A homeodomain is a highly conserved protein domain (first identified in Antp and Ubx proteins) containing 60 amino acids that fold into three conserved DNA-binding helics (indicating a role in transcriptional reglation). Many homeodomain proteins have been shown in vitro to bind to regulatory regions of genes known to regulate by genetic criteria. The DNA sequence encoding a homeodomain is a homeobox.

Specific and highly conserved residues in the homeodomain’s third helix (helix 3) bind the major groove of DNA, meaning all homeodomain proteins bind the same DNA sequence in vitro. Specific homeodomain proteins have different regulatory properties via interaction with different co-factors; the co-factor and the homeodomain protein bind a specific DNA sequence together, but are unable to bind it individually.

Linkage is the tendency of genes, which are closely located on the same chromosome, to segregate together. The physical distance two genes on the chromosome is proportional to how frequently they cross over together during homologous recombination. Therefore, frequency of recombination is a tool for mapping chromosomes. Linkage analysis follows DNA regions, allowing not only mapping of a chromosome but also identification of disease genes. Association analysis is a similar approach for identifying disease genes, but instead just analyzes which alleles are present in diseased individuals throughout a population.

Loci cross over together in proportion to how near each other they are. Adjacent loci almost always cross over together; far-apart loci rarely cross over together. The proportion of recombinants to nonrecombinants is the recombination frequency, measured in Morgans and labeled θ (theta). The smaller θ gets, the closer the two loci. Recombination frequency can be used to draft a chromosome map.

A low recombination frequency (θ≈0) means two loci are tightly linked (close together and almost always assort together), while a high recombination frequency (θ≈0.5) means two loci are unlinked and could even be on different chromosomes. θ can be used to calculate the LOD score (determining whether two loci are linked) and the map distance (how far apart are two loci).

To determine recombination frequency, recombination events must be deduced. This requires that: at least one parent be heterozygous (informative); and the phase of the alleles must be known. The phase of an allele is simply whether it is on the maternal or paternal homologue. Two alleles on the same homologue are in coupling (they are cis) and two alleles on opposite homologues are in repulsion (they are trans). In a DdMm individual, D could have the same phase as either M or m; more information is needed to deduce which homologue bears which allele.

Linkage Equilibrium

Imagine that genes HAIR and BRAIN are two genes present on Chromosome 13, and that HAIR and BRAIN each have two alleles. Alleles HAIR^brown and HAIR^blonde are equally prevalent throughout the population; thus, any Chromosome 13 is equally likely to bear HAIR^brown or HAIR^blonde. However, alleles BRAIN^smart and BRAIN^dumb are not equally prevalent throughout the population. In fact, BRAIN^dumb is four times as prevalent as BRAIN^smart; thus, any given Chromosome 13 has a 20% chance of bearing BRAIN^smart and a 80% chance of bearing BRAIN^dumb.

When two alleles are in linkage equilibrium, then 20% of Chromosome 13’s bearing HAIR^blonde or HAIR^brown would also bear HAIR^smart and 80% of Chromosome 13’s bearing HAIR^blonde or HAIR^brown would also bear HAIR^dumb. When an allele is in linkage disequilibrium, then it is more likely to associate with a certain allele of a different gene. For example, although BRAIN^smart and BRAIN^dumb are present on 20% and 80% of Chromosome 13’s, a Chromosome 13 with HAIR^blonde might also bear only BRAIN^dumb alleles while HAIR^brown bears the remaining 30% BRAIN^dumb and all the 20% BRAIN^smart alleles. In this case, HAIR^blonde and BRAIN^dumb are in strong linkage disequilibrium.

The LOD score (aka Z) gives an estimation of how closely two loci are linked (for example, a marker locus and a disease locus) and quantitates sample size (data reliability). A LOD score less than 2.0 means the two loci are not linked; a LOD score between 2.0 and 3.0 is inconclusive; and a LOD score greater than 3.0 strongly indicates linkage. Lod scores are always reported in association with the recombination frequency θ (theta), measured in Morgans, which describes linkage without taking into account sample size.

Step	Description
Step 1	Look at nothing more than affected/unaffected individuals and determine the mode of inheritance.
Step 2	Cross out individuals who cannot be identified as recombinants or nonrecombinants (uninformative individuals). Persons whose parents are not shown. Individuals without at least one heterozygous parent. Children are uninformative when the child and both parents have the same haplotype. If the allele of interest is dominant, then children with a homozygous recessive parent.
Step 3	Determine whether each informative individual is recombinant or nonrecombinant. Considering an informative individual’s haplotype, is it consistent with their parent’s haplotype and the mode of inheritance? Yes, consistent with parental haplotype -> Not Recombinant. No, inconsistent with parental haplotype -> Recombinant. Remember that even unaffected individuals can be recombinant!
Step 4	Count how many recombinants and non-recombinants there are.
Step 5	If you are provided a recombination frequency (θ, aka theta) then go straight to the equation below. If you are provided the gene-marker distance (measured in centimorgans or cM) then divide that value by 100 to calculate θ. For example, a marker 10cM from a gene yields a Θ of 10/100 = .10. If you are supposed to calculate the recombination frequency (θ), then use the equation below with θ values of .001, .10, .15, .20, .25, .30, .35, .40., .45 and .50. The correct θ value will yield the highest LOD Score.