Premed · Premed · Genetics
Lecture 4: Linkage and Genetic Mapping
Genetics
Learning Objectives
By the end of this lecture, students will be able to:
- Define genetic linkage and explain why linked genes deviate from independent assortment
- Distinguish between parental and recombinant offspring classes
- Calculate recombination frequency and convert it to map distance in centimorgans
- Construct genetic maps using two-point and three-point testcross data
- Determine gene order using a three-point cross
- Explain the relationship between physical distance and genetic map distance, including interference
Lecture Content
I. Discovery of Linkage
In 1905, William Bateson and Reginald Punnett observed puzzling deviations from the expected 9:3:3:1 ratio in sweet pea crosses. They found an excess of parental-type offspring and too few recombinant types, but they could not initially explain these results. The explanation came in 1911 from Thomas Hunt Morgan, working with Drosophila melanogaster. Morgan demonstrated that genes located on the same chromosome tend to be inherited together because they are physically linked. However, crossing over during meiosis can separate linked genes, producing recombinant offspring at a frequency that depends on the physical distance between the genes.
Genes on the same chromosome form a linkage group, and the number of linkage groups in an organism equals the haploid chromosome number. Humans have 23 linkage groups, while Drosophila has 4.
II. Recombination and Crossing Over
Crossing over is the physical exchange of chromosome segments between non-sister chromatids of homologous chromosomes during prophase I of meiosis. During the zygotene and pachytene stages, homologous chromosomes pair up (synapse), and double-strand breaks occur in non-sister chromatids. Strand invasion and resolution of these breaks create crossover products, which are visible cytologically as chiasmata. The result is recombination of alleles flanking the crossover point.
Parental (non-recombinant) gametes carry the same allele combinations as the original chromosomes, while recombinant gametes carry new allele combinations not present in the parental chromosomes. The frequency of recombination depends on the physical distance between genes: genes that are close together on a chromosome recombine infrequently, genes that are far apart recombine more often (up to 50%), and genes that are very far apart on the same chromosome or on different chromosomes recombine at 50%, appearing to assort independently.
<image>Panel A: Diagram of crossing over during meiosis I, showing paired homologous chromosomes with genes A/a and B/b, the formation of a chiasma between the genes, and the resulting four chromatids — two parental type and two recombinant type. Panel B: Comparison diagram showing expected offspring ratios from a testcross when genes are unlinked (1:1:1:1) versus linked with crossing over (majority parental, minority recombinant). Panel C: Graph showing the relationship between physical distance separating two genes on a chromosome and the observed recombination frequency, with the curve approaching 50% for very distant genes.</image>
III. Recombination Frequency and Map Distance
The recombination frequency (RF) is the proportion of recombinant offspring among all offspring from a testcross, calculated as RF = (number of recombinant offspring) / (total offspring) x 100%. One percent recombination frequency equals 1 map unit, also called 1 centimorgan (cM), named after Thomas Hunt Morgan.
Several important properties govern recombination frequency. RF ranges from 0% (completely linked genes) to 50% (unlinked or very distant genes) and never exceeds 50% because each crossover event involves only 2 of the 4 chromatids in a tetrad. Multiple crossovers between distant genes can cancel each other out, making the observed RF an underestimate of the true genetic distance. Map distances are additive for short intervals but become less reliable for long ones. As a rough physical correlation, 1 cM corresponds to approximately 1 Mb (1 million base pairs) in humans, though this ratio varies by organism, sex, and chromosomal region.
IV. Two-Point Testcross Mapping
The two-point testcross is the simplest method for determining linkage and map distance between two genes. The cross involves a dihybrid individual (AaBb, with alleles in a known cis or trans configuration) mated to a homozygous recessive individual (aabb). In the cis (coupling) configuration, the dominant alleles are on the same chromosome (AB/ab), while in the trans (repulsion) configuration, the dominant alleles are on different chromosomes (Ab/aB).
The procedure involves crossing the dihybrid to the homozygous recessive individual (testcross), scoring offspring phenotypes, identifying parental and recombinant classes (the rarest classes are recombinant), and then calculating the recombination frequency as (recombinants / total) x 100%, which directly gives the map distance in centimorgans. The limitations of two-point mapping are that it can only map two genes at a time, it does not reveal gene order when mapping three or more genes, and it underestimates true distance for genes that are far apart.
V. Three-Point Testcross Mapping
Three-point testcross mapping is a more efficient approach that maps three genes simultaneously and determines their order on the chromosome. The procedure begins by crossing a trihybrid (AaBbCc) to a triple homozygous recessive (aabbcc), then classifying all offspring into eight phenotypic classes. The two most common classes represent parental types, and the two rarest classes represent double crossovers.
Gene order is determined by comparing the double crossover class to the parental class: the allele that has "switched" position in the double crossover class identifies the middle gene. Distances between adjacent genes are calculated by summing the single crossovers in each interval plus the double crossovers, divided by the total number of offspring and multiplied by 100%. The total map distance equals the sum of the two intervals.
<image>Panel A: Complete worked example of a three-point testcross showing a table of eight offspring classes with their numbers, identification of parental, single crossover, and double crossover classes, and step-by-step gene order determination. Panel B: Resulting linear genetic map showing three genes with distances in centimorgans between them. Panel C: Diagram showing how double crossovers between the outer genes restore the parental configuration for those genes while switching only the middle gene, explaining why the middle gene is identified from the double crossover class.</image>
VI. Interference and the Coefficient of Coincidence
The coefficient of coincidence (c.o.c.) is the ratio of observed double crossovers to expected double crossovers. The expected double crossover frequency is calculated as the product of the recombination frequencies for the two adjacent intervals, expressed as decimals. Interference (I) measures the degree to which a crossover in one interval affects the likelihood of a crossover in the adjacent interval, calculated as I = 1 - c.o.c.
Positive interference (I > 0, c.o.c. < 1) means that a crossover in one interval decreases the probability of a crossover in the adjacent interval. This is the most common situation and arises from physical constraints imposed by chromosome structure and the synaptonemal complex. No interference (I = 0, c.o.c. = 1) means that crossovers in adjacent intervals occur independently. Negative interference (I < 0, c.o.c. > 1) means that a crossover in one interval increases the probability of a nearby crossover; this is rare.
VII. Genetic Maps vs. Physical Maps
Genetic (linkage) maps are based on recombination frequencies, measured in centimorgans, and depict relative order and distance between genes. They can vary between sexes (recombination rates are typically higher in females in humans) and are influenced by hotspots and coldspots of recombination. Physical maps, by contrast, are based on actual DNA sequence, measured in base pairs (bp, kb, Mb), and represent absolute distances. They are generated by restriction mapping, FISH, or genome sequencing.
The correlation between genetic and physical maps is generally good but not perfectly linear. Centromeric and heterochromatic regions tend to show low recombination per megabase, while subtelomeric regions often display high recombination rates.
The LOD score (logarithm of odds) is a statistical method used to test for linkage in human genetics, where controlled crosses are not possible. A LOD score of 3.0 or greater supports linkage with odds of 1000:1, while a LOD score of -2.0 or less excludes linkage at the tested distance.
<image>Panel A: Side-by-side comparison of a genetic map (in cM) and a physical map (in Mb) for a human chromosome, highlighting regions where the two maps show non-linear correspondence due to recombination hotspots and coldspots. Panel B: Diagram explaining LOD score analysis, showing a family pedigree with a hypothetical disease gene and a linked marker, with a graph of LOD score vs. recombination fraction showing the peak LOD score at the most likely map distance. Panel C: Table comparing properties of genetic maps and physical maps (units, basis, resolution, variability between sexes).</image>
