to figures in our textbook. However, I have deliberately not tried to alter the presentation to match the textbook too closely. The three point cross is a sufficiently complex topic so that it can probably be better understood when approached from two slightly different perspectives.

Three point crosses: When a genetic locus is first shown to be linked to a particular chromosome, its exact placement on the chromosome will generally not be known. The three point cross is a particularly useful technique for identifying the position of a previously unmapped locus relative to two other loci that have already been mapped. In this assay, a heterozygote for three linked genes is crossed with a homozygous recessive for all three. As will be discussed below, a three point cross makes it possible to determine which of the three loci is located between the other two. It also provides information on the occurrence of double crossovers, thus permitting calculation of corrected map distance between the two outside loci.

Overview of analysis of three point crosses: After verifying that the genetic loci under study are linked, the next order of business is to determine the relative positions of the three genes on the chromosome. This causes beginning genetics students more trouble than almost anything else in the course. The process is actually quite straightforward, but it requires a lot of concentration and precise analysis of the data. One of the problems is that some of the mutations are usually introduced from one parent and the rest from the other, such that there is not a simple +++/abc or ABC/abc heterozygote as the starting point. Three sequential steps are needed to determine gene order in a three point cross: 1) identification of the parental phenotypes, 2) identification of the double crossover phenotypes; and 3) comparison of those two phenotypes to identify the middle gene. Once gene order is known, it becomes possible to calculate map distances and the extent of interference that one crossing over event exerts on a second nearby event.

Paired events: When analyzing data from a three point cross, it is important to recognize that each crossover event will generate a reciprocal pair of phenotypic combinations (figure 15.14). Thus, if we start with a+b+c+ and abc, with the three loci known to occur in that order, a+b+c and abc+ will be a reciprocal pair generated by a crossover between b and c. Similarly, a+bc+ and ab+c will be the reciprocal products of a double crossover. The frequency of a crossover event is always determined by adding together the numbers of the two reciprocal phenotypes and then dividing by the total nunber of progeny.

The following paragraphs describe the analysis of a three point cross in greater detail.

1. Verify linkage: Because a three point cross is normally done as a test cross of an obligate heterozygote at all three loci with a triple recessive, the phenotypes of the progeny precisely reflect the genotypes of the gametes produced by the heterozygote. The heterozygote is initially produced by crossing true-breeding strains that are wild type at all loci except the three being tested. The three mutant alleles can all be on one chromosome (sometimes referred to as "in coupling") or two on one chromosome and the third on a separate chromosome (sometimes referred to as "in repulsion"). The specific combinations of mutant and wild type alleles that the heterozygote received from its true-breeding parents are referred to as "parental". If there is a detectable amount of linkage in the cross, which there must in order to obtain meaningful informaiton about map positions and distances, recombinant gametes will be less frequent than those with the original parental combinations of alleles. If the most plentiful class of phenotypes contains more than two different phenotypes in substantially equal numbers, linkage has not been demonstrated. This can mean that one of the loci is not linked to the others, or that it is linked but too distant on the chromosome to demonstrate linkage, or that something else is wrong with the experiment.

2. Identifying the parental genotypes. In many cases, the parental genotypes are already known from the genotypes of the true breeding parents of the obligate triple heterozygote. However, if this information is not available (which is frequently true in problems given to students to solve) or if there is a need to verify that the heterozygote has been constructed correctly, the two progeny phenotypes that are present in the largest numbers can be used to identify the two non-recombinant parental genotypes.

3. Identifying the double recombinant genotypes: After identifying the parental genotypes, the next step is to identify the double recombinants. Because the frequency of a double recombination is in theory the product of the frequencies of the two single recombination events, the double recombinants are expected to be least frequent reciprocal pair of recombinant phenotypes. Thus, double recombinants are identified by looking for the rarest phenotypic classes and verifying that they are a reciprocal pair. The four intermediate frequency phenotypes that remain will reflect the two possible single crossovers between the middle marker and one or the other of the end markers.

4. Identifying the middle locus: A double crossover is completely invisible in a two point cross because the second crossover between two loci restores the original pairing of the two loci (this assumes both crossovers involve the same two strands of the tetrad, as discussed in the previous lecture). It is only when there is a third locus between the two points of crossover that the genetic effects of a double crossover can be seen. This relationship is used to identify the middle locus in a three point cross. Thus, after the pair of phenotypes that reflect the double crossover is identified by virtue of being the least frequent, the combinations of alleles that they contain are compared to the combinations of alleles in the two parental genomes. The alleles at two of the loci in any double crossover will be identical to those of one of the parental classes, whereas the allele at the third locus will have been derived from the other parent. Specifically, the two outside alleles will remain in the same relationship to each other, while the one in the middle will have two new partners. If we start with ABC and abc, a double crossover will yield AbC and aBc. Thus, the allele that is switched relative to the other two is the one in the middle. This is a very basic concept that can be verified easily with a simple diagram when needed. However, it also has a long history of causing confusion to students in genetics courses. (Note that the textbook uses a diagram comparing all possible combinations to identify the middle locus.)

