Hartl, Jones - Genetics. Principlers and analysis - 1998 (522927), страница 50
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In yeast, by contrast, interference isincomplete even over short distances. For markers separated by 3 map units, the interference is in the range 0.3 to0.6; for those separated by 7 map units, it is in the range 0.1 to 0.3. In most organisms, when the total distancebetween the genetic markers is greater than about 30 map units, interference essentially disappears and thecoefficient of coincidence approaches 1.Genetic Mapping FunctionsThe effect of interference on the relationship between genetic map distance and the frequency of recombination isillustrated in Figure 4.15.
Each curve in Figure 4.15 is an example of a mapping function, which is themathematical relation between the genetic distance across an interval in map units (centimorgans) and the observedfrequency of recombination across the interval. In other words, a mapping function tells you how to convert a mapdistance between genetic markers into a recombination frequency between the markers.
As we have seen, when themap distance between the markers is small, the recombination frequency equals the map distance. This principle isreflected in the curves in Figure 4.15 in the region in which the map distance is smaller than about 10 cM. At lessthan this distance, all of the curves are nearly straight lines, which means that map distance and recombinationfrequency are equal; 1 map unit equals 1 percent recombination, and 10 map units equal 10 percent recombination.For distances greater than 10 map units, the recombination frequency becomes smaller than the map distance.
Howmuch smaller it is, for any given map distance, depends on the pattern of interference along the chromosome. Eachpattern of interference yields a different mapping function. In Figure 4.15, three types of mapping functions areshown. The upper curve is based on the assumption of com-Figure 4.15A mapping function is the relation between genetic map distance across an interval and theobserved frequency of recombination across the interval.
Map distance is defined as one-half theaverage number of crossovers converted into a percentage. The three mapping functionscorrespond to different assumptions about interference, i. In the top curve, i = 1 (completeinterference); in the bottom curve, i = 0 (no interference). The mapping function in themiddle is based on the assumption that i decreases as a linear function of distance.Page 145plete interference i, so that i = 1. With this mapping function, the linear relation holds all the way to a map distanceof 50 cM, for which the recombination frequency is 50 percent; for map distances larger than 50 cM, therecombination frequency remains constant at 50 percent.The bottom curve in Figure 4.15 is usually called Haldane's mapping function after its inventor. It assumes nointerference (i = 0), and the mathematical form of the function is r = (1/2)(1 — e- d/50), where d is the map distancein centimorgans.
Any mapping function for which i is between 0 and 1 must lie in the interval between the top andbottom curves. The example shown is Kosambi's mapping function, in which the interference is assumed todecrease as a linear function of distance according to i = 1 — 2r. Although simple in its underlying assumptions,the formula for Kosambi's function is not simple. (The formula is in one of the problems at the end of the chapter.)Haldane developed his mapping function in 1919, Kosambi his in 1943. Between these years and long afterward,geneticists had little interest in different mapping functions other than as curiosities, because there were few sets ofdata large enough to distinguish one reasonable function from the next.
In recent years, with the explosion in thenumber of genetic markers available in virtually all organisms, and with the resurgence of interest in geneticmapping because of its role in identifying the position of mutations as precisely as possible prior to cloning(isolating the DNA), mapping functions have again become moderately fashionable. Checked against large datasets, none of the simple mapping functions in Figure 4.15 fits perfectly, but alternatives that fit better are muchmore complex even than Kosambi's mapping function.Most mapping functions are almost linear near the origin, as are those in Figure 4.15. This near linearity impliesthat for map distances smaller than about 10 cM, whatever the pattern of chromosome interference, there are sofew double recombinants that the recombination frequency in percent essentially equals the map distance.
Hencethe map distance between two widely separated genetic markers can be estimated with some confidence bysumming the map distances across smaller segments between the markers, provided that each of the smallersegments is less than about 10 map units in length.Genetic Distance and Physical DistanceGenerally speaking, the greater the physical separation between genes along a chromosome, the greater the mapdistance between them. Physical distance and genetic map distance are usually correlated because a greaterdistance between genetic markers affords a greater chance for a crossover to take place; crossing-over is a physicalexchange between the chromatids of paired homologous chromosomes.On the other hand, the general correlation between physical distance and genetic map distance is by no meansabsolute. We have already noted that the frequency of recombination between genes may differ in males andfemales.
