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5.3 Mapping: Locating Genes Along a Chromosome   149


                       genes, and therefore an underestimation of the distance be-  measure of the physical distance. The two graphs then
                       tween them. This is not much of a problem when two genes     diverge increasingly from each other, so the RF becomes
                       are close enough together that DCOs take place infre-  a  less precise estimate at genetic distances greater than
                       quently. However, as the distance between two genes in-  5 m.u.
                       creases, double and multiple crossovers occur often enough   Geneticists have developed mathematical equations
                       to affect the relationship between recombination frequency   called mapping functions to compensate for the inaccura-
                       and map distance. This relationship cannot be linear be-  cies inherent in relating recombination frequencies to phys-
                       cause, as we have already seen, the RF for a two-point cross   ical distances. However, the corrections for large distances
                       cannot exceed 50% regardless of how far apart two genes   are at best imprecise because mapping functions are based
                       are on the same chromosome.                         on simplifying assumptions that are not completely true.
                          A second look at Fig. 5.11 makes it easy to see how   Thus, the best way to create an accurate map is by summing
                       DCOs result in underestimation of gene distances by RF.   many smaller intervals, locating widely separated genes
                       When genes A and B are close together, most meioses are   through linkage to common intermediaries. Maps are sub-
                       NCOs, and the occasional meiosis is an SCO. Each SCO   ject to continual refinement as more and more newly
                       produces exactly two recombinant gametes, and so a per-  discovered genes are included.
                       fect linear correspondence exists between the number of
                       crossovers and the number of recombinant gametes
                       (1 crossover: 2 recombinants). However, when genes A and   Nonuniform crossover frequencies
                       B are farther apart, DCOs occur. Only one of the four   Although we have been assuming thus far that crossovers
                       equally frequent DCOs (4-strand) preserves the linear rela-  are just as likely to occur between any two base pairs along
                       tionship between crossovers and recombinant gametes:   a chromosome, recombination is not in fact random. In
                       Two crossovers occur in a 4-strand DCO and four recombi-  human DNA, for example, most crossovers take place in
                       nant gametes (2 crossovers: 4 recombinants). In contrast,   so-called  recombination hotspots—small regions of
                       the other three types of DCOs result in fewer than four re-  DNA where the frequency of recombination is much
                       combinant gametes.                                  higher than average. As shown in Fig. 5.17, genes with
                          Figure 5.16 illustrates this discrepancy between the   hotspots between them (A and B) will be more distant from
                       actual number of crossovers (green line) and observed RF   each other on a genetic map (measured in m.u.) than an-
                       (purple line) as a function of the amount of DNA separat-  other gene pair (B and C) without a hotspot between them,
                       ing the two genes. As you can see, the two graphs are nearly   even though the physical distance (measured in bp of
                       identical for distances of 5 m.u. or less. At genetic  distances   DNA) separating each gene pair is the same. As hotspots
                       this small, the RF seen in a two-point cross is an accurate   are relatively frequent (a hotspot appears about every
                                                                           50,000 bp in human chromosomes), recombination fre-
                                                                           quency is nevertheless a reasonable estimation of physical
                       Figure 5.16  Recombination frequency underestimates   distance between most genes.
                       crossover frequency. The lines representing the RF observed in   Frequencies of recombination may also differ from
                       a testcross (purple) and the crossover frequency (green) are nearly   species to species. We know this because recent elucida-
                       coincident when genes A and B are close together. As two genes   tion of the complete DNA sequences of several organisms’
                       become farther apart, the RF value increasingly underestimates the   genomes has allowed investigators to compare the physical
                       actual crossover frequency; eventually no NCOs will take place and   distances between genes with genetic map distances. They
                       the maximum RF of 50% will be observed. The green line
                       represents crossover frequency/2 because every SCO produces    found that in humans, a map unit corresponds on average to
                       1/2 parental and 1/2 recombinant chromosomes.

                                      Genetic distance
                                        based on the                       Figure 5.17  Recombination hotspots. Genes A and B are
                                        frequency of
                                                                           separated by the same number of base pairs as genes B and C.
                           Recombination frequency  50%            Crossover frequency/2  much more distant from each other than do genes B and C on a
                                          crossovers
                                                                           Because A and B flank a recombination hotspot, they appear
                                                                           genetic map.
                                                                                                 A
                                                                                                                     C
                                                                                                           B
                                                                                       Physical map
                                                                                        (bp of DNA)
                                                          Observed
                                                                                                      X
                                                          RF
                                                                                 Crossover frequency
                                                                                                      X
                                                                                  (crossovers per bp)  XXXXXXXXXXXXXXXXXXXXX
                                                                                                      X
                              5%                                                                      X
                                                                                       Genetic map  A               B C
                                Physical distance between A and B (bp of DNA)           (map units)
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