5. Determine map distances: As prevously discussed, directly measured map distance in map units (centimorgans) is the sum of frequencies of all events in which two genes are recombined, converted to a percentage. In the example above, map distance AB is 100 x the sum of Abc + aBC + AbC + aBc divided by the total number of progeny examined. Map distance BC is 100 x the sum of ABc + abC + aBc + AbC divided by number of progeny.

6. Calculate Interference: For closely spaced markers, double crossovers usually do not occur as frequently as would be expected for randomly-occurring independent events. This phenomenon is called interference, which may be caused at least partially by structural problems associated with the formation of two chiasmata close to each other. However, interference can also occur over greater distances, suggesting other factors, such as the impact of three or four strand double crossing over, must also be involved. Interference is described mathematically as

I = 1.0 - (observed double recombinants / expected double recombinants).

The expected frequency of double recombination is the product of the two observed single recombinations (that is, the probability of the double event occurring if the two single events are totally independent). Thus, if observed double recombination is only 0.4 X the expected value, the interference is 1.0 - 0.4 = 0.6. Note that our textbook refers to observed frequency of double recombinants divided by expected frequency of double recombinants as the coefficient of coincidence, identified as "C". . When this approach is taken interference can be calculated as:

I = 1.0 - C

Summary of analysis of three point crosses:

  1. Verify linkage (absence of independent assortment).
  2. Identify parental classes (the two most frequent classes).
  3. Identify double recombinants (the two least frequent classes).
  4. Identify the middle locus (the one whose allele changes both partners).
  5. Determine map distance for each interval (100 x recombinants / total progeny).
  6. Calculate the interference value (I = 1.0 - observed/expected double reconbinants)
Adding intermediate map distances for greater accuracy: Double crossovers involving the same pair of strands in the tetrad reduce the frequency of observed crossing over between the outside markers in a three point cross. In addition, observed crossover frequencies can never exceed 50%. This causes directly measured distances to deviate increasingly from a linear relationship to true map distance as loci become farther apart, as discussed in the previous lecture. Thus, a direct measurement of the map distance between two loci becomes increasingly inaccurate as the separation between loci increases. It is therefore necessary to add together intermediate distances (ideally less than 10 map units each) to obtain a reasonably accurate total distance between more distant loci. As this is done, the numbers of double recombinants (each of which reflects two recombinaiton events) are added twice to the direct measurements of recombination between the outside markers. The following example is based on crossing over between ABC and abc, with the loci known to be arranged in that order.

Genetic maps: Mapping techniques such as these have been used to generate detailed genetic maps for many species. Genetic maps for chromosomes in various species are presented in figures 15.3, 15.9, 15.16, 15.17, and 15.19. Mapping techniques will be examined in greater detail in the next lecture.

Sex differences in recombination:As mentioned briefly in the previous lecture, differences in rates of recombination are often encountered between males and females. In the most extreme case, there is no recombination in male Drosophila. Recombination rates show a tendancy to be higher in the homogametic sex of many species. In humans and typical mammals, females exhibit higher rates of recombination than males. Note that in male Drosophila any autosomal linkage, no matter how great the map distance, will be seen as absolute linkage with no recombination. Thus, widely separated loci on the same autosome will behave very differently in male and female Drosophila.

Linkage in homogametic sex chromosomes: Studies of linkage in sex chromosomes that occur in pairs are done very much like studies on autosomes, except that the test cross is done with a hemizygous recessive partner. Alternatively, the results can be read without regard to the genotype of the heterogametic partner by only examining the phenotypes displayed by heterogametic offspring. Thus, for example, crossing over in an XX female Drosophila can be observed in the male progeny of any cross. If a male carrying recessive alleles for all loci under examination is mated to the heterozygous female, the results of crossing over can also be examined in the female progeny.

Multifactor chromosome mapping: As discussed in the textbook, it is possible in theory to do simultaneous mapping of four or more loci. However, the number of possible phenotypic combinations is multiplied by two for each new locus, and soon gets out of hand. Because of this, mapping is usually done in very short segments, with the results added together to generate more complex maps, as illustrated in figure 15.15. When large numbers of markers are involved, the process is usually computerized. As shown in figure 15.16, various types of polymorphic DNA markers now play a very important role in the overall process of chromosome mapping. We will examine that theme further in the next lecture as we study genetic mapping in humans.