Old Lecture 11
Textbook assignment: Chapter 5, pages 122-148, with primary emphasis on pages 122-132. .
Important concepts:
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 heterozygote as the starting point. Three sequential steps are needed to determine gene order in a three point cross, identification of the parental phenotypes, identification of the double crossover phenotypes; and 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. 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 more than two phenotypes appear 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 later in these notes). 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 be 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 goes through a rather extended discussion of identifying the middle locus based on comparisons of all possible combinations.)
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
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:
Summary of analysis of three point crosses:
Distance BC = (ABc + abC + AbC +aBc)
Distance AC = Distance AB + Distance BC
= (Abc + aBC + AbC + aBc) + (ABc + abC + AbC + aBc)
= Abc + aBC + ABc + abC + 2AbC + 2aBc)
Genetic maps: Mapping techniques such as these have been used to generate detailed genetic maps for many species. A partial map for Drosophila is presented in Figure 5.14. In addition to its X chromosome, which is also known as chromosome 1, Drosophila also has three autosomes, numbered 2, 3, and 4. Chromosomes 2 and 3 are both over 100 map units in length. Chromosome 4 is much smaller.
Sex differences in recombination: Differences between rates of recombination are often encountered between males and females. In what is probably 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.
Material beyond this point will only be covered superficially because of lack of time. I have attempted to provide brief summaries in these notes. You do not need to know more detail about these topics than is in the notes.
Mapping function: On pages 130-131, the textbook goes through an exercise that attempts to demonstrate why 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. Unfortunately, the explanation is so abbreviated that it cannot be followed in detail and the basic principles that are involved are not clearly explained.
Zero term of Poissson distribution A rather extended argument is presented that when a composite of two, three and four stranded recombination events are taken into account, any number of crossover events between two loci in a meiotic tetrad will on the average generate 50% recombinant gametes and 50% non-recombinant gametes (fig 5.12). Thus, the actual fraction of recombinant gametes generated in a population will reflect how frequently any number of crossovers greater than zero occurs between the two loci. Therefore, the real determinant of recombinational frequency is the probability of no crossovers, as opposed to 1, 2, 3, etc. This number is calculated with a mathematical formulation known as the Poisson distribution, which determines the probability of 0, 1, 2, 3, ...n events occurring when the mean number is small. Thus, for example, if the mean number of crossovers between two loci is 1.0, there is a 37% probability of no crossover in the region, balanced by a similar probability that two or more crossovers will occur in the region. When the mathematical calculations are done, the expected frequency of recombination (RF) is determined by the following formula:
where m is the mean number of recombinations expected in the region and e is the base of natural logarithms. When m is small, e-m , which is the zero term of the Poisson distribution, has a value close to 1.0. This causes RF to be quite small and initially to increase almost linearly with map distance. However, as m increases, the value of RF approaches 0.5 in an asymptotic manner (curve b in figure 5.13). Thus, for small map distances, the curve is close to linear with map distance, but as map distance becomes larger, it veers away more and more, since it can never rise above a 50% recombination frequency. The complexity of this and other mapping functions that have been proposed go far beyond what we can cover in this course. However, it is important to remember that the inaccuracy of direct measurement of long map distances makes it necessary to add many short distances to obtain an accurate genetic map.
Deletion mapping: In Drosophila and certain other insects, somatic chromosomes undergo pairing of homologs and multiple rounds of DNA replication without mitosis to generate large polytene chromosomes in certain tissues, such as the larval salivary gland (see figure 2.17). Small deletions disrupt the pairing of the two homologous chromosomes, and result in loop formation by the non-deleted chromosome (Fig. 9.21). Since small deletions often behave like recessive mutations, it is often possible to associate specific genes with the areas that form loops in heterozygotes between wild type and a deletion mutation. Linkage to such a gene then provides the basis for assigning other genes to the same chromosome, and provides a start toward a physical map of gene locations.
