The BIG Exception: We have looked at various exceptions to Mendel's ideas, but they have mostly been cases that illustrate that heredity is more complicated than Mendel assumed and not really exceptions to his ideas of how genes are transmitted. However, the exception we will take up now is a major exception to gene transmission as Mendel envisioned it. Mendel assumed that genes are all separate (independent) units of heredity, but in actuality they are clustered together (linked) in groups on chromosomes and therefore do not usually obey his Law of Independent Assortment.

• Chromosomes and the Chromosome Theory: Mendel proposed his theories of gene transmission just before chromosomes ("colored bodies") were discovered in the nucleus by Walter Flemming, but Mendel had no knowledge of them. Also, the events of mitosis and meiosis were subsequently elucidated.

• The Sutton/Boveri Chromosome Theory: In 1902 the Columbia University graduate student William Sutton and the imminent German scientist Theodor Boveri independently proposed the theory that genes are located on chromosomes. They reached this conclusion because of correlations between how genes and chromosomes behave when gametes are being formed.
• Genes (Alleles) and Chromosomes Both Occur in Pairs.
• Allele Pairs and Chromosome Pairs Both Separate from Each Other and Enter Separate Gametes.
• The Separation of Both Allele Pairs and Chromosome Pairs Are Independent
• The Proof of the Chromosome Theory: Thomas Hunt Morgan created a research group called the Drosophila Group at Columbia University (later moving to Cal Tech) and it was from this group that many of the important early discoveries in the new field of genetics came. The first of these was the proof of the chromosome theory in which Morgan and Bridges showed that a certain gene was on the X chromosome, and therefore the chromosome theory must be true.

• Morgan's Observations (1910): In one cross, a female white-eyed fly crossed with a male red-eyed fly produce females that were all red eyed and males that were all white eyed. When these F1 were crossed, they produced a 1:1:1:1 ratio of red females : white females : red males : white males. The reciprocal cross also gave strange results. By assuming that the white-eye gene is on the X chromosome (X-linked), Morgan was able to explain these strange results. (A male, with just one allele, is not said to be homozygous but hemizygous.)
• Bridges' "Final Proof" of the Chromosome Theory: In spite of Morgan's evidence, other scientists were not convinced that the chromosome theory was true until Morgan's student, Calvin Bridges, showed conclusively that the behavior of the white gene and that of the X chromosome were correlated. His experiment involved a rare event called non-disjunction and produced an XXY female. In the various sex chromosome combinations that resulted from these females, the X chromosome and the white gene seemed to be transmitted together. (This proof was the first article in the first volume of the journal  Genetics.)

• X Linkage in Humans: Genes on the X chromosome are said to be X linked. (Sex-Linked vs. X-linked genes) Human traits like hemophilia A and red-green colorblindness are inherited just like white eye-color in Drosophila is. Hemophilia A is a bleeding disorder due to reduced activity of coagulation factor VIII. (Various mutations in the factor VIII gene can cause hemophilia A.)
• Sex-Linked Genes: A gene on a sex chromosome (either the X or Y) is a sex-linked genes. However, since there are few genes on the Y chromosome, many refer to X-linked genes as sex-linked genes.
  
• X-linked Genes: These are genes on the X chromosome (other than on the pseudoautosomal reagions (PARs) of the X) and show the inheritance pattern described above. There are two PARs on the X, one at the tip of each telomere. The X's PARs are homologous to the Y's PARs and crossing over can occur between them. [What is distinctive about a sex chromosome?]
• Y-linked Genes: These are genes on the NRY (non-recombining region of the Y) -- that is, on the Y chromosome other than the PARs of the Y. (Y chromosome :-)) Like for the X, there are two PARs on the Y, one at the tip of each telomere.
  

• Linkage and Mapping: Genes are on chromosomes. Alleles are found at the same site, or locus, along the chromosome. Since more than one gene is located on each chromosome, two genes that are on the same homologous pair of chromosome will not obey Mendel's Law of Independent Assortment. That is, the segregation of one of these pairs of alleles will not be independent of the segregation of the other pair of alleles. Two alleles that are on the same chromosome will tend to move together into the same gamete (the segregation of one pair of alleles does effect the segregation of the other pair). This phenomenon is called linkage. This means for a two-point test cross, there are two possibilities.

• Parental and Recombinant Gametes: When considering a typical dihybrid cross, the gametes that the F1 individual makes will be of two types: 1) gametes that have the same combination of alleles as the P generation individuals, called parental gametes and 2) gametes that have the opposite combination of alleles as the P generation individuals. (In order to determine what proportion of the gametes were parental or recombinant, a test cross is performed.)
  
• Independent Assortment versus Linkage: If two genes are on different chromosome pairs, they will assort independently. That is, the number of parental gametes will be approximately equal to the number of recombinant gametes. If, however, two genes are located on the same chromosome pair, they will not assort independently but rather will be linked (they will show linkage). That is, the number of parental gametes will (usually) be significantly greater than the number of recombinant gametes (the product of crossing over).
  