An unequal frequency of recombination means that the sexes can have different map distances in theirgenetic maps, although the physical chromosomes of the two sexes are the same and the genes must have the samelinear order. An extreme example of a sex difference in recombination is in Drosophila, in which there is norecombination in males (as we noted earlier). Hence, in Drosophila males, the map distance between any pair ofgenes located in the same chromosome is 0. (Genes on different chromosomes do undergo independent assortmentin males.)The general correlation between physical distance and genetic map distance can even break down in a singlechromosome. For example, crossing-over is much less frequent in certain regions of the chromosome than in otherregions.
The term heterochromatin refers to certain regions of the chromosome that have a dense, compactstructure in interphase; these regions take up many of the standard dyes used to make chromosomes visible. Therest of the chromatin, which becomes visible only after chromosome condensation in mitosis or meiosis, is calledeuchromatin. In most organisms, the major heterochromatic regions are adjacent to the centromere; smaller blocksare present at the ends of the chromosome arms (the telomeres) and interspersed with the euchromatin. InPage 146general, crossing-over is much less frequent in regions of heterochromatin than in regions of euchromatin.Because there is less crossing-over in heterochromatin, a given length of heterochromatin will appear much shorterin the genetic map than an equal length of euchromatin. In heterochromatic regions, therefore, the genetic mapgives a distorted picture of the physical map.
An example of such distortion appears in Figure 4.16, whichcompares the physical map and the genetic map of chromosome 2 in Drosophila. The physical map is depicted asthe chromosome appears in metaphase of mitosis. Two genes near the tips and two near the euchromatinheterochromatin junction are indicated in the genetic map. The map distances across the euchromatic arms are 54.5and 49.5 map units, respectively, for a total euchromatic map distance of 104.0 map units. However, theheterochromatin, which constitutes approximately 25 percent of the entire chromosome, has aFigure 4.16Chromosome 2 in Drosophila as it appears in metaphase of mitosis(physical map, top) and in the genetic map (bottom).
Heterochromatin andeuchromatin are in contrasting colors. The genes indicated on the mapare net (net wing veins), pr (purple eye color), cn (cinnabar eye color), and sp (speck of wing pigment). The genes pr and cn are actually ineuchromatin but are located near the junction with heterochromatin.The total map length is 54.5 + 49.5 + 3.0 = 107.0 map units. Theheterochromatin accounts for 3.0 107.0 = 2.8 percent of the total maplength but constitutes approximately 25 percent of the physical lengthof the metaphase chromosome.genetic length in map units of only 3.0 percent. The distorted length of the heterochromatin in the genetic mapresults from the reduced frequency of crossing-over in the heterochromatin.
In spite of the distortion of the geneticmap across the heterochromatin, in the regions of euchromatin there is a good correlation between the physicaldistance between genes and their distance in map units in the genetic map.4.4—Genetic Mapping in Human PedigreesBefore the advent of recombinant DNA, mapping genes in human beings was very tedious and slow. There werenumerous practical obstacles to genetic mapping in human pedigrees:1. Most genes that cause genetic diseases are rare, so they are observed in only a small number of families.2. Many genes of interest in human genetics are recessive, so they are not detected in heterozygous genotypes.3. The number of offspring per human family is relatively small, so segregation cannot usually be detected insingle sibships.4. The human geneticist cannot perform testcrosses or backcrosses, because human matings are not manipulated byan experimenter.In recent years, because recombinant-DNA techniques allow direct access to the DNA, genetic mapping in humanpedigrees has been carried out primarily by using genetic markers present in the DNA itself, rather than through thephenotypes produced by mutant genes.
There are many minor differences in DNA sequence from one person to thenext. On the average, the DNA sequences at corresponding positions in any two chromosomes, taken from any twopeople, differ at approximately one in every thousand base pairs. Most of the differences in DNA sequence are notassociated with any inherited disease or disability. Indeed, many of the differencesPage 147are found in DNA sequences that do not code for proteins. Nevertheless, all of these differences can serve asconvenient genetic markers, and differences that are genetically linked to genes causing hereditary diseases areparticularly important.
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