Evidence that crossing over occurs in the tetrad: In certain organisms, such as Neurospora, it is possible to collect spores representing all four of the products of meiosis, which have also undergone one round of mitosis to generate 8 spores that remain oriented in an elongated ascus, such that they can be dissected out in order and used for detailed analysis of the products of meiosis and crossing over. Analysis of the patterns of distribution of recombinant spores make it clear that crossing over occurs at the four stranded stage, as illustrated in Fig. 5.16. We will examine tetrad mapping in greater detail in a future lecture.
Cytological demonstration of crossing over: Studies with chromosomes that contain cytologically detectable end markers have demonstrated clearly that physical crossing over actually occurs, such that ends that were formerly on different chromosomes can be combined on the same chromosome (see Fig. 5.17 in the textbook for an example in maize).
Mechanisms of crossing over: The mechanisms of crossing over are studied both at the cytological level and at the molecular level. Both types of studies have thus far left a number of questions unanswered. At the cytological level, there is still some controversy as to when the process occurs. On page 33, our text suggested that crossing over occurred in the pachytene and that chiasmata in the diplotene are evidence that crossing over has already occurred. However, on page 135, two conflicting theories are discussed, the chiasmatype theory, based on crossover in the pachytene, and the classical theory, which suggests that the actual breaking and rejoining may occur as the chiasmata are being pulled apart.
Molecular crossing over: Details of the exact molecular mechanisms of crossing over are still under study and occupy at least two full lectures in MCDB 3500. Because of the detailed coverage in MCDB 3500, and because of the complexity and uncertainty of the actual mechanisms that are involved, we do not try to cover them in detail in MCDB 2150. It is clear at the molecular level that intermediate structures known as Holliday structures (pages 317-319) physically join together the two DNA molecules that are crossing over for a measurable period of time. Unfortunately, the molecular studies are generally done in organisms like yeast that are not well suited for cytological study, such that the relationship between molecular stages and cytological stages has not yet been clarified. However, one interesting possibility is that the moecular links may form rather early (perhaps in zygonema) and persist until the chiasmata are resolved in diplonema or later. More study is clearly needed.
Mitotic crossing over: In certain rare cases, mitotic chromosomes pair and undergo crossing over. This can been seen, for example, in Drosophila, where heterozygous cells sometimes undergo recombination followed by mitotic separations that generate homozygous recessive cells. In double heterozygotes for fairly closely linked genes with the mutant alleles in a trans relationship, this can result in the formation of twin spots, with small patches of the two recessive phenotypes side by side, as illustrated in figure 5.19.
Sister chromatid exchange. Breakage and rejoining between sister chromatids has been shown to be a common phenomenon (fig. 5.20), although its significance is still not fully understood. There may be a correlation between certain human genetic diseases and increased rates of sister chromatid exchange.
Somatic cell hybridization: A variety of techniques are available for fusing together cultured cells to generate viable products that are essentially the summation of the two parental cells. In certain combinations, chromosomes from one of the parents are lost preferentially. This approach has been used to generate stable lines of mouse and Chinese hamster cells that contain only one or a few human chromosomes. This technique has made it possible to assign many human genes to specific human chromosomes, either by detecting the gene products in the cells containing the chromosomes, or by a molecular hybridizaiton process that we will examine later in the semester.
Linkage and Mendel: Chapter 5 concludes with a short discussion of how Mendel managed to avoid complications due to linkage in his original studies. Although some of the loci he worked with were on the same chromosomes (Table 1, page 141), most of them were so far separated that linkage would not be observed. There was one exception, the combination of tall vs. dwarf plants, together with full vs constricted pods. Mendel did not publish any results for this combination, and it is generally believed that he did not test this particular pair of loci together. Another point to observe in this article is the modern terminology for the loci that Mendel studied. It appears that none of the common textbooks, including ours, have employed the terminology that is actually employed by contemporary pea geneticists.