• Recombinant Gametes and Crossing Over: For linked genes, recombinant gametes are produced by crossing over occurring between the two genes. (Where do they come from for unlinked genes?) Even if a crossover occurs between the two genes, the products of a single meiotic event will be two parental and two recombinant gametes. The proof that recombinant gametes were the product of crossing over came from cytological studies that correlated chromosome changes with recombinant gametes. (McClintock Paper)(Chiasmata)
  
• Predicting the Outcome of a Dihybrid Cross Involving Linked Genes: In order to predict the outcome of a dihybrid cross involving two linked genes, the Punnett Square can be used. However, beside listing the types of gamete genotypes, the probability of each gamete occurring must be listed. This probability can be calculated if you know the distance between genes since the distance predicts the percentage of recombinant gametes. Then, when filling in the Punnett Square, besides combining the gamete genotypes, the probabilities of the gamete pairs are multiplied together, yielding the frequency of each genotype. (Problem Solving: see the second half of the LINKAGE tutorial video showing how to solve this type of problem.)
• Gene Mapping: For linked genes, the distance between the two genes is proportional to the frequency of crossing over. The further apart two genes are, the more likely it is that a crossover will occur between them (crossovers occur at random, more or less). For this reason, the percentage of recombinant gametes can be used as a relative measure of the distance between two linked genes. One percent recombinant gametes is defined as one map unit (mu) or centi-Morgan (cM). The distance between two genes can be measure this way. (Problem Solving: see the first half of the LINKAGE tutorial video showing how to determine if two genes are linked.) Also, the distance between three (or more) genes can be measured by determining the distance between each pair of genes (by performing a series of two-point test crosses). The maximum distance between two genes as measured by a two-point test cross is 50 cM (you can't get more than 50% recombinant gametes). This means that the two genes are so far apart that crossing over will always occur between the two. (Also, 2-strand double crossovers will go undetected.) However, by performing a series of test crosses, two genes may be measured to be further than 50 cM apart (by adding the pair-wise distances).
• The Three-Point Test Cross: Since two-point test crosses often overlook double crossovers, the standard tool of gene mapping is the three point test cross. (Many genes in organisms like Drosophila have been mapped. A gene's position on a chromosome is its locus.) A heterozygote for three linked genes is crossed to an individual homozygous for all three recessive alleles. Analyzing the progeny reveals the gene order, the distance between the genes, and the degree of interference. Here are the steps in performing a three-point test cross. (Problem Solving: see the THREE POINT TEST CROSS tutorial video showing how to analyze data from such a cross.)
• Determine the Gene Order: Determine the two classes of gametes that are parental. These will be the complementary pair that is the most numerous. Next, determine the two classes of gametes that are the result of double crossovers. These will be the complementary pair that is least numerous. Then, decide which pair of alleles of the double crossovers needs to be switched (inverted) to give the parental configuration. Place that pair in the middle and you have the gene order.
• Determine the Distance between the Genes: First (don't skip this step), rewrite the data with the genes in the right order and grouped into complementary pairs. Then, by comparison with the parental configuration, determine which pair results from a crossover between the first two genes. Add these two together plus the double crossovers and divide by the total. Multiply by 100 to change to percent recombination. This number is the distance between the first two genes in cM. Repeat the process to determine the distance between the second and third gene.
• Calculate the Coefficient of Coincidence: When a crossover occurs, it interferes with the occurrence of a second crossover nearby. The degree of interference is calculated as the coefficient of coincidence. This is a decimal that expresses what proportion of the expected double crossovers actually occurred. A coefficient of coincidence of 1.0 means there is no interference. A coefficient of coincidence of 0 means that there is complete interference (no double crossovers occurred). In Drosophila, for genes less than about 10 - 15 cM apart (the distance between to two outside genes in a 3-point test cross) there is complete interference. To calculate this decimal, calculate the actual proportion of double crossovers from the data and divide it by the expected proportion of double crossovers. The expected proportion is the product of the probabilities of each individual crossover probability (the distance in cM converted to a decimal).
• Mapping in Organisms with an Ordered Tetrads: Ascomycete fungi produce an ascus which has all four products of a single meiosis in a sac (called a tetrad). In some ascomycete fungi, these cells are maintained in the order in which they were produced by meiosis I and meiosis II (although a mitotic division of these spores occurs after meiosis so the ascus has 8 cells, not 4). This is called an ordered tetrad. In this case, it is possible to map the distance a single gene is from its centromere, since (in a monohybrid cross) if no crossover occur between the gene and its centromere, the two "top" meiotic products should have the same genes and the two "bottom" products should have the alternate gene. Neurospora is such a fungus that has been extensively used as a model organisms. (We will use a relative called Sordaria in lab to map a gene's distance from its centromere.)(Problem Solving: see the ORDERED TETRAD tutorial video showing how to map a gene's distance from its centromere in such a cross.)

• Somatic Cell Hybridization: This technique was used in the 1960s to map some human genes to chromosomes or even regions of a chromosome. Somatic cell hybridization involves fusing a human tissue culture cell with a mouse cell. In these cells, if the nuclei fuse, human chromosomes are preferentially lost, it is possible to get a cell that has all mouse chromosomes but only one human chromosome. If that cell still produces a specific human  product (like a protein), then the gene for that protein must be on the remaining human chromosome. If other combinations are encountered, then it may be possible to infer the locus of the gene.

• FISH (Fluorescent in situ Hybridization): This techniques involves hybridizing a probe DNA molecule (tagged with a fluorescent marker) to a spread of chromosomes. See this link.
• SNPs (Single Nucleotide Polymorphisms) and GWASs (Genome-Wide Associated Studies): These methodologies use common variants of a single DNA base pair as markers to hunt for genes related to a trait or disease. (SNP link; GWAS link--see especially "How are genome-wide association studies conducted?")
• LOD Score: Pedigree analysis of human traits can be used to infer linkage of two genes. The calculation involves estimating the probability that a specific pedigree was produced by two genes linked at a given distance versus the probability the pedigree was produced by two non-linked genes. (This is repeated for various distances.) This LOD score (log of the odds favoring linkage) is used to decide whether or not two genes are linked and to estimate the distance between them if they are. The highest LOD score gives and estimate of the distance. (Details of how to calculate LOD scores will not be on the test, but those of you headed toward medical school should take a look as this explanation of how to calculate LOD scores.)